TSTP Solution File: NUN053^4 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUN053^4 : TPTP v7.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n049.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Thu May 31 09:06:27 EDT 2018
% Result : Unknown 4.93s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN053^4 : TPTP v7.1.0. Released v7.1.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.24 % Computer : n049.star.cs.uiowa.edu
% 0.03/0.24 % Model : x86_64 x86_64
% 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.24 % Memory : 32218.625MB
% 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.24 % CPULimit : 300
% 0.03/0.24 % DateTime : Thu May 31 04:05:43 CDT 2018
% 0.03/0.24 % CPUTime :
% 0.08/0.49 Python 2.7.13
% 0.35/0.89 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.35/0.89 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM007^0.ax, trying next directory
% 0.35/0.89 FOF formula (<kernel.Constant object at 0x2aefba1e0128>, <kernel.DependentProduct object at 0x2aefba1e0e18>) of role type named typ_is_of
% 0.35/0.89 Using role type
% 0.35/0.89 Declaring is_of:(fofType->((fofType->Prop)->Prop))
% 0.35/0.89 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) is_of) (fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0))) of role definition named def_is_of
% 0.35/0.89 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) is_of) (fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)))
% 0.35/0.89 Defined: is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0))
% 0.35/0.89 FOF formula (<kernel.Constant object at 0x2aefba1e03f8>, <kernel.DependentProduct object at 0x2aefba1e0cf8>) of role type named typ_all_of
% 0.35/0.89 Using role type
% 0.35/0.89 Declaring all_of:((fofType->Prop)->((fofType->Prop)->Prop))
% 0.35/0.89 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) all_of) (fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2))))) of role definition named def_all_of
% 0.35/0.89 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) all_of) (fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))))
% 0.35/0.89 Defined: all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2))))
% 0.35/0.89 FOF formula (<kernel.Constant object at 0x2aefba1b6e60>, <kernel.DependentProduct object at 0x2aefba1e0d40>) of role type named typ_eps
% 0.35/0.89 Using role type
% 0.35/0.89 Declaring eps:((fofType->Prop)->fofType)
% 0.35/0.89 FOF formula (<kernel.Constant object at 0x2aefba1b6e60>, <kernel.DependentProduct object at 0x2aefba1e0d40>) of role type named typ_in
% 0.35/0.89 Using role type
% 0.35/0.89 Declaring in:(fofType->(fofType->Prop))
% 0.35/0.89 FOF formula (<kernel.Constant object at 0x2aefba62e488>, <kernel.DependentProduct object at 0x2aefba1e0d40>) of role type named typ_d_Subq
% 0.35/0.89 Using role type
% 0.35/0.89 Declaring d_Subq:(fofType->(fofType->Prop))
% 0.35/0.89 FOF formula (((eq (fofType->(fofType->Prop))) d_Subq) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1))))) of role definition named def_d_Subq
% 0.35/0.89 A new definition: (((eq (fofType->(fofType->Prop))) d_Subq) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))))
% 0.35/0.89 Defined: d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1))))
% 0.35/0.89 FOF formula (forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1)))) of role axiom named set_ext
% 0.35/0.89 A new axiom: (forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1))))
% 0.35/0.89 FOF formula (forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1)))) of role axiom named k_In_ind
% 0.35/0.89 A new axiom: (forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1))))
% 0.35/0.89 FOF formula (<kernel.Constant object at 0x2aefba1e0d40>, <kernel.Single object at 0x2aefba1e0098>) of role type named typ_emptyset
% 0.35/0.89 Using role type
% 0.35/0.89 Declaring emptyset:fofType
% 0.35/0.89 FOF formula (((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False) of role axiom named k_EmptyAx
% 0.35/0.89 A new axiom: (((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False)
% 0.35/0.89 FOF formula (<kernel.Constant object at 0x2aefba1e03f8>, <kernel.DependentProduct object at 0x2aefba1e0710>) of role type named typ_union
% 0.35/0.89 Using role type
% 0.35/0.89 Declaring union:(fofType->fofType)
% 0.35/0.89 FOF formula (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0)))))) of role axiom named k_UnionEq
% 0.35/0.89 A new axiom: (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0))))))
% 0.35/0.89 FOF formula (<kernel.Constant object at 0x2aefba1e0710>, <kernel.DependentProduct object at 0x2aefba1ddc20>) of role type named typ_power
% 0.35/0.89 Using role type
% 0.37/0.90 Declaring power:(fofType->fofType)
% 0.37/0.90 FOF formula (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0))) of role axiom named k_PowerEq
% 0.37/0.90 A new axiom: (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0)))
% 0.37/0.90 FOF formula (<kernel.Constant object at 0x2aefba1e05a8>, <kernel.DependentProduct object at 0x2aefba1dd3f8>) of role type named typ_repl
% 0.37/0.90 Using role type
% 0.37/0.90 Declaring repl:(fofType->((fofType->fofType)->fofType))
% 0.37/0.90 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3))))))) of role axiom named k_ReplEq
% 0.37/0.90 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3)))))))
% 0.37/0.90 FOF formula (<kernel.Constant object at 0x2aefba1e03f8>, <kernel.DependentProduct object at 0x2aefba1dd290>) of role type named typ_d_Union_closed
% 0.37/0.90 Using role type
% 0.37/0.90 Declaring d_Union_closed:(fofType->Prop)
% 0.37/0.90 FOF formula (((eq (fofType->Prop)) d_Union_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0))))) of role definition named def_d_Union_closed
% 0.37/0.90 A new definition: (((eq (fofType->Prop)) d_Union_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))))
% 0.37/0.90 Defined: d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0))))
% 0.37/0.90 FOF formula (<kernel.Constant object at 0x2aefba1e03f8>, <kernel.DependentProduct object at 0x2aefba1dd290>) of role type named typ_d_Power_closed
% 0.37/0.90 Using role type
% 0.37/0.90 Declaring d_Power_closed:(fofType->Prop)
% 0.37/0.90 FOF formula (((eq (fofType->Prop)) d_Power_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0))))) of role definition named def_d_Power_closed
% 0.37/0.90 A new definition: (((eq (fofType->Prop)) d_Power_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))))
% 0.37/0.90 Defined: d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0))))
% 0.37/0.90 FOF formula (<kernel.Constant object at 0x2aefba1e05a8>, <kernel.DependentProduct object at 0x2aefba1dd908>) of role type named typ_d_Repl_closed
% 0.37/0.90 Using role type
% 0.37/0.90 Declaring d_Repl_closed:(fofType->Prop)
% 0.37/0.90 FOF formula (((eq (fofType->Prop)) d_Repl_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0))))))) of role definition named def_d_Repl_closed
% 0.37/0.90 A new definition: (((eq (fofType->Prop)) d_Repl_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0)))))))
% 0.37/0.90 Defined: d_Repl_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0))))))
% 0.37/0.90 FOF formula (<kernel.Constant object at 0x2aefba1dd908>, <kernel.DependentProduct object at 0x2aefba1dd368>) of role type named typ_d_ZF_closed
% 0.37/0.90 Using role type
% 0.37/0.90 Declaring d_ZF_closed:(fofType->Prop)
% 0.37/0.90 FOF formula (((eq (fofType->Prop)) d_ZF_closed) (fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0)))) of role definition named def_d_ZF_closed
% 0.37/0.90 A new definition: (((eq (fofType->Prop)) d_ZF_closed) (fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))))
% 0.37/0.90 Defined: d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0)))
% 0.37/0.90 FOF formula (<kernel.Constant object at 0x2aefba1dd368>, <kernel.DependentProduct object at 0x2aefba1ddf80>) of role type named typ_univof
% 0.37/0.90 Using role type
% 0.37/0.90 Declaring univof:(fofType->fofType)
% 0.37/0.90 FOF formula (forall (X0:fofType), ((in X0) (univof X0))) of role axiom named k_UnivOf_In
% 0.37/0.90 A new axiom: (forall (X0:fofType), ((in X0) (univof X0)))
% 0.37/0.90 FOF formula (forall (X0:fofType), (d_ZF_closed (univof X0))) of role axiom named k_UnivOf_ZF_closed
% 0.38/0.92 A new axiom: (forall (X0:fofType), (d_ZF_closed (univof X0)))
% 0.38/0.92 FOF formula (<kernel.Constant object at 0x2aefba1dd8c0>, <kernel.DependentProduct object at 0x2aefba1dd638>) of role type named typ_if
% 0.38/0.92 Using role type
% 0.38/0.92 Declaring if:(Prop->(fofType->(fofType->fofType)))
% 0.38/0.92 FOF formula (((eq (Prop->(fofType->(fofType->fofType)))) if) (fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2))))))) of role definition named def_if
% 0.38/0.92 A new definition: (((eq (Prop->(fofType->(fofType->fofType)))) if) (fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2)))))))
% 0.38/0.92 Defined: if:=(fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2))))))
% 0.38/0.92 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2)))) of role axiom named if_i_correct
% 0.38/0.92 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2))))
% 0.38/0.92 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2))) of role axiom named if_i_0
% 0.38/0.92 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2)))
% 0.38/0.92 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1))) of role axiom named if_i_1
% 0.38/0.92 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1)))
% 0.38/0.92 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2))) of role axiom named if_i_or
% 0.38/0.92 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2)))
% 0.38/0.92 FOF formula (<kernel.Constant object at 0x2aefba1ddf80>, <kernel.DependentProduct object at 0x2aefba1ddd40>) of role type named typ_nIn
% 0.38/0.92 Using role type
% 0.38/0.92 Declaring nIn:(fofType->(fofType->Prop))
% 0.38/0.92 FOF formula (((eq (fofType->(fofType->Prop))) nIn) (fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False))) of role definition named def_nIn
% 0.38/0.92 A new definition: (((eq (fofType->(fofType->Prop))) nIn) (fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)))
% 0.38/0.92 Defined: nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False))
% 0.38/0.92 FOF formula (forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0))) of role axiom named k_PowerE
% 0.38/0.92 A new axiom: (forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0)))
% 0.38/0.92 FOF formula (forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0)))) of role axiom named k_PowerI
% 0.38/0.92 A new axiom: (forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0))))
% 0.38/0.92 FOF formula (forall (X0:fofType), ((in X0) (power X0))) of role axiom named k_Self_In_Power
% 0.38/0.92 A new axiom: (forall (X0:fofType), ((in X0) (power X0)))
% 0.38/0.92 FOF formula (<kernel.Constant object at 0x2aefba1dd5f0>, <kernel.DependentProduct object at 0x2aefba1ddd40>) of role type named typ_d_UPair
% 0.38/0.92 Using role type
% 0.38/0.92 Declaring d_UPair:(fofType->(fofType->fofType))
% 0.38/0.92 FOF formula (((eq (fofType->(fofType->fofType))) d_UPair) (fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1))))) of role definition named def_d_UPair
% 0.38/0.92 A new definition: (((eq (fofType->(fofType->fofType))) d_UPair) (fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))))
% 0.38/0.92 Defined: d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1))))
% 0.38/0.92 FOF formula (<kernel.Constant object at 0x2aefba1ddd40>, <kernel.DependentProduct object at 0x2aefba2c0200>) of role type named typ_d_Sing
% 0.38/0.92 Using role type
% 0.38/0.94 Declaring d_Sing:(fofType->fofType)
% 0.38/0.94 FOF formula (((eq (fofType->fofType)) d_Sing) (fun (X0:fofType)=> ((d_UPair X0) X0))) of role definition named def_d_Sing
% 0.38/0.94 A new definition: (((eq (fofType->fofType)) d_Sing) (fun (X0:fofType)=> ((d_UPair X0) X0)))
% 0.38/0.94 Defined: d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0))
% 0.38/0.94 FOF formula (<kernel.Constant object at 0x2aefba1dd290>, <kernel.DependentProduct object at 0x2aefba2c0200>) of role type named typ_binunion
% 0.38/0.94 Using role type
% 0.38/0.94 Declaring binunion:(fofType->(fofType->fofType))
% 0.38/0.94 FOF formula (((eq (fofType->(fofType->fofType))) binunion) (fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1)))) of role definition named def_binunion
% 0.38/0.94 A new definition: (((eq (fofType->(fofType->fofType))) binunion) (fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))))
% 0.38/0.94 Defined: binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1)))
% 0.38/0.94 FOF formula (<kernel.Constant object at 0x2aefba1dd290>, <kernel.DependentProduct object at 0x2aefba2c0200>) of role type named typ_famunion
% 0.38/0.94 Using role type
% 0.38/0.94 Declaring famunion:(fofType->((fofType->fofType)->fofType))
% 0.38/0.94 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1)))) of role definition named def_famunion
% 0.38/0.94 A new definition: (((eq (fofType->((fofType->fofType)->fofType))) famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))))
% 0.38/0.94 Defined: famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1)))
% 0.38/0.94 FOF formula (<kernel.Constant object at 0x2aefba1dd290>, <kernel.DependentProduct object at 0x2aefba2c03b0>) of role type named typ_d_Sep
% 0.38/0.94 Using role type
% 0.38/0.94 Declaring d_Sep:(fofType->((fofType->Prop)->fofType))
% 0.38/0.94 FOF formula (((eq (fofType->((fofType->Prop)->fofType))) d_Sep) (fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset))) of role definition named def_d_Sep
% 0.38/0.94 A new definition: (((eq (fofType->((fofType->Prop)->fofType))) d_Sep) (fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset)))
% 0.38/0.94 Defined: d_Sep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset))
% 0.38/0.94 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1))))) of role axiom named k_SepI
% 0.38/0.94 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1)))))
% 0.38/0.94 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0))) of role axiom named k_SepE1
% 0.38/0.94 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0)))
% 0.38/0.94 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2))) of role axiom named k_SepE2
% 0.38/0.94 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2)))
% 0.38/0.94 FOF formula (<kernel.Constant object at 0x2aefba2c0ab8>, <kernel.DependentProduct object at 0x2aefbac977a0>) of role type named typ_d_ReplSep
% 0.38/0.94 Using role type
% 0.38/0.94 Declaring d_ReplSep:(fofType->((fofType->Prop)->((fofType->fofType)->fofType)))
% 0.38/0.94 FOF formula (((eq (fofType->((fofType->Prop)->((fofType->fofType)->fofType)))) d_ReplSep) (fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1)))) of role definition named def_d_ReplSep
% 0.38/0.94 A new definition: (((eq (fofType->((fofType->Prop)->((fofType->fofType)->fofType)))) d_ReplSep) (fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))))
% 0.38/0.94 Defined: d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1)))
% 0.38/0.94 FOF formula (<kernel.Constant object at 0x2aefba2c0ab8>, <kernel.DependentProduct object at 0x2aefbac97a70>) of role type named typ_setminus
% 0.38/0.95 Using role type
% 0.38/0.95 Declaring setminus:(fofType->(fofType->fofType))
% 0.38/0.95 FOF formula (((eq (fofType->(fofType->fofType))) setminus) (fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1))))) of role definition named def_setminus
% 0.38/0.95 A new definition: (((eq (fofType->(fofType->fofType))) setminus) (fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))))
% 0.38/0.95 Defined: setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1))))
% 0.38/0.95 FOF formula (<kernel.Constant object at 0x2aefba2c01b8>, <kernel.DependentProduct object at 0x2aefbac974d0>) of role type named typ_d_In_rec_G
% 0.38/0.95 Using role type
% 0.38/0.95 Declaring d_In_rec_G:((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))
% 0.38/0.95 FOF formula (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))) d_In_rec_G) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2))))) of role definition named def_d_In_rec_G
% 0.38/0.95 A new definition: (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))) d_In_rec_G) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))))
% 0.38/0.95 Defined: d_In_rec_G:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2))))
% 0.38/0.95 FOF formula (<kernel.Constant object at 0x2aefbac974d0>, <kernel.DependentProduct object at 0x2aefbac97560>) of role type named typ_d_In_rec
% 0.38/0.95 Using role type
% 0.38/0.95 Declaring d_In_rec:((fofType->((fofType->fofType)->fofType))->(fofType->fofType))
% 0.38/0.95 FOF formula (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->fofType))) d_In_rec) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1)))) of role definition named def_d_In_rec
% 0.38/0.95 A new definition: (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->fofType))) d_In_rec) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1))))
% 0.38/0.95 Defined: d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1)))
% 0.38/0.95 FOF formula (<kernel.Constant object at 0x2aefbac97560>, <kernel.DependentProduct object at 0x2aefbac97680>) of role type named typ_ordsucc
% 0.38/0.95 Using role type
% 0.38/0.95 Declaring ordsucc:(fofType->fofType)
% 0.38/0.95 FOF formula (((eq (fofType->fofType)) ordsucc) (fun (X0:fofType)=> ((binunion X0) (d_Sing X0)))) of role definition named def_ordsucc
% 0.38/0.95 A new definition: (((eq (fofType->fofType)) ordsucc) (fun (X0:fofType)=> ((binunion X0) (d_Sing X0))))
% 0.38/0.95 Defined: ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0)))
% 0.38/0.95 FOF formula (forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset))) of role axiom named neq_ordsucc_0
% 0.38/0.95 A new axiom: (forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset)))
% 0.38/0.95 FOF formula (forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1))) of role axiom named ordsucc_inj
% 0.38/0.95 A new axiom: (forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1)))
% 0.38/0.95 FOF formula ((in emptyset) (ordsucc emptyset)) of role axiom named k_In_0_1
% 0.38/0.95 A new axiom: ((in emptyset) (ordsucc emptyset))
% 0.38/0.95 FOF formula (<kernel.Constant object at 0x2aefbac97758>, <kernel.DependentProduct object at 0x2aefbac975f0>) of role type named typ_nat_p
% 0.38/0.95 Using role type
% 0.38/0.95 Declaring nat_p:(fofType->Prop)
% 0.38/0.95 FOF formula (((eq (fofType->Prop)) nat_p) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0)))))) of role definition named def_nat_p
% 0.38/0.97 A new definition: (((eq (fofType->Prop)) nat_p) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))))
% 0.38/0.97 Defined: nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0)))))
% 0.38/0.97 FOF formula (forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0)))) of role axiom named nat_ordsucc
% 0.38/0.97 A new axiom: (forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0))))
% 0.38/0.97 FOF formula (nat_p (ordsucc emptyset)) of role axiom named nat_1
% 0.38/0.97 A new axiom: (nat_p (ordsucc emptyset))
% 0.38/0.97 FOF formula (forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1)))))) of role axiom named nat_ind
% 0.38/0.97 A new axiom: (forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1))))))
% 0.38/0.97 FOF formula (forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1)))))))) of role axiom named nat_inv
% 0.38/0.97 A new axiom: (forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1))))))))
% 0.38/0.97 FOF formula (<kernel.Constant object at 0x2aefbac97b00>, <kernel.Single object at 0x2aefbac97830>) of role type named typ_omega
% 0.38/0.97 Using role type
% 0.38/0.97 Declaring omega:fofType
% 0.38/0.97 FOF formula (((eq fofType) omega) ((d_Sep (univof emptyset)) nat_p)) of role definition named def_omega
% 0.38/0.97 A new definition: (((eq fofType) omega) ((d_Sep (univof emptyset)) nat_p))
% 0.38/0.97 Defined: omega:=((d_Sep (univof emptyset)) nat_p)
% 0.38/0.97 FOF formula (forall (X0:fofType), (((in X0) omega)->(nat_p X0))) of role axiom named omega_nat_p
% 0.38/0.97 A new axiom: (forall (X0:fofType), (((in X0) omega)->(nat_p X0)))
% 0.38/0.97 FOF formula (forall (X0:fofType), ((nat_p X0)->((in X0) omega))) of role axiom named nat_p_omega
% 0.38/0.97 A new axiom: (forall (X0:fofType), ((nat_p X0)->((in X0) omega)))
% 0.38/0.97 FOF formula (<kernel.Constant object at 0x2aefbac975a8>, <kernel.DependentProduct object at 0x2aefbac97830>) of role type named typ_d_Inj1
% 0.38/0.97 Using role type
% 0.38/0.97 Declaring d_Inj1:(fofType->fofType)
% 0.38/0.97 FOF formula (((eq (fofType->fofType)) d_Inj1) (d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1))))) of role definition named def_d_Inj1
% 0.38/0.97 A new definition: (((eq (fofType->fofType)) d_Inj1) (d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))))
% 0.38/0.97 Defined: d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1))))
% 0.38/0.97 FOF formula (<kernel.Constant object at 0x2aefbac97b00>, <kernel.DependentProduct object at 0x2aefbac97e60>) of role type named typ_d_Inj0
% 0.38/0.97 Using role type
% 0.38/0.97 Declaring d_Inj0:(fofType->fofType)
% 0.38/0.97 FOF formula (((eq (fofType->fofType)) d_Inj0) (fun (X0:fofType)=> ((repl X0) d_Inj1))) of role definition named def_d_Inj0
% 0.38/0.97 A new definition: (((eq (fofType->fofType)) d_Inj0) (fun (X0:fofType)=> ((repl X0) d_Inj1)))
% 0.38/0.97 Defined: d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1))
% 0.38/0.97 FOF formula (<kernel.Constant object at 0x2aefbac97e60>, <kernel.DependentProduct object at 0x2aefbac97830>) of role type named typ_d_Unj
% 0.38/0.97 Using role type
% 0.38/0.97 Declaring d_Unj:(fofType->fofType)
% 0.38/0.97 FOF formula (((eq (fofType->fofType)) d_Unj) (d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset)))))) of role definition named def_d_Unj
% 0.38/0.97 A new definition: (((eq (fofType->fofType)) d_Unj) (d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))))
% 0.38/0.97 Defined: d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset)))))
% 0.38/0.97 FOF formula (<kernel.Constant object at 0x2aefbac975a8>, <kernel.DependentProduct object at 0x2aefbac97830>) of role type named typ_pair
% 0.38/0.97 Using role type
% 0.38/0.97 Declaring pair:(fofType->(fofType->fofType))
% 0.38/0.97 FOF formula (((eq (fofType->(fofType->fofType))) pair) (fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1)))) of role definition named def_pair
% 0.38/0.98 A new definition: (((eq (fofType->(fofType->fofType))) pair) (fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))))
% 0.38/0.98 Defined: pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1)))
% 0.38/0.98 FOF formula (<kernel.Constant object at 0x2aefbac97830>, <kernel.DependentProduct object at 0x2aefbac97518>) of role type named typ_proj0
% 0.38/0.98 Using role type
% 0.38/0.98 Declaring proj0:(fofType->fofType)
% 0.38/0.98 FOF formula (((eq (fofType->fofType)) proj0) (fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj))) of role definition named def_proj0
% 0.38/0.98 A new definition: (((eq (fofType->fofType)) proj0) (fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj)))
% 0.38/0.98 Defined: proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj))
% 0.38/0.98 FOF formula (<kernel.Constant object at 0x2aefbac97518>, <kernel.DependentProduct object at 0x2aefbac973b0>) of role type named typ_proj1
% 0.38/0.98 Using role type
% 0.38/0.98 Declaring _TPTP_proj1:(fofType->fofType)
% 0.38/0.98 FOF formula (((eq (fofType->fofType)) _TPTP_proj1) (fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj))) of role definition named def_proj1
% 0.38/0.98 A new definition: (((eq (fofType->fofType)) _TPTP_proj1) (fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj)))
% 0.38/0.98 Defined: _TPTP_proj1:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj))
% 0.38/0.98 FOF formula (forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0)) of role axiom named proj0_pair_eq
% 0.38/0.98 A new axiom: (forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0))
% 0.38/0.98 FOF formula (forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1)) of role axiom named proj1_pair_eq
% 0.38/0.98 A new axiom: (forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1))
% 0.38/0.98 FOF formula (<kernel.Constant object at 0x2aefbac97ab8>, <kernel.DependentProduct object at 0x2aefbac979e0>) of role type named typ_d_Sigma
% 0.38/0.98 Using role type
% 0.38/0.98 Declaring d_Sigma:(fofType->((fofType->fofType)->fofType))
% 0.38/0.98 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) d_Sigma) (fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2)))))) of role definition named def_d_Sigma
% 0.38/0.98 A new definition: (((eq (fofType->((fofType->fofType)->fofType))) d_Sigma) (fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))))
% 0.38/0.98 Defined: d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2)))))
% 0.38/0.98 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1)))))) of role axiom named pair_Sigma
% 0.38/0.98 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1))))))
% 0.38/0.98 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))) of role axiom named k_Sigma_eta_proj0_proj1
% 0.38/0.98 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))))
% 0.38/0.98 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2))) of role axiom named proj_Sigma_eta
% 0.38/1.00 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)))
% 0.38/1.00 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0))) of role axiom named proj0_Sigma
% 0.38/1.00 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0)))
% 0.38/1.00 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))) of role axiom named proj1_Sigma
% 0.38/1.00 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))
% 0.38/1.00 FOF formula (<kernel.Constant object at 0x2aefbac97e60>, <kernel.DependentProduct object at 0x2aefbac97a70>) of role type named typ_setprod
% 0.38/1.00 Using role type
% 0.38/1.00 Declaring setprod:(fofType->(fofType->fofType))
% 0.38/1.00 FOF formula (((eq (fofType->(fofType->fofType))) setprod) (fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1)))) of role definition named def_setprod
% 0.38/1.00 A new definition: (((eq (fofType->(fofType->fofType))) setprod) (fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))))
% 0.38/1.00 Defined: setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1)))
% 0.38/1.00 FOF formula (<kernel.Constant object at 0x2aefbac97ea8>, <kernel.DependentProduct object at 0x2aefbac97518>) of role type named typ_ap
% 0.38/1.00 Using role type
% 0.38/1.00 Declaring ap:(fofType->(fofType->fofType))
% 0.38/1.00 FOF formula (((eq (fofType->(fofType->fofType))) ap) (fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1))) of role definition named def_ap
% 0.38/1.00 A new definition: (((eq (fofType->(fofType->fofType))) ap) (fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1)))
% 0.38/1.00 Defined: ap:=(fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1))
% 0.38/1.00 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2)))) of role axiom named beta
% 0.38/1.00 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2))))
% 0.38/1.00 FOF formula (<kernel.Constant object at 0x2aefbac97ef0>, <kernel.DependentProduct object at 0x2aefbd9615f0>) of role type named typ_pair_p
% 0.38/1.00 Using role type
% 0.38/1.00 Declaring pair_p:(fofType->Prop)
% 0.38/1.00 FOF formula (((eq (fofType->Prop)) pair_p) (fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0))) of role definition named def_pair_p
% 0.38/1.00 A new definition: (((eq (fofType->Prop)) pair_p) (fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)))
% 0.38/1.00 Defined: pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0))
% 0.38/1.00 FOF formula (<kernel.Constant object at 0x2aefbac97ea8>, <kernel.DependentProduct object at 0x2aefbd9610e0>) of role type named typ_d_Pi
% 0.38/1.00 Using role type
% 0.38/1.00 Declaring d_Pi:(fofType->((fofType->fofType)->fofType))
% 0.38/1.00 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) d_Pi) (fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))))) of role definition named def_d_Pi
% 0.38/1.00 A new definition: (((eq (fofType->((fofType->fofType)->fofType))) d_Pi) (fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))))))
% 0.38/1.00 Defined: d_Pi:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))))
% 0.48/1.02 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1)))) of role axiom named lam_Pi
% 0.48/1.02 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1))))
% 0.48/1.02 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))) of role axiom named ap_Pi
% 0.48/1.02 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))
% 0.48/1.02 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3)))))) of role axiom named k_Pi_ext
% 0.48/1.02 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3))))))
% 0.48/1.02 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2)))) of role axiom named xi_ext
% 0.48/1.02 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2))))
% 0.48/1.02 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset))))) of role axiom named k_If_In_01
% 0.48/1.02 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset)))))
% 0.48/1.02 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2)))) of role axiom named k_If_In_then_E
% 0.48/1.02 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2))))
% 0.48/1.02 FOF formula (<kernel.Constant object at 0x2aefbd961488>, <kernel.DependentProduct object at 0x2aefbd961128>) of role type named typ_imp
% 0.48/1.02 Using role type
% 0.48/1.02 Declaring imp:(Prop->(Prop->Prop))
% 0.48/1.02 FOF formula (((eq (Prop->(Prop->Prop))) imp) (fun (X0:Prop) (X1:Prop)=> (X0->X1))) of role definition named def_imp
% 0.48/1.02 A new definition: (((eq (Prop->(Prop->Prop))) imp) (fun (X0:Prop) (X1:Prop)=> (X0->X1)))
% 0.48/1.02 Defined: imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1))
% 0.48/1.02 FOF formula (<kernel.Constant object at 0x2aefbd961128>, <kernel.DependentProduct object at 0x2aefbd961710>) of role type named typ_d_not
% 0.48/1.02 Using role type
% 0.48/1.02 Declaring d_not:(Prop->Prop)
% 0.48/1.02 FOF formula (((eq (Prop->Prop)) d_not) (fun (X0:Prop)=> ((imp X0) False))) of role definition named def_d_not
% 0.48/1.02 A new definition: (((eq (Prop->Prop)) d_not) (fun (X0:Prop)=> ((imp X0) False)))
% 0.48/1.02 Defined: d_not:=(fun (X0:Prop)=> ((imp X0) False))
% 0.48/1.02 FOF formula (<kernel.Constant object at 0x2aefbd961710>, <kernel.DependentProduct object at 0x2aefbd961098>) of role type named typ_wel
% 0.48/1.02 Using role type
% 0.48/1.02 Declaring wel:(Prop->Prop)
% 0.48/1.02 FOF formula (((eq (Prop->Prop)) wel) (fun (X0:Prop)=> (d_not (d_not X0)))) of role definition named def_wel
% 0.48/1.02 A new definition: (((eq (Prop->Prop)) wel) (fun (X0:Prop)=> (d_not (d_not X0))))
% 0.48/1.02 Defined: wel:=(fun (X0:Prop)=> (d_not (d_not X0)))
% 0.48/1.02 FOF formula (forall (X0:Prop), ((wel X0)->X0)) of role axiom named l_et
% 0.48/1.02 A new axiom: (forall (X0:Prop), ((wel X0)->X0))
% 0.48/1.02 FOF formula (<kernel.Constant object at 0x2aefbd961758>, <kernel.Sort object at 0x2aefb2942518>) of role type named typ_obvious
% 0.48/1.02 Using role type
% 0.48/1.02 Declaring obvious:Prop
% 0.48/1.02 FOF formula (((eq Prop) obvious) ((imp False) False)) of role definition named def_obvious
% 0.48/1.02 A new definition: (((eq Prop) obvious) ((imp False) False))
% 0.48/1.03 Defined: obvious:=((imp False) False)
% 0.48/1.03 FOF formula (<kernel.Constant object at 0x2aefbd961518>, <kernel.DependentProduct object at 0x2aefbd9612d8>) of role type named typ_l_ec
% 0.48/1.03 Using role type
% 0.48/1.03 Declaring l_ec:(Prop->(Prop->Prop))
% 0.48/1.03 FOF formula (((eq (Prop->(Prop->Prop))) l_ec) (fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1)))) of role definition named def_l_ec
% 0.48/1.03 A new definition: (((eq (Prop->(Prop->Prop))) l_ec) (fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))))
% 0.48/1.03 Defined: l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1)))
% 0.48/1.03 FOF formula (<kernel.Constant object at 0x2aefbd9612d8>, <kernel.DependentProduct object at 0x2aefbd961758>) of role type named typ_d_and
% 0.48/1.03 Using role type
% 0.48/1.03 Declaring d_and:(Prop->(Prop->Prop))
% 0.48/1.03 FOF formula (((eq (Prop->(Prop->Prop))) d_and) (fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1)))) of role definition named def_d_and
% 0.48/1.03 A new definition: (((eq (Prop->(Prop->Prop))) d_and) (fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))))
% 0.48/1.03 Defined: d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1)))
% 0.48/1.03 FOF formula (<kernel.Constant object at 0x2aefbd961758>, <kernel.DependentProduct object at 0x2aefbd961518>) of role type named typ_l_or
% 0.48/1.03 Using role type
% 0.48/1.03 Declaring l_or:(Prop->(Prop->Prop))
% 0.48/1.03 FOF formula (((eq (Prop->(Prop->Prop))) l_or) (fun (X0:Prop)=> (imp (d_not X0)))) of role definition named def_l_or
% 0.48/1.03 A new definition: (((eq (Prop->(Prop->Prop))) l_or) (fun (X0:Prop)=> (imp (d_not X0))))
% 0.48/1.03 Defined: l_or:=(fun (X0:Prop)=> (imp (d_not X0)))
% 0.48/1.03 FOF formula (<kernel.Constant object at 0x2aefbd961518>, <kernel.DependentProduct object at 0x2aefbd961440>) of role type named typ_orec
% 0.48/1.03 Using role type
% 0.48/1.03 Declaring orec:(Prop->(Prop->Prop))
% 0.48/1.03 FOF formula (((eq (Prop->(Prop->Prop))) orec) (fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1)))) of role definition named def_orec
% 0.48/1.03 A new definition: (((eq (Prop->(Prop->Prop))) orec) (fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))))
% 0.48/1.03 Defined: orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1)))
% 0.48/1.04 FOF formula (<kernel.Constant object at 0x2aefbd961440>, <kernel.DependentProduct object at 0x2aefbd961758>) of role type named typ_l_iff
% 0.48/1.04 Using role type
% 0.48/1.04 Declaring l_iff:(Prop->(Prop->Prop))
% 0.48/1.04 FOF formula (((eq (Prop->(Prop->Prop))) l_iff) (fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0)))) of role definition named def_l_iff
% 0.48/1.04 A new definition: (((eq (Prop->(Prop->Prop))) l_iff) (fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))))
% 0.48/1.04 Defined: l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0)))
% 0.48/1.04 FOF formula (<kernel.Constant object at 0x2aefbd961758>, <kernel.DependentProduct object at 0x2aefbd961998>) of role type named typ_all
% 0.48/1.04 Using role type
% 0.48/1.04 Declaring all:(fofType->((fofType->Prop)->Prop))
% 0.48/1.04 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) all) (fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0))))) of role definition named def_all
% 0.48/1.04 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) all) (fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))))
% 0.48/1.04 Defined: all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0))))
% 0.48/1.04 FOF formula (<kernel.Constant object at 0x2aefbd961998>, <kernel.DependentProduct object at 0x2aefbd961d88>) of role type named typ_non
% 0.48/1.04 Using role type
% 0.48/1.04 Declaring non:(fofType->((fofType->Prop)->(fofType->Prop)))
% 0.48/1.04 FOF formula (((eq (fofType->((fofType->Prop)->(fofType->Prop)))) non) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2)))) of role definition named def_non
% 0.48/1.04 A new definition: (((eq (fofType->((fofType->Prop)->(fofType->Prop)))) non) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))))
% 0.48/1.04 Defined: non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2)))
% 0.48/1.04 FOF formula (<kernel.Constant object at 0x2aefbd961d88>, <kernel.DependentProduct object at 0x2aefbd9614d0>) of role type named typ_l_some
% 0.48/1.04 Using role type
% 0.48/1.04 Declaring l_some:(fofType->((fofType->Prop)->Prop))
% 0.48/1.04 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) l_some) (fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1))))) of role definition named def_l_some
% 0.48/1.05 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) l_some) (fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1)))))
% 0.48/1.05 Defined: l_some:=(fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1))))
% 0.48/1.05 FOF formula (<kernel.Constant object at 0x2aefbd9614d0>, <kernel.DependentProduct object at 0x2aefbd961dd0>) of role type named typ_or3
% 0.48/1.05 Using role type
% 0.48/1.05 Declaring or3:(Prop->(Prop->(Prop->Prop)))
% 0.48/1.05 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) or3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2)))) of role definition named def_or3
% 0.48/1.05 A new definition: (((eq (Prop->(Prop->(Prop->Prop)))) or3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))))
% 0.48/1.05 Defined: or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2)))
% 0.48/1.05 FOF formula (<kernel.Constant object at 0x2aefbd961dd0>, <kernel.DependentProduct object at 0x2aefbd961f38>) of role type named typ_and3
% 0.48/1.05 Using role type
% 0.48/1.05 Declaring and3:(Prop->(Prop->(Prop->Prop)))
% 0.48/1.05 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) and3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2)))) of role definition named def_and3
% 0.48/1.05 A new definition: (((eq (Prop->(Prop->(Prop->Prop)))) and3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))))
% 0.48/1.05 Defined: and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2)))
% 0.48/1.05 FOF formula (<kernel.Constant object at 0x2aefbd961f38>, <kernel.DependentProduct object at 0x2aefbd961e18>) of role type named typ_ec3
% 0.48/1.05 Using role type
% 0.48/1.05 Declaring ec3:(Prop->(Prop->(Prop->Prop)))
% 0.48/1.05 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) ec3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0)))) of role definition named def_ec3
% 0.48/1.05 A new definition: (((eq (Prop->(Prop->(Prop->Prop)))) ec3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0))))
% 0.48/1.05 Defined: ec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0)))
% 0.48/1.05 FOF formula (<kernel.Constant object at 0x2aefbd961e18>, <kernel.DependentProduct object at 0x2aefbd961ea8>) of role type named typ_orec3
% 0.48/1.05 Using role type
% 0.48/1.05 Declaring orec3:(Prop->(Prop->(Prop->Prop)))
% 0.48/1.05 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) orec3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2)))) of role definition named def_orec3
% 0.48/1.05 A new definition: (((eq (Prop->(Prop->(Prop->Prop)))) orec3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))))
% 0.48/1.05 Defined: orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2)))
% 0.48/1.05 FOF formula (<kernel.Constant object at 0x2aefbd961ea8>, <kernel.DependentProduct object at 0x2aefbd961b90>) of role type named typ_e_is
% 0.48/1.05 Using role type
% 0.48/1.05 Declaring e_is:(fofType->(fofType->(fofType->Prop)))
% 0.48/1.05 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) e_is) (fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y))) of role definition named def_e_is
% 0.48/1.05 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) e_is) (fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)))
% 0.48/1.05 Defined: e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y))
% 0.48/1.05 FOF formula (forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1)))) of role axiom named refis
% 0.48/1.05 A new axiom: (forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1))))
% 0.48/1.05 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3)))))))) of role axiom named e_isp
% 0.48/1.05 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3))))))))
% 0.48/1.07 FOF formula (<kernel.Constant object at 0x2aefbd961d40>, <kernel.DependentProduct object at 0x2aefbd961d88>) of role type named typ_amone
% 0.48/1.07 Using role type
% 0.48/1.07 Declaring amone:(fofType->((fofType->Prop)->Prop))
% 0.48/1.07 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) amone) (fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3))))))))) of role definition named def_amone
% 0.48/1.07 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) amone) (fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3)))))))))
% 0.48/1.07 Defined: amone:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3))))))))
% 0.48/1.07 FOF formula (<kernel.Constant object at 0x2aefbd961d88>, <kernel.DependentProduct object at 0x2aefbd961a70>) of role type named typ_one
% 0.48/1.07 Using role type
% 0.48/1.07 Declaring one:(fofType->((fofType->Prop)->Prop))
% 0.48/1.07 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) one) (fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1)))) of role definition named def_one
% 0.48/1.07 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) one) (fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))))
% 0.48/1.07 Defined: one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1)))
% 0.48/1.07 FOF formula (<kernel.Constant object at 0x2aefbd961a70>, <kernel.DependentProduct object at 0x2aefbd961f38>) of role type named typ_ind
% 0.48/1.07 Using role type
% 0.48/1.07 Declaring ind:(fofType->((fofType->Prop)->fofType))
% 0.48/1.07 FOF formula (((eq (fofType->((fofType->Prop)->fofType))) ind) (fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2)))))) of role definition named def_ind
% 0.48/1.07 A new definition: (((eq (fofType->((fofType->Prop)->fofType))) ind) (fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))))
% 0.48/1.07 Defined: ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2)))))
% 0.48/1.07 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0))))) of role axiom named ind_p
% 0.48/1.07 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0)))))
% 0.48/1.07 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1)))) of role axiom named oneax
% 0.48/1.07 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1))))
% 0.48/1.07 FOF formula (<kernel.Constant object at 0x2aefbd961f38>, <kernel.DependentProduct object at 0x2aefbd961560>) of role type named typ_injective
% 0.48/1.07 Using role type
% 0.48/1.07 Declaring injective:(fofType->(fofType->(fofType->Prop)))
% 0.48/1.07 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) injective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4)))))))) of role definition named def_injective
% 0.48/1.07 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) injective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4))))))))
% 0.48/1.07 Defined: injective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4)))))))
% 0.48/1.07 FOF formula (<kernel.Constant object at 0x2aefbd961d88>, <kernel.DependentProduct object at 0x2aefbd9671b8>) of role type named typ_image
% 0.48/1.07 Using role type
% 0.48/1.07 Declaring image:(fofType->(fofType->(fofType->(fofType->Prop))))
% 0.48/1.07 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) image) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4)))))) of role definition named def_image
% 0.48/1.08 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) image) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))))
% 0.48/1.08 Defined: image:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4)))))
% 0.48/1.08 FOF formula (<kernel.Constant object at 0x2aefbd961d88>, <kernel.DependentProduct object at 0x2aefbd967200>) of role type named typ_tofs
% 0.48/1.08 Using role type
% 0.48/1.08 Declaring tofs:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.48/1.08 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) tofs) (fun (X0:fofType) (X1:fofType)=> ap)) of role definition named def_tofs
% 0.48/1.08 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) tofs) (fun (X0:fofType) (X1:fofType)=> ap))
% 0.48/1.08 Defined: tofs:=(fun (X0:fofType) (X1:fofType)=> ap)
% 0.48/1.08 FOF formula (<kernel.Constant object at 0x2aefbd961d88>, <kernel.DependentProduct object at 0x2aefbd967998>) of role type named typ_soft
% 0.48/1.08 Using role type
% 0.48/1.08 Declaring soft:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.48/1.08 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) soft) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4)))))) of role definition named def_soft
% 0.48/1.08 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) soft) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))))
% 0.48/1.08 Defined: soft:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4)))))
% 0.48/1.08 FOF formula (<kernel.Constant object at 0x2aefbd967998>, <kernel.DependentProduct object at 0x2aefbd967290>) of role type named typ_inverse
% 0.48/1.08 Using role type
% 0.48/1.08 Declaring inverse:(fofType->(fofType->(fofType->fofType)))
% 0.48/1.08 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) inverse) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset))))) of role definition named def_inverse
% 0.48/1.08 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) inverse) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset)))))
% 0.48/1.08 Defined: inverse:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset))))
% 0.48/1.08 FOF formula (<kernel.Constant object at 0x2aefbd967290>, <kernel.DependentProduct object at 0x2aefbd967908>) of role type named typ_surjective
% 0.48/1.08 Using role type
% 0.48/1.08 Declaring surjective:(fofType->(fofType->(fofType->Prop)))
% 0.48/1.08 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) surjective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2)))) of role definition named def_surjective
% 0.48/1.08 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) surjective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))))
% 0.48/1.08 Defined: surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2)))
% 0.48/1.08 FOF formula (<kernel.Constant object at 0x2aefbd967908>, <kernel.DependentProduct object at 0x2aefbd967248>) of role type named typ_bijective
% 0.48/1.08 Using role type
% 0.48/1.08 Declaring bijective:(fofType->(fofType->(fofType->Prop)))
% 0.48/1.08 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) bijective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2)))) of role definition named def_bijective
% 0.48/1.08 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) bijective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))))
% 0.48/1.08 Defined: bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2)))
% 0.57/1.10 FOF formula (<kernel.Constant object at 0x2aefbd967248>, <kernel.DependentProduct object at 0x2aefbd9673b0>) of role type named typ_invf
% 0.57/1.10 Using role type
% 0.57/1.10 Declaring invf:(fofType->(fofType->(fofType->fofType)))
% 0.57/1.10 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) invf) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2)))) of role definition named def_invf
% 0.57/1.10 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) invf) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))))
% 0.57/1.10 Defined: invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2)))
% 0.57/1.10 FOF formula (<kernel.Constant object at 0x2aefbd9673b0>, <kernel.DependentProduct object at 0x2aefbd967290>) of role type named typ_inj_h
% 0.57/1.10 Using role type
% 0.57/1.10 Declaring inj_h:(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 0.57/1.10 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) inj_h) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5)))))) of role definition named def_inj_h
% 0.57/1.10 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) inj_h) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5))))))
% 0.57/1.10 Defined: inj_h:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5)))))
% 0.57/1.10 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3))))))) of role axiom named e_fisi
% 0.57/1.10 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3)))))))
% 0.57/1.10 FOF formula (<kernel.Constant object at 0x2aefbd967ab8>, <kernel.DependentProduct object at 0x2aefbd9672d8>) of role type named typ_e_in
% 0.57/1.10 Using role type
% 0.57/1.10 Declaring e_in:(fofType->((fofType->Prop)->(fofType->fofType)))
% 0.57/1.10 FOF formula (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) e_in) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2)) of role definition named def_e_in
% 0.57/1.10 A new definition: (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) e_in) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2))
% 0.57/1.10 Defined: e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2)
% 0.57/1.10 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0)))))) of role axiom named e_in_p
% 0.57/1.10 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 0.57/1.10 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2))))) of role axiom named e_inp
% 0.57/1.10 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2)))))
% 0.57/1.10 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))) of role axiom named otax1
% 0.57/1.10 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 0.57/1.10 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2))))) of role axiom named otax2
% 0.57/1.12 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2)))))
% 0.57/1.12 FOF formula (<kernel.Constant object at 0x2aefbd967050>, <kernel.DependentProduct object at 0x2aefbd967e18>) of role type named typ_out
% 0.57/1.12 Using role type
% 0.57/1.12 Declaring out:(fofType->((fofType->Prop)->(fofType->fofType)))
% 0.57/1.12 FOF formula (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) out) (fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))) of role definition named def_out
% 0.57/1.12 A new definition: (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) out) (fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))))
% 0.57/1.12 Defined: out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 0.57/1.12 FOF formula (<kernel.Constant object at 0x2aefbd967e18>, <kernel.DependentProduct object at 0x2aefbd967758>) of role type named typ_d_pair
% 0.57/1.12 Using role type
% 0.57/1.12 Declaring d_pair:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.57/1.12 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) d_pair) (fun (X0:fofType) (X1:fofType)=> pair)) of role definition named def_d_pair
% 0.57/1.12 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) d_pair) (fun (X0:fofType) (X1:fofType)=> pair))
% 0.57/1.12 Defined: d_pair:=(fun (X0:fofType) (X1:fofType)=> pair)
% 0.57/1.12 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1))))))))) of role axiom named e_pair_p
% 0.57/1.12 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1)))))))))
% 0.57/1.12 FOF formula (<kernel.Constant object at 0x2aefbd967b00>, <kernel.DependentProduct object at 0x2aefbd967c68>) of role type named typ_first
% 0.57/1.12 Using role type
% 0.57/1.12 Declaring first:(fofType->(fofType->(fofType->fofType)))
% 0.57/1.12 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) first) (fun (X0:fofType) (X1:fofType)=> proj0)) of role definition named def_first
% 0.57/1.12 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) first) (fun (X0:fofType) (X1:fofType)=> proj0))
% 0.57/1.12 Defined: first:=(fun (X0:fofType) (X1:fofType)=> proj0)
% 0.57/1.12 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0)))))) of role axiom named first_p
% 0.57/1.12 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 0.57/1.12 FOF formula (<kernel.Constant object at 0x2aefbd967050>, <kernel.DependentProduct object at 0x2aefbd967710>) of role type named typ_second
% 0.57/1.12 Using role type
% 0.57/1.12 Declaring second:(fofType->(fofType->(fofType->fofType)))
% 0.57/1.12 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) second) (fun (X0:fofType) (X1:fofType)=> _TPTP_proj1)) of role definition named def_second
% 0.57/1.12 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) second) (fun (X0:fofType) (X1:fofType)=> _TPTP_proj1))
% 0.57/1.12 Defined: second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1)
% 0.57/1.12 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1)))))) of role axiom named second_p
% 0.57/1.12 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1))))))
% 0.57/1.14 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2)))) of role axiom named pairis1
% 0.57/1.14 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2))))
% 0.57/1.14 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2)))))) of role axiom named firstis1
% 0.57/1.14 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2))))))
% 0.57/1.14 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3)))))) of role axiom named secondis1
% 0.57/1.14 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3))))))
% 0.57/1.14 FOF formula (<kernel.Constant object at 0x2aefbd967ef0>, <kernel.DependentProduct object at 0x2aefbd967680>) of role type named typ_prop1
% 0.57/1.14 Using role type
% 0.57/1.14 Declaring prop1:(Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 0.57/1.14 FOF formula (((eq (Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))) prop1) (fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3))))) of role definition named def_prop1
% 0.57/1.14 A new definition: (((eq (Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))) prop1) (fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3)))))
% 0.57/1.14 Defined: prop1:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3))))
% 0.57/1.14 FOF formula (<kernel.Constant object at 0x2aefbd967680>, <kernel.DependentProduct object at 0x2aefbd967ef0>) of role type named typ_ite
% 0.57/1.14 Using role type
% 0.57/1.14 Declaring ite:(Prop->(fofType->(fofType->(fofType->fofType))))
% 0.57/1.14 FOF formula (((eq (Prop->(fofType->(fofType->(fofType->fofType))))) ite) (fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3)))) of role definition named def_ite
% 0.57/1.14 A new definition: (((eq (Prop->(fofType->(fofType->(fofType->fofType))))) ite) (fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))))
% 0.57/1.14 Defined: ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3)))
% 0.57/1.14 FOF formula (<kernel.Constant object at 0x2aefbd967ef0>, <kernel.DependentProduct object at 0x2aefbd967488>) of role type named typ_wissel_wa
% 0.57/1.14 Using role type
% 0.57/1.14 Declaring wissel_wa:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.57/1.14 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) wissel_wa) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3))) of role definition named def_wissel_wa
% 0.57/1.14 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) wissel_wa) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3)))
% 0.57/1.14 Defined: wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3))
% 0.57/1.14 FOF formula (<kernel.Constant object at 0x2aefbd967488>, <kernel.DependentProduct object at 0x2aefbd967fc8>) of role type named typ_wissel_wb
% 0.57/1.15 Using role type
% 0.57/1.15 Declaring wissel_wb:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.57/1.15 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) wissel_wb) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3)))) of role definition named def_wissel_wb
% 0.57/1.15 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) wissel_wb) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3))))
% 0.57/1.15 Defined: wissel_wb:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3)))
% 0.57/1.15 FOF formula (<kernel.Constant object at 0x2aefbd967fc8>, <kernel.DependentProduct object at 0x2aefbd967d88>) of role type named typ_wissel
% 0.57/1.15 Using role type
% 0.57/1.15 Declaring wissel:(fofType->(fofType->(fofType->fofType)))
% 0.57/1.15 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) wissel) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2)))) of role definition named def_wissel
% 0.57/1.15 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) wissel) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))))
% 0.57/1.15 Defined: wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2)))
% 0.57/1.15 FOF formula (<kernel.Constant object at 0x2aefbd967878>, <kernel.DependentProduct object at 0x2aefbd967830>) of role type named typ_changef
% 0.57/1.15 Using role type
% 0.57/1.15 Declaring changef:(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 0.57/1.15 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) changef) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5)))))) of role definition named def_changef
% 0.57/1.15 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) changef) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5))))))
% 0.57/1.15 Defined: changef:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5)))))
% 0.57/1.15 FOF formula (<kernel.Constant object at 0x2aefbd967248>, <kernel.DependentProduct object at 0x2aefbd967d88>) of role type named typ_r_ec
% 0.57/1.15 Using role type
% 0.57/1.15 Declaring r_ec:(Prop->(Prop->Prop))
% 0.57/1.15 FOF formula (((eq (Prop->(Prop->Prop))) r_ec) (fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1)))) of role definition named def_r_ec
% 0.57/1.15 A new definition: (((eq (Prop->(Prop->Prop))) r_ec) (fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))))
% 0.57/1.15 Defined: r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1)))
% 0.57/1.15 FOF formula (<kernel.Constant object at 0x2aefbd967d88>, <kernel.DependentProduct object at 0x2aefbd967830>) of role type named typ_esti
% 0.57/1.15 Using role type
% 0.57/1.15 Declaring esti:(fofType->(fofType->(fofType->Prop)))
% 0.57/1.15 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) esti) (fun (X0:fofType)=> in)) of role definition named def_esti
% 0.57/1.15 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) esti) (fun (X0:fofType)=> in))
% 0.57/1.15 Defined: esti:=(fun (X0:fofType)=> in)
% 0.57/1.15 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0))))) of role axiom named setof_p
% 0.57/1.15 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0)))))
% 0.57/1.15 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1)))))) of role axiom named estii
% 0.57/1.15 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1))))))
% 0.57/1.15 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2))))) of role axiom named estie
% 0.57/1.17 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2)))))
% 0.57/1.17 FOF formula (<kernel.Constant object at 0x2aefbd967830>, <kernel.DependentProduct object at 0x2aefbd96e638>) of role type named typ_empty
% 0.57/1.17 Using role type
% 0.57/1.17 Declaring empty:(fofType->(fofType->Prop))
% 0.57/1.17 FOF formula (((eq (fofType->(fofType->Prop))) empty) (fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))))) of role definition named def_empty
% 0.57/1.17 A new definition: (((eq (fofType->(fofType->Prop))) empty) (fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))))
% 0.57/1.17 Defined: empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))))
% 0.57/1.17 FOF formula (<kernel.Constant object at 0x2aefbd967830>, <kernel.DependentProduct object at 0x2aefbd96e440>) of role type named typ_nonempty
% 0.57/1.17 Using role type
% 0.57/1.17 Declaring nonempty:(fofType->(fofType->Prop))
% 0.57/1.17 FOF formula (((eq (fofType->(fofType->Prop))) nonempty) (fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))) of role definition named def_nonempty
% 0.57/1.17 A new definition: (((eq (fofType->(fofType->Prop))) nonempty) (fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))))
% 0.57/1.17 Defined: nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))
% 0.57/1.17 FOF formula (<kernel.Constant object at 0x2aefbd967830>, <kernel.DependentProduct object at 0x2aefbd96e098>) of role type named typ_incl
% 0.57/1.17 Using role type
% 0.57/1.17 Declaring incl:(fofType->(fofType->(fofType->Prop)))
% 0.57/1.17 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) incl) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2)))))) of role definition named def_incl
% 0.57/1.17 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) incl) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2))))))
% 0.57/1.17 Defined: incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2)))))
% 0.57/1.17 FOF formula (<kernel.Constant object at 0x2aefbd96e098>, <kernel.DependentProduct object at 0x2aefbd96e638>) of role type named typ_st_disj
% 0.57/1.17 Using role type
% 0.57/1.17 Declaring st_disj:(fofType->(fofType->(fofType->Prop)))
% 0.57/1.17 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) st_disj) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2)))))) of role definition named def_st_disj
% 0.57/1.17 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) st_disj) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2))))))
% 0.57/1.17 Defined: st_disj:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2)))))
% 0.57/1.17 FOF formula (forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2)))))))) of role axiom named isseti
% 0.57/1.17 A new axiom: (forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2))))))))
% 0.57/1.17 FOF formula (<kernel.Constant object at 0x2aefbd96e2d8>, <kernel.DependentProduct object at 0x2aefbd96e710>) of role type named typ_nissetprop
% 0.57/1.17 Using role type
% 0.57/1.17 Declaring nissetprop:(fofType->(fofType->(fofType->(fofType->Prop))))
% 0.57/1.17 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) nissetprop) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2))))) of role definition named def_nissetprop
% 0.65/1.18 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) nissetprop) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2)))))
% 0.65/1.18 Defined: nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2))))
% 0.65/1.18 FOF formula (<kernel.Constant object at 0x2aefbd96e710>, <kernel.DependentProduct object at 0x2aefbd96e098>) of role type named typ_unmore
% 0.65/1.18 Using role type
% 0.65/1.18 Declaring unmore:(fofType->(fofType->(fofType->fofType)))
% 0.65/1.18 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) unmore) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4)))))))) of role definition named def_unmore
% 0.65/1.18 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) unmore) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4))))))))
% 0.65/1.18 Defined: unmore:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4)))))))
% 0.65/1.18 FOF formula (<kernel.Constant object at 0x2aefbd96e098>, <kernel.DependentProduct object at 0x2aefbd96e908>) of role type named typ_ecelt
% 0.65/1.18 Using role type
% 0.65/1.18 Declaring ecelt:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.65/1.18 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ecelt) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2)))) of role definition named def_ecelt
% 0.65/1.18 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ecelt) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))))
% 0.65/1.18 Defined: ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2)))
% 0.65/1.18 FOF formula (<kernel.Constant object at 0x2aefbd96e908>, <kernel.DependentProduct object at 0x2aefbd96e8c0>) of role type named typ_ecp
% 0.65/1.18 Using role type
% 0.65/1.18 Declaring ecp:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.65/1.18 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) ecp) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3)))) of role definition named def_ecp
% 0.65/1.18 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) ecp) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3))))
% 0.65/1.18 Defined: ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3)))
% 0.65/1.18 FOF formula (<kernel.Constant object at 0x2aefbd96e8c0>, <kernel.DependentProduct object at 0x2aefbd96ec20>) of role type named typ_anec
% 0.65/1.18 Using role type
% 0.65/1.18 Declaring anec:(fofType->((fofType->(fofType->Prop))->(fofType->Prop)))
% 0.65/1.18 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->Prop)))) anec) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2)))) of role definition named def_anec
% 0.65/1.18 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->Prop)))) anec) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))))
% 0.65/1.18 Defined: anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2)))
% 0.65/1.18 FOF formula (<kernel.Constant object at 0x2aefbd96ec20>, <kernel.DependentProduct object at 0x2aefbd96e908>) of role type named typ_ect
% 0.65/1.18 Using role type
% 0.65/1.18 Declaring ect:(fofType->((fofType->(fofType->Prop))->fofType))
% 0.65/1.18 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->fofType))) ect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1)))) of role definition named def_ect
% 0.65/1.18 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->fofType))) ect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))))
% 0.65/1.20 Defined: ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1)))
% 0.65/1.20 FOF formula (<kernel.Constant object at 0x2aefbd96e908>, <kernel.DependentProduct object at 0x2aefbd96e560>) of role type named typ_ectset
% 0.65/1.20 Using role type
% 0.65/1.20 Declaring ectset:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.65/1.20 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectset) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1)))) of role definition named def_ectset
% 0.65/1.20 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectset) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))))
% 0.65/1.20 Defined: ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1)))
% 0.65/1.20 FOF formula (<kernel.Constant object at 0x2aefbd96e560>, <kernel.DependentProduct object at 0x2aefbd96e3b0>) of role type named typ_ectelt
% 0.65/1.20 Using role type
% 0.65/1.20 Declaring ectelt:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.65/1.20 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectelt) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2)))) of role definition named def_ectelt
% 0.65/1.20 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectelt) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))))
% 0.65/1.20 Defined: ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2)))
% 0.65/1.20 FOF formula (<kernel.Constant object at 0x2aefbd96e3b0>, <kernel.DependentProduct object at 0x2aefbd96eb00>) of role type named typ_ecect
% 0.65/1.20 Using role type
% 0.65/1.20 Declaring ecect:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.65/1.20 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ecect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1)))) of role definition named def_ecect
% 0.65/1.20 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ecect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))))
% 0.65/1.20 Defined: ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1)))
% 0.65/1.20 FOF formula (<kernel.Constant object at 0x2aefbd96eb00>, <kernel.DependentProduct object at 0x2aefbd96e320>) of role type named typ_fixfu
% 0.65/1.20 Using role type
% 0.65/1.20 Declaring fixfu:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.65/1.20 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) fixfu) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5))))))))) of role definition named def_fixfu
% 0.65/1.20 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) fixfu) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))))
% 0.65/1.20 Defined: fixfu:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5))))))))
% 0.65/1.20 FOF formula (<kernel.Constant object at 0x2aefbd96e320>, <kernel.DependentProduct object at 0x2aefbd96e998>) of role type named typ_d_10_prop1
% 0.65/1.20 Using role type
% 0.65/1.20 Declaring d_10_prop1:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))
% 0.65/1.20 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))) d_10_prop1) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5)))) of role definition named def_d_10_prop1
% 0.65/1.22 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))) d_10_prop1) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5))))
% 0.65/1.22 Defined: d_10_prop1:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5)))
% 0.65/1.22 FOF formula (<kernel.Constant object at 0x2aefbd96e998>, <kernel.DependentProduct object at 0x2aefbd96ebd8>) of role type named typ_prop2
% 0.65/1.22 Using role type
% 0.65/1.22 Declaring prop2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))
% 0.65/1.22 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))) prop2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5)))) of role definition named def_prop2
% 0.65/1.22 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))) prop2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5))))
% 0.65/1.22 Defined: prop2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5)))
% 0.65/1.22 FOF formula (<kernel.Constant object at 0x2aefbd96ebd8>, <kernel.DependentProduct object at 0x2aefbd96ee18>) of role type named typ_indeq
% 0.65/1.22 Using role type
% 0.65/1.22 Declaring indeq:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 0.65/1.22 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))) indeq) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4)))) of role definition named def_indeq
% 0.65/1.22 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))) indeq) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4))))
% 0.65/1.22 Defined: indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4)))
% 0.65/1.22 FOF formula (<kernel.Constant object at 0x2aefbd96ee18>, <kernel.DependentProduct object at 0x2aefbd96ed88>) of role type named typ_fixfu2
% 0.65/1.22 Using role type
% 0.65/1.22 Declaring fixfu2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.65/1.22 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) fixfu2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7)))))))))))))) of role definition named def_fixfu2
% 0.65/1.22 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) fixfu2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7))))))))))))))
% 0.65/1.22 Defined: fixfu2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7)))))))))))))
% 0.65/1.23 FOF formula (<kernel.Constant object at 0x2aefbd96ed88>, <kernel.DependentProduct object at 0x2aefbd96e0e0>) of role type named typ_d_11_i
% 0.65/1.23 Using role type
% 0.65/1.23 Declaring d_11_i:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 0.65/1.23 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))) d_11_i) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2))))) of role definition named def_d_11_i
% 0.65/1.23 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))) d_11_i) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2)))))
% 0.65/1.23 Defined: d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2))))
% 0.65/1.23 FOF formula (<kernel.Constant object at 0x2aefbd96e0e0>, <kernel.DependentProduct object at 0x2aefbd96e9e0>) of role type named typ_indeq2
% 0.65/1.23 Using role type
% 0.65/1.23 Declaring indeq2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))
% 0.65/1.23 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))) indeq2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4)))) of role definition named def_indeq2
% 0.65/1.23 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))) indeq2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4))))
% 0.65/1.23 Defined: indeq2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4)))
% 0.65/1.23 FOF formula (<kernel.Constant object at 0x2aefbd96e9e0>, <kernel.Single object at 0x2aefbd96e0e0>) of role type named typ_nat
% 0.65/1.23 Using role type
% 0.65/1.23 Declaring nat:fofType
% 0.65/1.23 FOF formula (((eq fofType) nat) ((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset))))) of role definition named def_nat
% 0.65/1.23 A new definition: (((eq fofType) nat) ((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))))
% 0.65/1.23 Defined: nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset))))
% 0.65/1.23 FOF formula (<kernel.Constant object at 0x2aefbd96e0e0>, <kernel.DependentProduct object at 0x2aefbd96eb00>) of role type named typ_n_is
% 0.65/1.23 Using role type
% 0.65/1.23 Declaring n_is:(fofType->(fofType->Prop))
% 0.65/1.23 FOF formula (((eq (fofType->(fofType->Prop))) n_is) (e_is nat)) of role definition named def_n_is
% 0.65/1.23 A new definition: (((eq (fofType->(fofType->Prop))) n_is) (e_is nat))
% 0.65/1.23 Defined: n_is:=(e_is nat)
% 0.65/1.23 FOF formula (<kernel.Constant object at 0x2aefbd96e998>, <kernel.DependentProduct object at 0x2aefbd96ef38>) of role type named typ_nis
% 0.65/1.23 Using role type
% 0.65/1.23 Declaring nis:(fofType->(fofType->Prop))
% 0.65/1.23 FOF formula (((eq (fofType->(fofType->Prop))) nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1)))) of role definition named def_nis
% 0.65/1.23 A new definition: (((eq (fofType->(fofType->Prop))) nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))))
% 0.65/1.23 Defined: nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1)))
% 0.65/1.23 FOF formula (<kernel.Constant object at 0x2aefbd96ef38>, <kernel.DependentProduct object at 0x2aefbd96eb00>) of role type named typ_n_in
% 0.65/1.23 Using role type
% 0.65/1.23 Declaring n_in:(fofType->(fofType->Prop))
% 0.65/1.23 FOF formula (((eq (fofType->(fofType->Prop))) n_in) (esti nat)) of role definition named def_n_in
% 0.65/1.23 A new definition: (((eq (fofType->(fofType->Prop))) n_in) (esti nat))
% 0.65/1.24 Defined: n_in:=(esti nat)
% 0.65/1.24 FOF formula (<kernel.Constant object at 0x2aefbd96ed40>, <kernel.DependentProduct object at 0x2aefbd96eb00>) of role type named typ_n_some
% 0.65/1.24 Using role type
% 0.65/1.24 Declaring n_some:((fofType->Prop)->Prop)
% 0.65/1.24 FOF formula (((eq ((fofType->Prop)->Prop)) n_some) (l_some nat)) of role definition named def_n_some
% 0.65/1.24 A new definition: (((eq ((fofType->Prop)->Prop)) n_some) (l_some nat))
% 0.65/1.24 Defined: n_some:=(l_some nat)
% 0.65/1.24 FOF formula (<kernel.Constant object at 0x2aefbd96ef80>, <kernel.DependentProduct object at 0x2aefbd96eb00>) of role type named typ_n_all
% 0.65/1.24 Using role type
% 0.65/1.24 Declaring n_all:((fofType->Prop)->Prop)
% 0.65/1.24 FOF formula (((eq ((fofType->Prop)->Prop)) n_all) (all nat)) of role definition named def_n_all
% 0.65/1.24 A new definition: (((eq ((fofType->Prop)->Prop)) n_all) (all nat))
% 0.65/1.24 Defined: n_all:=(all nat)
% 0.65/1.24 FOF formula (<kernel.Constant object at 0x2aefbd96ed40>, <kernel.DependentProduct object at 0x2aefbd96ee18>) of role type named typ_n_one
% 0.65/1.24 Using role type
% 0.65/1.24 Declaring n_one:((fofType->Prop)->Prop)
% 0.65/1.24 FOF formula (((eq ((fofType->Prop)->Prop)) n_one) (one nat)) of role definition named def_n_one
% 0.65/1.24 A new definition: (((eq ((fofType->Prop)->Prop)) n_one) (one nat))
% 0.65/1.24 Defined: n_one:=(one nat)
% 0.65/1.24 FOF formula (<kernel.Constant object at 0x2aefbd96e8c0>, <kernel.Single object at 0x2aefbd96ed40>) of role type named typ_n_1
% 0.65/1.24 Using role type
% 0.65/1.24 Declaring n_1:fofType
% 0.65/1.24 FOF formula (((eq fofType) n_1) (ordsucc emptyset)) of role definition named def_n_1
% 0.65/1.24 A new definition: (((eq fofType) n_1) (ordsucc emptyset))
% 0.65/1.24 Defined: n_1:=(ordsucc emptyset)
% 0.65/1.24 FOF formula ((is_of n_1) (fun (X0:fofType)=> ((in X0) nat))) of role axiom named n_1_p
% 0.65/1.24 A new axiom: ((is_of n_1) (fun (X0:fofType)=> ((in X0) nat)))
% 0.65/1.24 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat))))) of role axiom named suc_p
% 0.65/1.24 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat)))))
% 0.65/1.24 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1))) of role axiom named n_ax3
% 0.65/1.24 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1)))
% 0.65/1.24 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1)))))) of role axiom named n_ax4
% 0.65/1.24 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1))))))
% 0.65/1.24 FOF formula (<kernel.Constant object at 0x2aefbd96ed40>, <kernel.DependentProduct object at 0x2aefbd973320>) of role type named typ_cond1
% 0.65/1.24 Using role type
% 0.65/1.24 Declaring cond1:(fofType->Prop)
% 0.65/1.24 FOF formula (((eq (fofType->Prop)) cond1) (n_in n_1)) of role definition named def_cond1
% 0.65/1.24 A new definition: (((eq (fofType->Prop)) cond1) (n_in n_1))
% 0.65/1.24 Defined: cond1:=(n_in n_1)
% 0.65/1.24 FOF formula (<kernel.Constant object at 0x2aefbd973200>, <kernel.DependentProduct object at 0x2aefbd9735f0>) of role type named typ_cond2
% 0.65/1.24 Using role type
% 0.65/1.24 Declaring cond2:(fofType->Prop)
% 0.65/1.24 FOF formula (((eq (fofType->Prop)) cond2) (fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0)))))) of role definition named def_cond2
% 0.65/1.24 A new definition: (((eq (fofType->Prop)) cond2) (fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))))
% 0.65/1.24 Defined: cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0)))))
% 0.65/1.24 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0))))))) of role axiom named n_ax5
% 0.65/1.24 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0)))))))
% 0.65/1.24 FOF formula (<kernel.Constant object at 0x2aefbd9733b0>, <kernel.DependentProduct object at 0x2aefbd973518>) of role type named typ_i1_s
% 0.65/1.26 Using role type
% 0.65/1.26 Declaring i1_s:((fofType->Prop)->fofType)
% 0.65/1.26 FOF formula (((eq ((fofType->Prop)->fofType)) i1_s) (d_Sep nat)) of role definition named def_i1_s
% 0.65/1.26 A new definition: (((eq ((fofType->Prop)->fofType)) i1_s) (d_Sep nat))
% 0.65/1.26 Defined: i1_s:=(d_Sep nat)
% 0.65/1.26 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM007^1.ax, trying next directory
% 0.65/1.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1))))))) of role axiom named satz1
% 0.65/1.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1)))))))
% 0.65/1.26 FOF formula (<kernel.Constant object at 0x2aefba1e0488>, <kernel.DependentProduct object at 0x2aefba1e0e18>) of role type named typ_d_22_prop1
% 0.65/1.26 Using role type
% 0.65/1.26 Declaring d_22_prop1:(fofType->Prop)
% 0.65/1.26 FOF formula (((eq (fofType->Prop)) d_22_prop1) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))) of role definition named def_d_22_prop1
% 0.65/1.26 A new definition: (((eq (fofType->Prop)) d_22_prop1) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 0.65/1.26 Defined: d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0))
% 0.65/1.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))) of role axiom named satz2
% 0.65/1.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 0.65/1.26 FOF formula (<kernel.Constant object at 0x2aefba1e05a8>, <kernel.DependentProduct object at 0x2aefba1e05f0>) of role type named typ_d_23_prop1
% 0.65/1.26 Using role type
% 0.65/1.26 Declaring d_23_prop1:(fofType->Prop)
% 0.65/1.26 FOF formula (((eq (fofType->Prop)) d_23_prop1) (fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))) of role definition named def_d_23_prop1
% 0.65/1.26 A new definition: (((eq (fofType->Prop)) d_23_prop1) (fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 0.65/1.26 Defined: d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))
% 0.65/1.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))) of role axiom named satz3
% 0.65/1.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 0.65/1.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))) of role axiom named satz3a
% 0.65/1.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 0.65/1.26 FOF formula (<kernel.Constant object at 0x2aefba1e0488>, <kernel.DependentProduct object at 0x2aefba1e05f0>) of role type named typ_d_24_prop1
% 0.65/1.26 Using role type
% 0.65/1.26 Declaring d_24_prop1:(fofType->Prop)
% 0.65/1.26 FOF formula (((eq (fofType->Prop)) d_24_prop1) (fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1))))))) of role definition named def_d_24_prop1
% 0.65/1.26 A new definition: (((eq (fofType->Prop)) d_24_prop1) (fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))))
% 0.65/1.26 Defined: d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1))))))
% 0.65/1.26 FOF formula (<kernel.Constant object at 0x2aefba1e05a8>, <kernel.DependentProduct object at 0x2aefba1e0710>) of role type named typ_d_24_prop2
% 0.65/1.26 Using role type
% 0.65/1.26 Declaring d_24_prop2:(fofType->(fofType->Prop))
% 0.65/1.26 FOF formula (((eq (fofType->(fofType->Prop))) d_24_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1)))) of role definition named def_d_24_prop2
% 0.65/1.26 A new definition: (((eq (fofType->(fofType->Prop))) d_24_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1))))
% 0.65/1.28 Defined: d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1)))
% 0.65/1.28 FOF formula (<kernel.Constant object at 0x2aefba1e07e8>, <kernel.DependentProduct object at 0x2aefba1e0998>) of role type named typ_prop3
% 0.65/1.28 Using role type
% 0.65/1.28 Declaring prop3:(fofType->(fofType->(fofType->Prop)))
% 0.65/1.28 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2)))) of role definition named def_prop3
% 0.65/1.28 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))))
% 0.65/1.28 Defined: prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2)))
% 0.65/1.28 FOF formula (<kernel.Constant object at 0x2aefba1e0c20>, <kernel.DependentProduct object at 0x2aefba1dde60>) of role type named typ_prop4
% 0.65/1.28 Using role type
% 0.65/1.28 Declaring prop4:(fofType->Prop)
% 0.65/1.28 FOF formula (((eq (fofType->Prop)) prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))) of role definition named def_prop4
% 0.65/1.28 A new definition: (((eq (fofType->Prop)) prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))))
% 0.65/1.28 Defined: prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))
% 0.65/1.28 FOF formula (<kernel.Constant object at 0x2aefba1e07e8>, <kernel.DependentProduct object at 0x2aefba1dd518>) of role type named typ_d_24_g
% 0.65/1.28 Using role type
% 0.65/1.28 Declaring d_24_g:(fofType->fofType)
% 0.65/1.28 FOF formula (((eq (fofType->fofType)) d_24_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1)))))) of role definition named def_d_24_g
% 0.65/1.28 A new definition: (((eq (fofType->fofType)) d_24_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))))
% 0.65/1.28 Defined: d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1)))))
% 0.65/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2)))))))))) of role axiom named satz4
% 0.65/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2))))))))))
% 0.65/1.28 FOF formula (<kernel.Constant object at 0x2aefba1e0c20>, <kernel.DependentProduct object at 0x2aefba1ddef0>) of role type named typ_plus
% 0.65/1.28 Using role type
% 0.65/1.28 Declaring plus:(fofType->fofType)
% 0.65/1.28 FOF formula (((eq (fofType->fofType)) plus) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))) of role definition named def_plus
% 0.65/1.28 A new definition: (((eq (fofType->fofType)) plus) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))))
% 0.65/1.28 Defined: plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))
% 0.65/1.28 FOF formula (<kernel.Constant object at 0x2aefba1e07e8>, <kernel.DependentProduct object at 0x2aefba1dd638>) of role type named typ_n_pl
% 0.65/1.28 Using role type
% 0.65/1.28 Declaring n_pl:(fofType->(fofType->fofType))
% 0.65/1.28 FOF formula (((eq (fofType->(fofType->fofType))) n_pl) (fun (X0:fofType)=> (ap (plus X0)))) of role definition named def_n_pl
% 0.65/1.28 A new definition: (((eq (fofType->(fofType->fofType))) n_pl) (fun (X0:fofType)=> (ap (plus X0))))
% 0.65/1.28 Defined: n_pl:=(fun (X0:fofType)=> (ap (plus X0)))
% 0.65/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0)))) of role axiom named satz4a
% 0.65/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0))))
% 0.65/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1))))))) of role axiom named satz4b
% 0.76/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1)))))))
% 0.76/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0)))) of role axiom named satz4c
% 0.76/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0))))
% 0.76/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1))))))) of role axiom named satz4d
% 0.76/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1)))))))
% 0.76/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1)))) of role axiom named satz4e
% 0.76/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1))))
% 0.76/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1))))))) of role axiom named satz4f
% 0.76/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1)))))))
% 0.76/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0)))) of role axiom named satz4g
% 0.76/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0))))
% 0.76/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1)))))) of role axiom named satz4h
% 0.76/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1))))))
% 0.76/1.30 FOF formula (<kernel.Constant object at 0x2aefba1ddef0>, <kernel.DependentProduct object at 0x2aefba1dd5f0>) of role type named typ_d_25_prop1
% 0.76/1.30 Using role type
% 0.76/1.30 Declaring d_25_prop1:(fofType->(fofType->(fofType->Prop)))
% 0.76/1.30 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_25_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2))))) of role definition named def_d_25_prop1
% 0.76/1.30 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_25_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))))
% 0.76/1.30 Defined: d_25_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2))))
% 0.76/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2))))))))) of role axiom named satz5
% 0.76/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))))))))
% 0.76/1.30 FOF formula (<kernel.Constant object at 0x2aefba1dd5f0>, <kernel.DependentProduct object at 0x2aefba1dd9e0>) of role type named typ_d_26_prop1
% 0.76/1.30 Using role type
% 0.76/1.30 Declaring d_26_prop1:(fofType->(fofType->Prop))
% 0.76/1.30 FOF formula (((eq (fofType->(fofType->Prop))) d_26_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))) of role definition named def_d_26_prop1
% 0.76/1.30 A new definition: (((eq (fofType->(fofType->Prop))) d_26_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))))
% 0.79/1.32 Defined: d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))
% 0.79/1.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))))) of role axiom named satz6
% 0.79/1.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))))))
% 0.79/1.32 FOF formula (<kernel.Constant object at 0x2aefba1ddef0>, <kernel.DependentProduct object at 0x2aefba1dd0e0>) of role type named typ_d_27_prop1
% 0.79/1.32 Using role type
% 0.79/1.32 Declaring d_27_prop1:(fofType->(fofType->Prop))
% 0.79/1.32 FOF formula (((eq (fofType->(fofType->Prop))) d_27_prop1) (fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))) of role definition named def_d_27_prop1
% 0.79/1.32 A new definition: (((eq (fofType->(fofType->Prop))) d_27_prop1) (fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))
% 0.79/1.32 Defined: d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))
% 0.79/1.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))))) of role axiom named satz7
% 0.79/1.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))))
% 0.79/1.32 FOF formula (<kernel.Constant object at 0x2aefba1dd0e0>, <kernel.DependentProduct object at 0x2aefba1dd9e0>) of role type named typ_d_28_prop1
% 0.79/1.32 Using role type
% 0.79/1.32 Declaring d_28_prop1:(fofType->(fofType->(fofType->Prop)))
% 0.79/1.32 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_28_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2)))) of role definition named def_d_28_prop1
% 0.79/1.32 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_28_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))))
% 0.79/1.32 Defined: d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2)))
% 0.79/1.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2))))))))) of role axiom named satz8
% 0.79/1.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2)))))))))
% 0.79/1.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2)))))))) of role axiom named satz8a
% 0.79/1.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2))))))))
% 0.79/1.32 FOF formula (<kernel.Constant object at 0x2aefba1dd518>, <kernel.DependentProduct object at 0x2aefba2c0368>) of role type named typ_diffprop
% 0.79/1.32 Using role type
% 0.79/1.32 Declaring diffprop:(fofType->(fofType->(fofType->Prop)))
% 0.79/1.32 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))) of role definition named def_diffprop
% 0.79/1.32 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))
% 0.79/1.32 Defined: diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))
% 0.79/1.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))))))) of role axiom named satz8b
% 0.79/1.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))))))
% 0.79/1.34 FOF formula (<kernel.Constant object at 0x2aefba1dd7a0>, <kernel.DependentProduct object at 0x2aefba2c01b8>) of role type named typ_d_29_ii
% 0.79/1.34 Using role type
% 0.79/1.34 Declaring d_29_ii:(fofType->(fofType->Prop))
% 0.79/1.34 FOF formula (((eq (fofType->(fofType->Prop))) d_29_ii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1)))) of role definition named def_d_29_ii
% 0.79/1.34 A new definition: (((eq (fofType->(fofType->Prop))) d_29_ii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))))
% 0.79/1.34 Defined: d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1)))
% 0.79/1.34 FOF formula (<kernel.Constant object at 0x2aefba2c0518>, <kernel.DependentProduct object at 0x2aefbac97998>) of role type named typ_iii
% 0.79/1.34 Using role type
% 0.79/1.34 Declaring iii:(fofType->(fofType->Prop))
% 0.79/1.34 FOF formula (((eq (fofType->(fofType->Prop))) iii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0)))) of role definition named def_iii
% 0.79/1.34 A new definition: (((eq (fofType->(fofType->Prop))) iii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))))
% 0.79/1.34 Defined: iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0)))
% 0.79/1.34 FOF formula (<kernel.Constant object at 0x2aefba2c0ab8>, <kernel.DependentProduct object at 0x2aefbac974d0>) of role type named typ_d_29_prop1
% 0.79/1.34 Using role type
% 0.79/1.34 Declaring d_29_prop1:(fofType->(fofType->Prop))
% 0.79/1.34 FOF formula (((eq (fofType->(fofType->Prop))) d_29_prop1) (fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))) of role definition named def_d_29_prop1
% 0.79/1.34 A new definition: (((eq (fofType->(fofType->Prop))) d_29_prop1) (fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))
% 0.79/1.34 Defined: d_29_prop1:=(fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))
% 0.79/1.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2))))))))) of role axiom named satz9
% 0.79/1.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2)))))))))
% 0.79/1.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0))))))) of role axiom named satz9a
% 0.79/1.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 0.79/1.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0))))))) of role axiom named satz9b
% 0.79/1.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 0.79/1.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))) of role axiom named satz10
% 0.79/1.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 0.79/1.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))) of role axiom named satz10a
% 0.79/1.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 0.79/1.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))) of role axiom named satz10b
% 0.79/1.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 0.79/1.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0)))))) of role axiom named satz11
% 0.79/1.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0))))))
% 0.79/1.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0)))))) of role axiom named satz12
% 0.79/1.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0))))))
% 0.79/1.36 FOF formula (<kernel.Constant object at 0x2aefbac97d40>, <kernel.DependentProduct object at 0x2aefbac973f8>) of role type named typ_moreis
% 0.79/1.36 Using role type
% 0.79/1.36 Declaring moreis:(fofType->(fofType->Prop))
% 0.79/1.36 FOF formula (((eq (fofType->(fofType->Prop))) moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1)))) of role definition named def_moreis
% 0.79/1.36 A new definition: (((eq (fofType->(fofType->Prop))) moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))))
% 0.79/1.36 Defined: moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1)))
% 0.79/1.36 FOF formula (<kernel.Constant object at 0x2aefbac973f8>, <kernel.DependentProduct object at 0x2aefbac97560>) of role type named typ_lessis
% 0.79/1.36 Using role type
% 0.79/1.36 Declaring lessis:(fofType->(fofType->Prop))
% 0.79/1.36 FOF formula (((eq (fofType->(fofType->Prop))) lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1)))) of role definition named def_lessis
% 0.79/1.36 A new definition: (((eq (fofType->(fofType->Prop))) lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))))
% 0.79/1.36 Defined: lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1)))
% 0.79/1.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0)))))) of role axiom named satz13
% 0.79/1.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0))))))
% 0.79/1.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0)))))) of role axiom named satz14
% 0.79/1.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0))))))
% 0.79/1.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1))))))) of role axiom named satz10c
% 0.79/1.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1)))))))
% 0.79/1.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1))))))) of role axiom named satz10d
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1)))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1)))))) of role axiom named satz10e
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1)))))) of role axiom named satz10f
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1))))))) of role axiom named satz10g
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1)))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1))))))) of role axiom named satz10h
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1)))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1)))))) of role axiom named satz10j
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1)))))) of role axiom named satz10k
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2))))))))) of role axiom named satz15
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2))))))))) of role axiom named satz16a
% 0.79/1.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 0.79/1.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2))))))))) of role axiom named satz16b
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2)))))))))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2))))))))) of role axiom named satz16c
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2)))))))))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2))))))))) of role axiom named satz16d
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2)))))))))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((lessis X1) X2)->((lessis X0) X2))))))))) of role axiom named satz17
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((lessis X1) X2)->((lessis X0) X2)))))))))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0))))) of role axiom named satz18
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0)))))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1)))))) of role axiom named satz18a
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1))))))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0))) of role axiom named satz18b
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0)))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0)))) of role axiom named satz18c
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0))))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19a
% 0.88/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.88/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19b
% 0.88/1.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.88/1.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19c
% 0.88/1.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.88/1.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19d
% 0.88/1.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.88/1.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19e
% 0.88/1.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.88/1.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19f
% 0.88/1.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.88/1.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz19g
% 0.88/1.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.88/1.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1)))))))))))) of role axiom named satz19h
% 0.88/1.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 0.88/1.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz19j
% 0.88/1.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.88/1.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1)))))))))))) of role axiom named satz19k
% 0.88/1.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 0.88/1.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19l
% 0.88/1.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.88/1.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19m
% 0.88/1.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.88/1.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19n
% 0.88/1.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.88/1.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19o
% 0.88/1.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.88/1.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1)))))))) of role axiom named satz20a
% 0.96/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1))))))))
% 0.96/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1)))))))) of role axiom named satz20b
% 0.96/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1))))))))
% 0.96/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1)))))))) of role axiom named satz20c
% 0.96/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1))))))))
% 0.96/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1)))))))) of role axiom named satz20d
% 0.96/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1))))))))
% 0.96/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1)))))))) of role axiom named satz20e
% 0.96/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1))))))))
% 0.96/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1)))))))) of role axiom named satz20f
% 0.96/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1))))))))
% 0.96/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz21
% 0.96/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.96/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz21a
% 0.96/1.52 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.96/1.52 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz22a
% 0.96/1.52 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.96/1.52 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz22b
% 0.96/1.52 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.96/1.52 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz22c
% 0.96/1.52 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.96/1.52 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz22d
% 0.96/1.52 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.96/1.52 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz23
% 0.96/1.52 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz23a
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1))) of role axiom named satz24
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1)))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1)) of role axiom named satz24a
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1))) of role axiom named satz24b
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1)))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0)))) of role axiom named satz24c
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0))))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1))))))) of role axiom named satz25
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1)))))))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0))))))) of role axiom named satz25a
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0)))))))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0)))))) of role axiom named satz25b
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0))))))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0)))))) of role axiom named satz25c
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0))))))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0)))))) of role axiom named satz26
% 0.96/1.54 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0))))))
% 0.96/1.54 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0)))))) of role axiom named satz26a
% 0.96/1.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0))))))
% 0.96/1.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0)))))) of role axiom named satz26b
% 0.96/1.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0))))))
% 0.96/1.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0)))))) of role axiom named satz26c
% 0.96/1.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0))))))
% 0.96/1.56 FOF formula (<kernel.Constant object at 0x2aefbd9428c0>, <kernel.DependentProduct object at 0x2aefbd942560>) of role type named typ_lbprop
% 0.96/1.56 Using role type
% 0.96/1.56 Declaring lbprop:((fofType->Prop)->(fofType->(fofType->Prop)))
% 0.96/1.56 FOF formula (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) lbprop) (fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2)))) of role definition named def_lbprop
% 0.96/1.56 A new definition: (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) lbprop) (fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))))
% 0.96/1.56 Defined: lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2)))
% 0.96/1.56 FOF formula (<kernel.Constant object at 0x2aefbd942560>, <kernel.DependentProduct object at 0x2aefbd942638>) of role type named typ_n_lb
% 0.96/1.56 Using role type
% 0.96/1.56 Declaring n_lb:((fofType->Prop)->(fofType->Prop))
% 0.96/1.56 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) n_lb) (fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1)))) of role definition named def_n_lb
% 0.96/1.56 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) n_lb) (fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))))
% 0.96/1.56 Defined: n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1)))
% 0.96/1.56 FOF formula (<kernel.Constant object at 0x2aefbd942638>, <kernel.DependentProduct object at 0x2aefbd942e18>) of role type named typ_min
% 0.96/1.56 Using role type
% 0.96/1.56 Declaring min:((fofType->Prop)->(fofType->Prop))
% 0.96/1.56 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) min) (fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1)))) of role definition named def_min
% 0.96/1.56 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) min) (fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))))
% 0.96/1.56 Defined: min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1)))
% 0.96/1.56 FOF formula (forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0)))) of role axiom named satz27
% 0.96/1.56 A new axiom: (forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0))))
% 0.96/1.56 FOF formula (forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0)))) of role axiom named satz27a
% 0.96/1.56 A new axiom: (forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0))))
% 0.96/1.56 FOF formula (<kernel.Constant object at 0x2aefbd942d88>, <kernel.DependentProduct object at 0x2aefbd942cf8>) of role type named typ_d_428_prop1
% 0.96/1.56 Using role type
% 0.96/1.56 Declaring d_428_prop1:(fofType->(fofType->Prop))
% 0.96/1.56 FOF formula (((eq (fofType->(fofType->Prop))) d_428_prop1) (fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))) of role definition named def_d_428_prop1
% 0.96/1.56 A new definition: (((eq (fofType->(fofType->Prop))) d_428_prop1) (fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))))
% 0.96/1.56 Defined: d_428_prop1:=(fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))
% 0.96/1.56 FOF formula (<kernel.Constant object at 0x2aefbd942cf8>, <kernel.DependentProduct object at 0x2aefbd942950>) of role type named typ_d_428_prop2
% 0.96/1.57 Using role type
% 0.96/1.57 Declaring d_428_prop2:(fofType->(fofType->Prop))
% 0.96/1.57 FOF formula (((eq (fofType->(fofType->Prop))) d_428_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1)))) of role definition named def_d_428_prop2
% 0.96/1.57 A new definition: (((eq (fofType->(fofType->Prop))) d_428_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1))))
% 0.96/1.57 Defined: d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1)))
% 0.96/1.57 FOF formula (<kernel.Constant object at 0x2aefbd942950>, <kernel.DependentProduct object at 0x2aefbd942908>) of role type named typ_d_428_prop4
% 0.96/1.57 Using role type
% 0.96/1.57 Declaring d_428_prop4:(fofType->Prop)
% 0.96/1.57 FOF formula (((eq (fofType->Prop)) d_428_prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))) of role definition named def_d_428_prop4
% 0.96/1.57 A new definition: (((eq (fofType->Prop)) d_428_prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))))
% 0.96/1.57 Defined: d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))
% 0.96/1.57 FOF formula (<kernel.Constant object at 0x2aefbd942908>, <kernel.Single object at 0x2aefbd942950>) of role type named typ_d_428_id
% 0.96/1.57 Using role type
% 0.96/1.57 Declaring d_428_id:fofType
% 0.96/1.57 FOF formula (((eq fofType) d_428_id) ((d_Sigma nat) (fun (X0:fofType)=> X0))) of role definition named def_d_428_id
% 0.96/1.57 A new definition: (((eq fofType) d_428_id) ((d_Sigma nat) (fun (X0:fofType)=> X0)))
% 0.96/1.57 Defined: d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0))
% 0.96/1.57 FOF formula (<kernel.Constant object at 0x2aefbd942950>, <kernel.DependentProduct object at 0x2aefbd942440>) of role type named typ_d_428_g
% 0.96/1.57 Using role type
% 0.96/1.57 Declaring d_428_g:(fofType->fofType)
% 0.96/1.57 FOF formula (((eq (fofType->fofType)) d_428_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1))))) of role definition named def_d_428_g
% 0.96/1.57 A new definition: (((eq (fofType->fofType)) d_428_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))))
% 0.96/1.57 Defined: d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1))))
% 0.96/1.57 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))))))) of role axiom named satz28
% 0.96/1.57 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))))))
% 0.96/1.57 FOF formula (<kernel.Constant object at 0x2aefbd942560>, <kernel.DependentProduct object at 0x2aefbd942ea8>) of role type named typ_times
% 0.96/1.57 Using role type
% 0.96/1.57 Declaring times:(fofType->fofType)
% 0.96/1.57 FOF formula (((eq (fofType->fofType)) times) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))) of role definition named def_times
% 0.96/1.57 A new definition: (((eq (fofType->fofType)) times) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))))
% 0.96/1.57 Defined: times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))
% 0.96/1.57 FOF formula (<kernel.Constant object at 0x2aefbd942ea8>, <kernel.DependentProduct object at 0x2aefbd942638>) of role type named typ_n_ts
% 0.96/1.57 Using role type
% 0.96/1.57 Declaring n_ts:(fofType->(fofType->fofType))
% 0.96/1.57 FOF formula (((eq (fofType->(fofType->fofType))) n_ts) (fun (X0:fofType)=> (ap (times X0)))) of role definition named def_n_ts
% 0.96/1.57 A new definition: (((eq (fofType->(fofType->fofType))) n_ts) (fun (X0:fofType)=> (ap (times X0))))
% 0.96/1.57 Defined: n_ts:=(fun (X0:fofType)=> (ap (times X0)))
% 0.96/1.57 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0))) of role axiom named satz28a
% 0.96/1.57 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0)))
% 1.05/1.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0)))))) of role axiom named satz28b
% 1.05/1.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0))))))
% 1.05/1.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0))) of role axiom named satz28c
% 1.05/1.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0)))
% 1.05/1.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1)))))) of role axiom named satz28d
% 1.05/1.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1))))))
% 1.05/1.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1)))) of role axiom named satz28e
% 1.05/1.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1))))
% 1.05/1.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1))))))) of role axiom named satz28f
% 1.05/1.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1)))))))
% 1.05/1.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0)))) of role axiom named satz28g
% 1.05/1.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0))))
% 1.05/1.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1)))))) of role axiom named satz28h
% 1.05/1.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1))))))
% 1.05/1.59 FOF formula (<kernel.Constant object at 0x2aefbd942b00>, <kernel.DependentProduct object at 0x2aefbd95f290>) of role type named typ_d_429_prop1
% 1.05/1.59 Using role type
% 1.05/1.59 Declaring d_429_prop1:(fofType->(fofType->Prop))
% 1.05/1.59 FOF formula (((eq (fofType->(fofType->Prop))) d_429_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))) of role definition named def_d_429_prop1
% 1.05/1.59 A new definition: (((eq (fofType->(fofType->Prop))) d_429_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))))
% 1.05/1.59 Defined: d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))
% 1.05/1.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))))) of role axiom named satz29
% 1.05/1.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))))))
% 1.05/1.59 FOF formula (<kernel.Constant object at 0x2aefbd9427e8>, <kernel.DependentProduct object at 0x2aefbd95f2d8>) of role type named typ_d_430_prop1
% 1.05/1.59 Using role type
% 1.05/1.59 Declaring d_430_prop1:(fofType->(fofType->(fofType->Prop)))
% 1.05/1.59 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_430_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2))))) of role definition named def_d_430_prop1
% 1.05/1.59 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_430_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))))
% 1.09/1.62 Defined: d_430_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2))))
% 1.09/1.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2))))))))) of role axiom named satz30
% 1.09/1.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))))))))
% 1.09/1.62 FOF formula (<kernel.Constant object at 0x2aefbd942b00>, <kernel.DependentProduct object at 0x2aefbd95f440>) of role type named typ_d_431_prop1
% 1.09/1.62 Using role type
% 1.09/1.62 Declaring d_431_prop1:(fofType->(fofType->(fofType->Prop)))
% 1.09/1.62 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_431_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2))))) of role definition named def_d_431_prop1
% 1.09/1.62 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_431_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))))
% 1.09/1.62 Defined: d_431_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2))))
% 1.09/1.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2))))))))) of role axiom named satz31
% 1.09/1.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))))))))
% 1.09/1.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32a
% 1.09/1.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.09/1.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32b
% 1.09/1.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.09/1.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32c
% 1.09/1.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.09/1.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32d
% 1.09/1.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.09/1.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32e
% 1.09/1.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.09/1.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32f
% 1.09/1.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.09/1.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz32g
% 1.09/1.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.09/1.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1)))))))))))) of role axiom named satz32h
% 1.09/1.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 1.09/1.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz32j
% 1.09/1.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.09/1.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1)))))))))))) of role axiom named satz32k
% 1.09/1.67 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 1.09/1.67 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32l
% 1.09/1.67 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.09/1.67 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32m
% 1.09/1.67 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.09/1.67 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32n
% 1.09/1.67 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.09/1.67 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32o
% 1.09/1.67 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.09/1.67 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1)))))))) of role axiom named satz33a
% 1.09/1.67 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1))))))))
% 1.09/1.67 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1)))))))) of role axiom named satz33b
% 1.09/1.67 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1))))))))
% 1.09/1.67 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1)))))))) of role axiom named satz33c
% 1.09/1.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1))))))))
% 1.09/1.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz34
% 1.09/1.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.09/1.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz34a
% 1.09/1.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.09/1.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz35a
% 1.09/1.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.09/1.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz35b
% 1.09/1.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.09/1.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz35c
% 1.09/1.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.09/1.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz35d
% 1.18/1.72 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.18/1.72 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz36
% 1.18/1.72 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.18/1.72 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz36a
% 1.18/1.72 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.18/1.72 FOF formula (<kernel.Constant object at 0x2aefbd95f758>, <kernel.DependentProduct object at 0x2aefbd95f320>) of role type named typ_n_mn
% 1.18/1.72 Using role type
% 1.18/1.72 Declaring n_mn:(fofType->(fofType->fofType))
% 1.18/1.72 FOF formula (((eq (fofType->(fofType->fofType))) n_mn) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1)))) of role definition named def_n_mn
% 1.18/1.72 A new definition: (((eq (fofType->(fofType->fofType))) n_mn) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))))
% 1.18/1.72 Defined: n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1)))
% 1.18/1.72 FOF formula (<kernel.Constant object at 0x2aefbd95f320>, <kernel.DependentProduct object at 0x2aefbd95f2d8>) of role type named typ_d_1to
% 1.18/1.72 Using role type
% 1.18/1.72 Declaring d_1to:(fofType->fofType)
% 1.18/1.72 FOF formula (((eq (fofType->fofType)) d_1to) (fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0))))) of role definition named def_d_1to
% 1.18/1.72 A new definition: (((eq (fofType->fofType)) d_1to) (fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.18/1.72 Defined: d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.18/1.72 FOF formula (<kernel.Constant object at 0x2aefbd95f2d8>, <kernel.DependentProduct object at 0x2aefbd95f560>) of role type named typ_outn
% 1.18/1.72 Using role type
% 1.18/1.72 Declaring outn:(fofType->(fofType->fofType))
% 1.18/1.72 FOF formula (((eq (fofType->(fofType->fofType))) outn) (fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0))))) of role definition named def_outn
% 1.18/1.72 A new definition: (((eq (fofType->(fofType->fofType))) outn) (fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.18/1.72 Defined: outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.18/1.72 FOF formula (<kernel.Constant object at 0x2aefbd95f560>, <kernel.DependentProduct object at 0x2aefbd95fc68>) of role type named typ_inn
% 1.18/1.72 Using role type
% 1.18/1.72 Declaring inn:(fofType->(fofType->fofType))
% 1.18/1.73 FOF formula (((eq (fofType->(fofType->fofType))) inn) (fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0))))) of role definition named def_inn
% 1.18/1.73 A new definition: (((eq (fofType->(fofType->fofType))) inn) (fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.18/1.73 Defined: inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95fc68>, <kernel.Single object at 0x2aefbd95f560>) of role type named typ_n_1o
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring n_1o:fofType
% 1.18/1.73 FOF formula (((eq fofType) n_1o) ((outn n_1) n_1)) of role definition named def_n_1o
% 1.18/1.73 A new definition: (((eq fofType) n_1o) ((outn n_1) n_1))
% 1.18/1.73 Defined: n_1o:=((outn n_1) n_1)
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95f560>, <kernel.DependentProduct object at 0x2aefbd95fcb0>) of role type named typ_singlet_u0
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring singlet_u0:(fofType->fofType)
% 1.18/1.73 FOF formula (((eq (fofType->fofType)) singlet_u0) (inn n_1)) of role definition named def_singlet_u0
% 1.18/1.73 A new definition: (((eq (fofType->fofType)) singlet_u0) (inn n_1))
% 1.18/1.73 Defined: singlet_u0:=(inn n_1)
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95f2d8>, <kernel.Single object at 0x2aefbd95f560>) of role type named typ_n_2
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring n_2:fofType
% 1.18/1.73 FOF formula (((eq fofType) n_2) ((n_pl n_1) n_1)) of role definition named def_n_2
% 1.18/1.73 A new definition: (((eq fofType) n_2) ((n_pl n_1) n_1))
% 1.18/1.73 Defined: n_2:=((n_pl n_1) n_1)
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95f560>, <kernel.Single object at 0x2aefbd95f2d8>) of role type named typ_n_1t
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring n_1t:fofType
% 1.18/1.73 FOF formula (((eq fofType) n_1t) ((outn n_2) n_1)) of role definition named def_n_1t
% 1.18/1.73 A new definition: (((eq fofType) n_1t) ((outn n_2) n_1))
% 1.18/1.73 Defined: n_1t:=((outn n_2) n_1)
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95f2d8>, <kernel.Single object at 0x2aefbd95f560>) of role type named typ_n_2t
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring n_2t:fofType
% 1.18/1.73 FOF formula (((eq fofType) n_2t) ((outn n_2) n_2)) of role definition named def_n_2t
% 1.18/1.73 A new definition: (((eq fofType) n_2t) ((outn n_2) n_2))
% 1.18/1.73 Defined: n_2t:=((outn n_2) n_2)
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95f560>, <kernel.DependentProduct object at 0x2aefbd95fd40>) of role type named typ_pair_u0
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring pair_u0:(fofType->fofType)
% 1.18/1.73 FOF formula (((eq (fofType->fofType)) pair_u0) (inn n_2)) of role definition named def_pair_u0
% 1.18/1.73 A new definition: (((eq (fofType->fofType)) pair_u0) (inn n_2))
% 1.18/1.73 Defined: pair_u0:=(inn n_2)
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95fb90>, <kernel.DependentProduct object at 0x2aefb294c128>) of role type named typ_pair1type
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring pair1type:(fofType->fofType)
% 1.18/1.73 FOF formula (((eq (fofType->fofType)) pair1type) (fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0)))) of role definition named def_pair1type
% 1.18/1.73 A new definition: (((eq (fofType->fofType)) pair1type) (fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))))
% 1.18/1.73 Defined: pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0)))
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95f560>, <kernel.DependentProduct object at 0x2aefbd95f2d8>) of role type named typ_pair1
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring pair1:(fofType->(fofType->(fofType->fofType)))
% 1.18/1.73 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) pair1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2))))) of role definition named def_pair1
% 1.18/1.73 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) pair1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2)))))
% 1.18/1.73 Defined: pair1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2))))
% 1.18/1.73 FOF formula (<kernel.Constant object at 0x2aefbd95f3b0>, <kernel.DependentProduct object at 0x2aefb294c128>) of role type named typ_first1
% 1.18/1.73 Using role type
% 1.18/1.73 Declaring first1:(fofType->(fofType->fofType))
% 1.18/1.74 FOF formula (((eq (fofType->(fofType->fofType))) first1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t))) of role definition named def_first1
% 1.18/1.74 A new definition: (((eq (fofType->(fofType->fofType))) first1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)))
% 1.18/1.74 Defined: first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t))
% 1.18/1.74 FOF formula (<kernel.Constant object at 0x2aefbd95f3b0>, <kernel.DependentProduct object at 0x2aefb294c440>) of role type named typ_second1
% 1.18/1.74 Using role type
% 1.18/1.74 Declaring second1:(fofType->(fofType->fofType))
% 1.18/1.74 FOF formula (((eq (fofType->(fofType->fofType))) second1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t))) of role definition named def_second1
% 1.18/1.74 A new definition: (((eq (fofType->(fofType->fofType))) second1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)))
% 1.18/1.74 Defined: second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t))
% 1.18/1.74 FOF formula (<kernel.Constant object at 0x2aefbd95f3b0>, <kernel.DependentProduct object at 0x2aefb294c1b8>) of role type named typ_pair_q0
% 1.18/1.74 Using role type
% 1.18/1.74 Declaring pair_q0:(fofType->(fofType->fofType))
% 1.18/1.74 FOF formula (((eq (fofType->(fofType->fofType))) pair_q0) (fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1)))) of role definition named def_pair_q0
% 1.18/1.74 A new definition: (((eq (fofType->(fofType->fofType))) pair_q0) (fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))))
% 1.18/1.74 Defined: pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1)))
% 1.18/1.74 FOF formula (<kernel.Constant object at 0x2aefb294c1b8>, <kernel.DependentProduct object at 0x2aefb294c560>) of role type named typ_d_1out
% 1.18/1.74 Using role type
% 1.18/1.74 Declaring d_1out:(fofType->fofType)
% 1.18/1.74 FOF formula (((eq (fofType->fofType)) d_1out) (fun (X0:fofType)=> ((outn X0) n_1))) of role definition named def_d_1out
% 1.18/1.74 A new definition: (((eq (fofType->fofType)) d_1out) (fun (X0:fofType)=> ((outn X0) n_1)))
% 1.18/1.74 Defined: d_1out:=(fun (X0:fofType)=> ((outn X0) n_1))
% 1.18/1.74 FOF formula (<kernel.Constant object at 0x2aefb294c560>, <kernel.DependentProduct object at 0x2aefb294c050>) of role type named typ_xout
% 1.18/1.74 Using role type
% 1.18/1.74 Declaring xout:(fofType->fofType)
% 1.18/1.74 FOF formula (((eq (fofType->fofType)) xout) (fun (X0:fofType)=> ((outn X0) X0))) of role definition named def_xout
% 1.18/1.74 A new definition: (((eq (fofType->fofType)) xout) (fun (X0:fofType)=> ((outn X0) X0)))
% 1.18/1.74 Defined: xout:=(fun (X0:fofType)=> ((outn X0) X0))
% 1.18/1.74 FOF formula (<kernel.Constant object at 0x2aefb294c050>, <kernel.DependentProduct object at 0x2aefb294c2d8>) of role type named typ_left1to
% 1.18/1.74 Using role type
% 1.18/1.74 Declaring left1to:(fofType->(fofType->(fofType->fofType)))
% 1.18/1.74 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) left1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2)))) of role definition named def_left1to
% 1.18/1.74 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) left1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))))
% 1.18/1.74 Defined: left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2)))
% 1.18/1.74 FOF formula (<kernel.Constant object at 0x2aefb294c2d8>, <kernel.DependentProduct object at 0x2aefb294c7a0>) of role type named typ_right1to
% 1.18/1.74 Using role type
% 1.18/1.74 Declaring right1to:(fofType->(fofType->(fofType->fofType)))
% 1.18/1.74 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) right1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2))))) of role definition named def_right1to
% 1.18/1.74 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) right1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))))
% 1.18/1.74 Defined: right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2))))
% 1.18/1.74 FOF formula (<kernel.Constant object at 0x2aefb294c7a0>, <kernel.DependentProduct object at 0x2aefb294c8c0>) of role type named typ_left
% 1.18/1.74 Using role type
% 1.18/1.74 Declaring left:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.18/1.74 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4)))))) of role definition named def_left
% 1.18/1.75 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4))))))
% 1.18/1.75 Defined: left:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4)))))
% 1.18/1.75 FOF formula (<kernel.Constant object at 0x2aefb294c8c0>, <kernel.DependentProduct object at 0x2aefb294c248>) of role type named typ_right
% 1.18/1.75 Using role type
% 1.18/1.75 Declaring right:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.18/1.75 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) right) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4)))))) of role definition named def_right
% 1.18/1.75 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) right) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4))))))
% 1.18/1.75 Defined: right:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4)))))
% 1.18/1.75 FOF formula (<kernel.Constant object at 0x2aefb294c248>, <kernel.DependentProduct object at 0x2aefb294c4d0>) of role type named typ_left_f1
% 1.18/1.75 Using role type
% 1.18/1.75 Declaring left_f1:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.18/1.75 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1))) of role definition named def_left_f1
% 1.18/1.75 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)))
% 1.18/1.75 Defined: left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1))
% 1.18/1.75 FOF formula (<kernel.Constant object at 0x2aefb294c4d0>, <kernel.DependentProduct object at 0x2aefb294c0e0>) of role type named typ_left_f2
% 1.18/1.75 Using role type
% 1.18/1.75 Declaring left_f2:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.18/1.75 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f2) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3)))) of role definition named def_left_f2
% 1.18/1.75 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f2) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3))))
% 1.18/1.75 Defined: left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3)))
% 1.18/1.75 FOF formula (<kernel.Constant object at 0x2aefb294c0e0>, <kernel.Single object at 0x2aefb294c4d0>) of role type named typ_frac
% 1.18/1.75 Using role type
% 1.18/1.75 Declaring frac:fofType
% 1.18/1.75 FOF formula (((eq fofType) frac) (pair1type nat)) of role definition named def_frac
% 1.18/1.75 A new definition: (((eq fofType) frac) (pair1type nat))
% 1.18/1.75 Defined: frac:=(pair1type nat)
% 1.18/1.75 FOF formula (<kernel.Constant object at 0x2aefb294c950>, <kernel.DependentProduct object at 0x2aefb294c998>) of role type named typ_n_fr
% 1.18/1.75 Using role type
% 1.18/1.75 Declaring n_fr:(fofType->(fofType->fofType))
% 1.18/1.75 FOF formula (((eq (fofType->(fofType->fofType))) n_fr) (pair1 nat)) of role definition named def_n_fr
% 1.18/1.75 A new definition: (((eq (fofType->(fofType->fofType))) n_fr) (pair1 nat))
% 1.18/1.75 Defined: n_fr:=(pair1 nat)
% 1.18/1.75 FOF formula (<kernel.Constant object at 0x2aefb294c7a0>, <kernel.DependentProduct object at 0x2aefb294c440>) of role type named typ_num
% 1.18/1.75 Using role type
% 1.18/1.75 Declaring num:(fofType->fofType)
% 1.18/1.75 FOF formula (((eq (fofType->fofType)) num) (first1 nat)) of role definition named def_num
% 1.18/1.75 A new definition: (((eq (fofType->fofType)) num) (first1 nat))
% 1.18/1.75 Defined: num:=(first1 nat)
% 1.18/1.75 FOF formula (<kernel.Constant object at 0x2aefb294ca70>, <kernel.DependentProduct object at 0x2aefb294c248>) of role type named typ_den
% 1.18/1.75 Using role type
% 1.18/1.75 Declaring den:(fofType->fofType)
% 1.18/1.75 FOF formula (((eq (fofType->fofType)) den) (second1 nat)) of role definition named def_den
% 1.18/1.78 A new definition: (((eq (fofType->fofType)) den) (second1 nat))
% 1.18/1.78 Defined: den:=(second1 nat)
% 1.18/1.78 FOF formula (<kernel.Constant object at 0x2aefb294c4d0>, <kernel.DependentProduct object at 0x2aefb294c710>) of role type named typ_n_eq
% 1.18/1.78 Using role type
% 1.18/1.78 Declaring n_eq:(fofType->(fofType->Prop))
% 1.18/1.78 FOF formula (((eq (fofType->(fofType->Prop))) n_eq) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))) of role definition named def_n_eq
% 1.18/1.78 A new definition: (((eq (fofType->(fofType->Prop))) n_eq) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))
% 1.18/1.78 Defined: n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.18/1.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0))) of role axiom named satz37
% 1.18/1.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0)))
% 1.18/1.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0)))))) of role axiom named satz38
% 1.18/1.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0))))))
% 1.18/1.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2))))))))) of role axiom named satz39
% 1.18/1.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2)))))))))
% 1.18/1.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))))))) of role axiom named satz40
% 1.18/1.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1)))))))
% 1.18/1.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0))))) of role axiom named satz40a
% 1.18/1.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0)))))
% 1.18/1.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz40b
% 1.18/1.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.18/1.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1)))))))) of role axiom named satz40c
% 1.18/1.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1))))))))
% 1.18/1.78 FOF formula (<kernel.Constant object at 0x2aefb294ca70>, <kernel.DependentProduct object at 0x2aefb294cd40>) of role type named typ_moref
% 1.26/1.80 Using role type
% 1.26/1.80 Declaring moref:(fofType->(fofType->Prop))
% 1.26/1.80 FOF formula (((eq (fofType->(fofType->Prop))) moref) (fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))) of role definition named def_moref
% 1.26/1.80 A new definition: (((eq (fofType->(fofType->Prop))) moref) (fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))
% 1.26/1.80 Defined: moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.26/1.80 FOF formula (<kernel.Constant object at 0x2aefb294cd40>, <kernel.DependentProduct object at 0x2aefb294c248>) of role type named typ_lessf
% 1.26/1.80 Using role type
% 1.26/1.80 Declaring lessf:(fofType->(fofType->Prop))
% 1.26/1.80 FOF formula (((eq (fofType->(fofType->Prop))) lessf) (fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))) of role definition named def_lessf
% 1.26/1.80 A new definition: (((eq (fofType->(fofType->Prop))) lessf) (fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))
% 1.26/1.80 Defined: lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.26/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))) of role axiom named satz41
% 1.26/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 1.26/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))) of role axiom named satz41a
% 1.26/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 1.26/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))) of role axiom named satz41b
% 1.26/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 1.26/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0)))))) of role axiom named satz42
% 1.26/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0))))))
% 1.26/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0)))))) of role axiom named satz43
% 1.26/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0))))))
% 1.26/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3)))))))))))) of role axiom named satz44
% 1.26/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3))))))))))))
% 1.26/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3)))))))))))) of role axiom named satz45
% 1.26/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3))))))))))))
% 1.26/1.82 FOF formula (<kernel.Constant object at 0x2aefb294cfc8>, <kernel.DependentProduct object at 0x2aefb294ce60>) of role type named typ_moreq
% 1.26/1.82 Using role type
% 1.26/1.82 Declaring moreq:(fofType->(fofType->Prop))
% 1.26/1.82 FOF formula (((eq (fofType->(fofType->Prop))) moreq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1)))) of role definition named def_moreq
% 1.26/1.82 A new definition: (((eq (fofType->(fofType->Prop))) moreq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))))
% 1.26/1.82 Defined: moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1)))
% 1.26/1.82 FOF formula (<kernel.Constant object at 0x2aefb294c518>, <kernel.DependentProduct object at 0x2aefb294cb90>) of role type named typ_lesseq
% 1.26/1.82 Using role type
% 1.26/1.82 Declaring lesseq:(fofType->(fofType->Prop))
% 1.26/1.82 FOF formula (((eq (fofType->(fofType->Prop))) lesseq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1)))) of role definition named def_lesseq
% 1.26/1.82 A new definition: (((eq (fofType->(fofType->Prop))) lesseq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))))
% 1.26/1.82 Defined: lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1)))
% 1.26/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1))))))) of role axiom named satz41c
% 1.26/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1)))))))
% 1.26/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1))))))) of role axiom named satz41d
% 1.26/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1)))))))
% 1.26/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1)))))) of role axiom named satz41e
% 1.26/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1))))))
% 1.26/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1)))))) of role axiom named satz41f
% 1.26/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1))))))
% 1.26/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1))))))) of role axiom named satz41g
% 1.26/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1)))))))
% 1.26/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1))))))) of role axiom named satz41h
% 1.26/1.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1)))))))
% 1.26/1.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1)))))) of role axiom named satz41j
% 1.26/1.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1))))))
% 1.26/1.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1)))))) of role axiom named satz41k
% 1.26/1.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1))))))
% 1.26/1.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3)))))))))))) of role axiom named satz46
% 1.26/1.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3))))))))))))
% 1.26/1.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3)))))))))))) of role axiom named satz47
% 1.26/1.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3))))))))))))
% 1.26/1.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0)))))) of role axiom named satz48
% 1.26/1.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0))))))
% 1.26/1.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0)))))) of role axiom named satz49
% 1.26/1.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0))))))
% 1.26/1.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2))))))))) of role axiom named satz50
% 1.26/1.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 1.26/1.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2))))))))) of role axiom named satz51a
% 1.26/1.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 1.26/1.87 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2))))))))) of role axiom named satz51b
% 1.26/1.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2)))))))))
% 1.26/1.87 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2))))))))) of role axiom named satz51c
% 1.26/1.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2)))))))))
% 1.26/1.87 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2))))))))) of role axiom named satz51d
% 1.26/1.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2)))))))))
% 1.26/1.87 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lesseq X1) X2)->((lesseq X0) X2))))))))) of role axiom named satz52
% 1.26/1.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lesseq X1) X2)->((lesseq X0) X2)))))))))
% 1.26/1.87 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0))))) of role axiom named satz53
% 1.26/1.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0)))))
% 1.26/1.87 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0))))) of role axiom named satz54
% 1.26/1.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0)))))
% 1.26/1.87 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1))))))))) of role axiom named satz55
% 1.26/1.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1)))))))))
% 1.26/1.87 FOF formula (<kernel.Constant object at 0x2aefb2957320>, <kernel.DependentProduct object at 0x2aefb2957d40>) of role type named typ_n_pf
% 1.26/1.87 Using role type
% 1.26/1.87 Declaring n_pf:(fofType->(fofType->fofType))
% 1.26/1.87 FOF formula (((eq (fofType->(fofType->fofType))) n_pf) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1))))) of role definition named def_n_pf
% 1.36/1.89 A new definition: (((eq (fofType->(fofType->fofType))) n_pf) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1)))))
% 1.36/1.89 Defined: n_pf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1))))
% 1.36/1.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz56
% 1.36/1.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.36/1.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2)))))))) of role axiom named satz57
% 1.36/1.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2))))))))
% 1.36/1.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))))))))) of role axiom named satz57a
% 1.36/1.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2)))))))))
% 1.36/1.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_pf X0) X1)) ((n_pf X1) X0)))))) of role axiom named satz58
% 1.36/1.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_pf X0) X1)) ((n_pf X1) X0))))))
% 1.36/1.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2))))))))) of role axiom named satz59
% 1.36/1.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2)))))))))
% 1.36/1.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((moref ((n_pf X0) X1)) X0))))) of role axiom named satz60
% 1.36/1.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((moref ((n_pf X0) X1)) X0)))))
% 1.36/1.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((lessf X0) ((n_pf X0) X1)))))) of role axiom named satz60a
% 1.36/1.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((lessf X0) ((n_pf X0) X1))))))
% 1.39/1.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2))))))))) of role axiom named satz61
% 1.39/1.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 1.39/1.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))))))))) of role axiom named satz62b
% 1.39/1.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 1.39/1.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X0) X2)) ((n_pf X1) X2))))))))) of role axiom named satz62c
% 1.39/1.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 1.39/1.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1))))))))) of role axiom named satz62d
% 1.39/1.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 1.39/1.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))))))))) of role axiom named satz62e
% 1.39/1.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 1.39/1.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X2) X0)) ((n_pf X2) X1))))))))) of role axiom named satz62f
% 1.39/1.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 1.39/1.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz62g
% 1.39/1.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.39/1.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1)))))))))))) of role axiom named satz62h
% 1.39/1.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 1.39/1.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz62j
% 1.39/1.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.39/1.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1)))))))))))) of role axiom named satz62k
% 1.39/1.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 1.39/1.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1)))))))) of role axiom named satz63a
% 1.39/1.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1))))))))
% 1.39/1.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1)))))))) of role axiom named satz63b
% 1.39/1.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1))))))))
% 1.39/1.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1)))))))) of role axiom named satz63c
% 1.39/1.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1))))))))
% 1.39/1.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1)))))))) of role axiom named satz63d
% 1.39/1.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1))))))))
% 1.39/1.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1)))))))) of role axiom named satz63e
% 1.39/1.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1))))))))
% 1.39/1.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1)))))))) of role axiom named satz63f
% 1.39/1.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1))))))))
% 1.39/1.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz64
% 1.39/1.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.39/1.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz64a
% 1.39/1.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.39/1.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz65a
% 1.39/1.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.39/1.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz65b
% 1.47/2.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.47/2.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz65c
% 1.47/2.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.47/2.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz65d
% 1.47/2.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.47/2.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz66
% 1.47/2.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.47/2.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz66a
% 1.47/2.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.47/2.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3))))))))))) of role axiom named satz67b
% 1.47/2.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 1.47/2.02 FOF formula (<kernel.Constant object at 0x2aefb2957fc8>, <kernel.DependentProduct object at 0x2aefb29573f8>) of role type named typ_d_367_vo
% 1.47/2.02 Using role type
% 1.47/2.02 Declaring d_367_vo:(fofType->(fofType->fofType))
% 1.47/2.02 FOF formula (((eq (fofType->(fofType->fofType))) d_367_vo) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))) of role definition named def_d_367_vo
% 1.47/2.02 A new definition: (((eq (fofType->(fofType->fofType))) d_367_vo) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))))
% 1.47/2.02 Defined: d_367_vo:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))
% 1.47/2.02 FOF formula (<kernel.Constant object at 0x2aefb2957758>, <kernel.DependentProduct object at 0x2aefb295c170>) of role type named typ_d_367_w
% 1.47/2.02 Using role type
% 1.47/2.02 Declaring d_367_w:(fofType->(fofType->fofType))
% 1.47/2.02 FOF formula (((eq (fofType->(fofType->fofType))) d_367_w) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1))))) of role definition named def_d_367_w
% 1.47/2.02 A new definition: (((eq (fofType->(fofType->fofType))) d_367_w) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1)))))
% 1.47/2.02 Defined: d_367_w:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1))))
% 1.47/2.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0)))))))) of role axiom named satz67a
% 1.47/2.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0))))))))
% 1.47/2.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0)))))) of role axiom named k_satz67c
% 1.47/2.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0))))))
% 1.47/2.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1)))))))) of role axiom named satz67d
% 1.47/2.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1))))))))
% 1.47/2.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1)))))))))) of role axiom named satz67e
% 1.47/2.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1))))))))))
% 1.47/2.02 FOF formula (<kernel.Constant object at 0x2aefb2957758>, <kernel.DependentProduct object at 0x2aefb295c248>) of role type named typ_n_tf
% 1.47/2.02 Using role type
% 1.47/2.02 Declaring n_tf:(fofType->(fofType->fofType))
% 1.47/2.02 FOF formula (((eq (fofType->(fofType->fofType))) n_tf) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1))))) of role definition named def_n_tf
% 1.47/2.05 A new definition: (((eq (fofType->(fofType->fofType))) n_tf) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1)))))
% 1.47/2.05 Defined: n_tf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1))))
% 1.47/2.05 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz68
% 1.47/2.05 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.47/2.05 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_tf X0) X1)) ((n_tf X1) X0)))))) of role axiom named satz69
% 1.47/2.05 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_tf X0) X1)) ((n_tf X1) X0))))))
% 1.47/2.05 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2))))))))) of role axiom named satz70
% 1.47/2.05 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2)))))))))
% 1.47/2.05 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2))))))))) of role axiom named satz71
% 1.47/2.05 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2)))))))))
% 1.47/2.05 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2))))))))) of role axiom named satz72a
% 1.47/2.05 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 1.47/2.05 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))))))))) of role axiom named satz72b
% 1.47/2.05 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 1.47/2.05 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X0) X2)) ((n_tf X1) X2))))))))) of role axiom named satz72c
% 1.47/2.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 1.47/2.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1))))))))) of role axiom named satz72d
% 1.47/2.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 1.47/2.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))))))))) of role axiom named satz72e
% 1.47/2.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 1.47/2.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X2) X0)) ((n_tf X2) X1))))))))) of role axiom named satz72f
% 1.47/2.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 1.47/2.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz72g
% 1.47/2.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.47/2.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1)))))))))))) of role axiom named satz72h
% 1.47/2.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 1.47/2.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz72j
% 1.47/2.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1)))))))))))) of role axiom named satz72k
% 1.55/2.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 1.55/2.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1)))))))) of role axiom named satz73a
% 1.55/2.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1))))))))
% 1.55/2.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1)))))))) of role axiom named satz73b
% 1.55/2.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1))))))))
% 1.55/2.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1)))))))) of role axiom named satz73c
% 1.55/2.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1))))))))
% 1.55/2.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1)))))))) of role axiom named satz73d
% 1.55/2.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1))))))))
% 1.55/2.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1)))))))) of role axiom named satz73e
% 1.55/2.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1))))))))
% 1.55/2.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1)))))))) of role axiom named satz73f
% 1.55/2.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1))))))))
% 1.55/2.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz74
% 1.55/2.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz74a
% 1.55/2.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz75a
% 1.55/2.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz75b
% 1.55/2.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz75c
% 1.55/2.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz75d
% 1.55/2.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz76
% 1.55/2.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz76a
% 1.55/2.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.55/2.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3))))))))))) of role axiom named satz77b
% 1.55/2.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 1.55/2.15 FOF formula (<kernel.Constant object at 0x2aefb295c830>, <kernel.DependentProduct object at 0x2aefb295c320>) of role type named typ_d_477_v
% 1.55/2.15 Using role type
% 1.55/2.15 Declaring d_477_v:(fofType->(fofType->fofType))
% 1.55/2.15 FOF formula (((eq (fofType->(fofType->fofType))) d_477_v) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1))))) of role definition named def_d_477_v
% 1.55/2.15 A new definition: (((eq (fofType->(fofType->fofType))) d_477_v) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1)))))
% 1.55/2.15 Defined: d_477_v:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1))))
% 1.55/2.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0))))))) of role axiom named satz77a
% 1.55/2.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0)))))))
% 1.55/2.16 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM007^2.ax, trying next directory
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e0440>, <kernel.DependentProduct object at 0x2aefba1e0d40>) of role type named typ_inf
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring inf:(fofType->(fofType->Prop))
% 1.55/2.16 FOF formula (((eq (fofType->(fofType->Prop))) inf) (esti frac)) of role definition named def_inf
% 1.55/2.16 A new definition: (((eq (fofType->(fofType->Prop))) inf) (esti frac))
% 1.55/2.16 Defined: inf:=(esti frac)
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e0098>, <kernel.Single object at 0x2aefba1e0440>) of role type named typ_rat
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring rat:fofType
% 1.55/2.16 FOF formula (((eq fofType) rat) ((ect frac) n_eq)) of role definition named def_rat
% 1.55/2.16 A new definition: (((eq fofType) rat) ((ect frac) n_eq))
% 1.55/2.16 Defined: rat:=((ect frac) n_eq)
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e0440>, <kernel.DependentProduct object at 0x2aefba1e03f8>) of role type named typ_rt_is
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring rt_is:(fofType->(fofType->Prop))
% 1.55/2.16 FOF formula (((eq (fofType->(fofType->Prop))) rt_is) (e_is rat)) of role definition named def_rt_is
% 1.55/2.16 A new definition: (((eq (fofType->(fofType->Prop))) rt_is) (e_is rat))
% 1.55/2.16 Defined: rt_is:=(e_is rat)
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e09e0>, <kernel.DependentProduct object at 0x2aefba1e0950>) of role type named typ_rt_nis
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring rt_nis:(fofType->(fofType->Prop))
% 1.55/2.16 FOF formula (((eq (fofType->(fofType->Prop))) rt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1)))) of role definition named def_rt_nis
% 1.55/2.16 A new definition: (((eq (fofType->(fofType->Prop))) rt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1))))
% 1.55/2.16 Defined: rt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1)))
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e0950>, <kernel.DependentProduct object at 0x2aefba1e0488>) of role type named typ_rt_some
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring rt_some:((fofType->Prop)->Prop)
% 1.55/2.16 FOF formula (((eq ((fofType->Prop)->Prop)) rt_some) (l_some rat)) of role definition named def_rt_some
% 1.55/2.16 A new definition: (((eq ((fofType->Prop)->Prop)) rt_some) (l_some rat))
% 1.55/2.16 Defined: rt_some:=(l_some rat)
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e0c20>, <kernel.DependentProduct object at 0x2aefba1e0488>) of role type named typ_rt_all
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring rt_all:((fofType->Prop)->Prop)
% 1.55/2.16 FOF formula (((eq ((fofType->Prop)->Prop)) rt_all) (all rat)) of role definition named def_rt_all
% 1.55/2.16 A new definition: (((eq ((fofType->Prop)->Prop)) rt_all) (all rat))
% 1.55/2.16 Defined: rt_all:=(all rat)
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e0950>, <kernel.DependentProduct object at 0x2aefba1e0440>) of role type named typ_rt_one
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring rt_one:((fofType->Prop)->Prop)
% 1.55/2.16 FOF formula (((eq ((fofType->Prop)->Prop)) rt_one) (one rat)) of role definition named def_rt_one
% 1.55/2.16 A new definition: (((eq ((fofType->Prop)->Prop)) rt_one) (one rat))
% 1.55/2.16 Defined: rt_one:=(one rat)
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e05a8>, <kernel.DependentProduct object at 0x2aefba1dddd0>) of role type named typ_rt_in
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring rt_in:(fofType->(fofType->Prop))
% 1.55/2.16 FOF formula (((eq (fofType->(fofType->Prop))) rt_in) (esti rat)) of role definition named def_rt_in
% 1.55/2.16 A new definition: (((eq (fofType->(fofType->Prop))) rt_in) (esti rat))
% 1.55/2.16 Defined: rt_in:=(esti rat)
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e0440>, <kernel.DependentProduct object at 0x2aefba1dd560>) of role type named typ_ratof
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring ratof:(fofType->fofType)
% 1.55/2.16 FOF formula (((eq (fofType->fofType)) ratof) ((ectelt frac) n_eq)) of role definition named def_ratof
% 1.55/2.16 A new definition: (((eq (fofType->fofType)) ratof) ((ectelt frac) n_eq))
% 1.55/2.16 Defined: ratof:=((ectelt frac) n_eq)
% 1.55/2.16 FOF formula (<kernel.Constant object at 0x2aefba1e0440>, <kernel.DependentProduct object at 0x2aefba1dd638>) of role type named typ_class
% 1.55/2.16 Using role type
% 1.55/2.16 Declaring class:(fofType->fofType)
% 1.55/2.16 FOF formula (((eq (fofType->fofType)) class) ((ecect frac) n_eq)) of role definition named def_class
% 1.55/2.16 A new definition: (((eq (fofType->fofType)) class) ((ecect frac) n_eq))
% 1.64/2.18 Defined: class:=((ecect frac) n_eq)
% 1.64/2.18 FOF formula (<kernel.Constant object at 0x2aefba1e0950>, <kernel.DependentProduct object at 0x2aefba1ddf80>) of role type named typ_fixf
% 1.64/2.18 Using role type
% 1.64/2.18 Declaring fixf:(fofType->(fofType->Prop))
% 1.64/2.18 FOF formula (((eq (fofType->(fofType->Prop))) fixf) ((fixfu2 frac) n_eq)) of role definition named def_fixf
% 1.64/2.18 A new definition: (((eq (fofType->(fofType->Prop))) fixf) ((fixfu2 frac) n_eq))
% 1.64/2.18 Defined: fixf:=((fixfu2 frac) n_eq)
% 1.64/2.18 FOF formula (<kernel.Constant object at 0x2aefba1ddf80>, <kernel.DependentProduct object at 0x2aefba1dd7e8>) of role type named typ_indrat
% 1.64/2.18 Using role type
% 1.64/2.18 Declaring indrat:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.64/2.18 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) indrat) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1))) of role definition named def_indrat
% 1.64/2.18 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) indrat) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1)))
% 1.64/2.18 Defined: indrat:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1))
% 1.64/2.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0))) of role axiom named satz78
% 1.64/2.18 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0)))
% 1.64/2.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0)))))) of role axiom named satz79
% 1.64/2.18 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0))))))
% 1.64/2.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2))))))))) of role axiom named satz80
% 1.64/2.18 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2)))))))))
% 1.64/2.18 FOF formula (<kernel.Constant object at 0x2aefba1dd5f0>, <kernel.DependentProduct object at 0x2aefba1dd7a0>) of role type named typ_rt_more
% 1.64/2.18 Using role type
% 1.64/2.18 Declaring rt_more:(fofType->(fofType->Prop))
% 1.64/2.18 FOF formula (((eq (fofType->(fofType->Prop))) rt_more) (fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3)))))))) of role definition named def_rt_more
% 1.64/2.18 A new definition: (((eq (fofType->(fofType->Prop))) rt_more) (fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))))))
% 1.64/2.18 Defined: rt_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3)))))))
% 1.64/2.18 FOF formula (<kernel.Constant object at 0x2aefba1dd7a0>, <kernel.DependentProduct object at 0x2aefba1dd200>) of role type named typ_propm
% 1.64/2.18 Using role type
% 1.64/2.18 Declaring propm:(fofType->(fofType->(fofType->(fofType->Prop))))
% 1.64/2.18 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) propm) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3)))) of role definition named def_propm
% 1.64/2.18 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) propm) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))
% 1.64/2.18 Defined: propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3)))
% 1.66/2.20 FOF formula (<kernel.Constant object at 0x2aefba1dd200>, <kernel.DependentProduct object at 0x2aefba1dd710>) of role type named typ_rt_less
% 1.66/2.20 Using role type
% 1.66/2.20 Declaring rt_less:(fofType->(fofType->Prop))
% 1.66/2.20 FOF formula (((eq (fofType->(fofType->Prop))) rt_less) (fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3)))))))) of role definition named def_rt_less
% 1.66/2.20 A new definition: (((eq (fofType->(fofType->Prop))) rt_less) (fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))))))
% 1.66/2.20 Defined: rt_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3)))))))
% 1.66/2.20 FOF formula (<kernel.Constant object at 0x2aefba1dd710>, <kernel.DependentProduct object at 0x2aefba1dd3f8>) of role type named typ_propl
% 1.66/2.20 Using role type
% 1.66/2.20 Declaring propl:(fofType->(fofType->(fofType->(fofType->Prop))))
% 1.66/2.20 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) propl) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3)))) of role definition named def_propl
% 1.66/2.20 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) propl) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))
% 1.66/2.20 Defined: propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3)))
% 1.66/2.20 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))) of role axiom named satz81
% 1.66/2.20 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 1.66/2.20 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))) of role axiom named satz81a
% 1.66/2.20 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 1.66/2.20 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))) of role axiom named satz81b
% 1.66/2.20 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 1.66/2.20 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0)))))) of role axiom named satz82
% 1.66/2.20 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0))))))
% 1.66/2.20 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0)))))) of role axiom named satz83
% 1.66/2.20 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0))))))
% 1.66/2.20 FOF formula (<kernel.Constant object at 0x2aefba1dd3f8>, <kernel.DependentProduct object at 0x2aefba2c0128>) of role type named typ_rt_moreis
% 1.66/2.20 Using role type
% 1.66/2.20 Declaring rt_moreis:(fofType->(fofType->Prop))
% 1.69/2.22 FOF formula (((eq (fofType->(fofType->Prop))) rt_moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1)))) of role definition named def_rt_moreis
% 1.69/2.22 A new definition: (((eq (fofType->(fofType->Prop))) rt_moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1))))
% 1.69/2.22 Defined: rt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1)))
% 1.69/2.22 FOF formula (<kernel.Constant object at 0x2aefba1dd368>, <kernel.DependentProduct object at 0x2aefba2c0518>) of role type named typ_rt_lessis
% 1.69/2.22 Using role type
% 1.69/2.22 Declaring rt_lessis:(fofType->(fofType->Prop))
% 1.69/2.22 FOF formula (((eq (fofType->(fofType->Prop))) rt_lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1)))) of role definition named def_rt_lessis
% 1.69/2.22 A new definition: (((eq (fofType->(fofType->Prop))) rt_lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1))))
% 1.69/2.22 Defined: rt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1)))
% 1.69/2.22 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1))))))) of role axiom named satz81c
% 1.69/2.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1)))))))
% 1.69/2.22 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1))))))) of role axiom named satz81d
% 1.69/2.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1)))))))
% 1.69/2.22 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1)))))) of role axiom named satz81e
% 1.69/2.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1))))))
% 1.69/2.22 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1)))))) of role axiom named satz81f
% 1.69/2.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1))))))
% 1.69/2.22 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1))))))) of role axiom named satz81g
% 1.69/2.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1)))))))
% 1.69/2.22 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(d_not ((rt_moreis X0) X1))))))) of role axiom named satz81h
% 1.69/2.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(d_not ((rt_moreis X0) X1)))))))
% 1.69/2.22 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_moreis X0) X1))->((rt_less X0) X1)))))) of role axiom named satz81j
% 1.69/2.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_moreis X0) X1))->((rt_less X0) X1))))))
% 1.69/2.22 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_lessis X0) X1))->((rt_more X0) X1)))))) of role axiom named satz81k
% 1.69/2.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_lessis X0) X1))->((rt_more X0) X1))))))
% 1.69/2.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->((rt_lessis X1) X0)))))) of role axiom named satz84
% 1.69/2.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->((rt_lessis X1) X0))))))
% 1.69/2.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->((rt_moreis X1) X0)))))) of role axiom named satz85
% 1.69/2.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->((rt_moreis X1) X0))))))
% 1.69/2.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2))))))))) of role axiom named satz86
% 1.69/2.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 1.69/2.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2))))))))) of role axiom named satz87a
% 1.69/2.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 1.69/2.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_lessis X1) X2)->((rt_less X0) X2))))))))) of role axiom named satz87b
% 1.69/2.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_lessis X1) X2)->((rt_less X0) X2)))))))))
% 1.69/2.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_moreis X0) X1)->(((rt_more X1) X2)->((rt_more X0) X2))))))))) of role axiom named satz87c
% 1.69/2.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_moreis X0) X1)->(((rt_more X1) X2)->((rt_more X0) X2)))))))))
% 1.69/2.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_moreis X1) X2)->((rt_more X0) X2))))))))) of role axiom named satz87d
% 1.69/2.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_moreis X1) X2)->((rt_more X0) X2)))))))))
% 1.69/2.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X1) X2)->((rt_lessis X0) X2))))))))) of role axiom named satz88
% 1.69/2.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X1) X2)->((rt_lessis X0) X2)))))))))
% 1.69/2.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_more X1) X0))))) of role axiom named satz89
% 1.69/2.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_more X1) X0)))))
% 1.69/2.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_less X1) X0))))) of role axiom named satz90
% 1.69/2.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_less X1) X0)))))
% 1.69/2.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rt_less X0) X2)) ((rt_less X2) X1))))))))) of role axiom named satz91
% 1.69/2.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rt_less X0) X2)) ((rt_less X2) X1)))))))))
% 1.69/2.26 FOF formula (<kernel.Constant object at 0x2aefbac97680>, <kernel.Single object at 0x2aefbac97b90>) of role type named typ_plusfrt
% 1.69/2.26 Using role type
% 1.69/2.26 Declaring plusfrt:fofType
% 1.69/2.26 FOF formula (((eq fofType) plusfrt) ((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_pf X0) X1))))))) of role definition named def_plusfrt
% 1.69/2.26 A new definition: (((eq fofType) plusfrt) ((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_pf X0) X1)))))))
% 1.69/2.26 Defined: plusfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_pf X0) X1))))))
% 1.69/2.26 FOF formula (<kernel.Constant object at 0x2aefbac97b90>, <kernel.DependentProduct object at 0x2aefbac97f38>) of role type named typ_rt_pl
% 1.69/2.26 Using role type
% 1.69/2.26 Declaring rt_pl:(fofType->(fofType->fofType))
% 1.69/2.26 FOF formula (((eq (fofType->(fofType->fofType))) rt_pl) (fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) plusfrt))) of role definition named def_rt_pl
% 1.69/2.26 A new definition: (((eq (fofType->(fofType->fofType))) rt_pl) (fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) plusfrt)))
% 1.69/2.26 Defined: rt_pl:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) plusfrt))
% 1.69/2.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_pl X0) X1)) ((rt_pl X1) X0)))))) of role axiom named satz92
% 1.69/2.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_pl X0) X1)) ((rt_pl X1) X0))))))
% 1.69/2.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_pl ((rt_pl X0) X1)) X2)) ((rt_pl X0) ((rt_pl X1) X2))))))))) of role axiom named satz93
% 1.69/2.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_pl ((rt_pl X0) X1)) X2)) ((rt_pl X0) ((rt_pl X1) X2)))))))))
% 1.69/2.26 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_more ((rt_pl X0) X1)) X0))))) of role axiom named satz94
% 1.69/2.26 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_more ((rt_pl X0) X1)) X0)))))
% 1.69/2.29 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_less X0) ((rt_pl X0) X1)))))) of role axiom named satz94a
% 1.69/2.29 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_less X0) ((rt_pl X0) X1))))))
% 1.69/2.29 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))))))))) of role axiom named satz95
% 1.69/2.29 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 1.69/2.29 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))))))))) of role axiom named satz96b
% 1.69/2.29 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 1.69/2.29 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))))))))) of role axiom named satz96c
% 1.69/2.29 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 1.69/2.29 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X2) X0)) ((rt_pl X2) X1))))))))) of role axiom named satz96d
% 1.69/2.29 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 1.69/2.29 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X2) X0)) ((rt_pl X2) X1))))))))) of role axiom named satz96e
% 1.69/2.29 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 1.69/2.29 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X2) X0)) ((rt_pl X2) X1))))))))) of role axiom named satz96f
% 1.69/2.29 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 1.69/2.29 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_more X0) X1)))))))) of role axiom named satz97a
% 1.77/2.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_more X0) X1))))))))
% 1.77/2.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_is X0) X1)))))))) of role axiom named satz97b
% 1.77/2.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_is X0) X1))))))))
% 1.77/2.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_less X0) X1)))))))) of role axiom named satz97c
% 1.77/2.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_less X0) X1))))))))
% 1.77/2.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))) of role axiom named satz98
% 1.77/2.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 1.77/2.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))) of role axiom named satz98a
% 1.77/2.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 1.77/2.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))) of role axiom named satz99a
% 1.77/2.32 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 1.77/2.32 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))) of role axiom named satz99b
% 1.77/2.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 1.77/2.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))) of role axiom named satz99c
% 1.77/2.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 1.77/2.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))) of role axiom named satz99d
% 1.77/2.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 1.77/2.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))) of role axiom named satz100
% 1.77/2.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 1.77/2.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))) of role axiom named satz100a
% 1.77/2.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 1.77/2.34 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_some (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))))))) of role axiom named satz101a
% 1.77/2.34 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_some (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 1.77/2.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_pl X1) X2)) X0)->(((rt_is ((rt_pl X1) X3)) X0)->((rt_is X2) X3))))))))))) of role axiom named satz101b
% 1.77/2.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_pl X1) X2)) X0)->(((rt_is ((rt_pl X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 1.77/2.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_one (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))))))) of role axiom named satz101
% 1.77/2.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_one (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 1.77/2.36 FOF formula (<kernel.Constant object at 0x2aefbac97320>, <kernel.DependentProduct object at 0x2aefbac97128>) of role type named typ_rt_mn
% 1.77/2.36 Using role type
% 1.77/2.36 Declaring rt_mn:(fofType->(fofType->fofType))
% 1.77/2.36 FOF formula (((eq (fofType->(fofType->fofType))) rt_mn) (fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))) of role definition named def_rt_mn
% 1.77/2.36 A new definition: (((eq (fofType->(fofType->fofType))) rt_mn) (fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))))
% 1.77/2.36 Defined: rt_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))
% 1.77/2.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl X1) ((rt_mn X0) X1))) X0)))))) of role axiom named satz101c
% 1.77/2.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl X1) ((rt_mn X0) X1))) X0))))))
% 1.77/2.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl X1) ((rt_mn X0) X1)))))))) of role axiom named satz101d
% 1.77/2.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl X1) ((rt_mn X0) X1))))))))
% 1.77/2.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl ((rt_mn X0) X1)) X1)) X0)))))) of role axiom named satz101e
% 1.77/2.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl ((rt_mn X0) X1)) X1)) X0))))))
% 1.77/2.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl ((rt_mn X0) X1)) X1))))))) of role axiom named satz101f
% 1.77/2.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl ((rt_mn X0) X1)) X1)))))))
% 1.77/2.36 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_is ((rt_pl X1) X2)) X0)->((rt_is X2) ((rt_mn X0) X1)))))))))) of role axiom named satz101g
% 1.77/2.36 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_is ((rt_pl X1) X2)) X0)->((rt_is X2) ((rt_mn X0) X1))))))))))
% 1.86/2.39 FOF formula (<kernel.Constant object at 0x2aefbac975a8>, <kernel.Single object at 0x2aefbac97320>) of role type named typ_timesfrt
% 1.86/2.39 Using role type
% 1.86/2.39 Declaring timesfrt:fofType
% 1.86/2.39 FOF formula (((eq fofType) timesfrt) ((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_tf X0) X1))))))) of role definition named def_timesfrt
% 1.86/2.39 A new definition: (((eq fofType) timesfrt) ((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_tf X0) X1)))))))
% 1.86/2.39 Defined: timesfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_tf X0) X1))))))
% 1.86/2.39 FOF formula (<kernel.Constant object at 0x2aefbac971b8>, <kernel.DependentProduct object at 0x2aefbd942128>) of role type named typ_rt_ts
% 1.86/2.39 Using role type
% 1.86/2.39 Declaring rt_ts:(fofType->(fofType->fofType))
% 1.86/2.39 FOF formula (((eq (fofType->(fofType->fofType))) rt_ts) (fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) timesfrt))) of role definition named def_rt_ts
% 1.86/2.39 A new definition: (((eq (fofType->(fofType->fofType))) rt_ts) (fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) timesfrt)))
% 1.86/2.39 Defined: rt_ts:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) timesfrt))
% 1.86/2.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X0) X1)) ((rt_ts X1) X0)))))) of role axiom named satz102
% 1.86/2.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X0) X1)) ((rt_ts X1) X0))))))
% 1.86/2.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts ((rt_ts X0) X1)) X2)) ((rt_ts X0) ((rt_ts X1) X2))))))))) of role axiom named satz103
% 1.86/2.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts ((rt_ts X0) X1)) X2)) ((rt_ts X0) ((rt_ts X1) X2)))))))))
% 1.86/2.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts X0) ((rt_pl X1) X2))) ((rt_pl ((rt_ts X0) X1)) ((rt_ts X0) X2))))))))) of role axiom named satz104
% 1.86/2.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts X0) ((rt_pl X1) X2))) ((rt_pl ((rt_ts X0) X1)) ((rt_ts X0) X2)))))))))
% 1.86/2.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))))))))) of role axiom named satz105a
% 1.86/2.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 1.86/2.39 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))))))))) of role axiom named satz105b
% 1.86/2.39 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 1.86/2.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))))))))) of role axiom named satz105c
% 1.86/2.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 1.86/2.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X2) X0)) ((rt_ts X2) X1))))))))) of role axiom named satz105d
% 1.86/2.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 1.86/2.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X2) X0)) ((rt_ts X2) X1))))))))) of role axiom named satz105e
% 1.86/2.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 1.86/2.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X2) X0)) ((rt_ts X2) X1))))))))) of role axiom named satz105f
% 1.86/2.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 1.86/2.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_more X0) X1)))))))) of role axiom named satz106a
% 1.86/2.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_more X0) X1))))))))
% 1.86/2.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_is X0) X1)))))))) of role axiom named satz106b
% 1.86/2.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_is X0) X1))))))))
% 1.86/2.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_less X0) X1)))))))) of role axiom named satz106c
% 1.86/2.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_less X0) X1))))))))
% 1.86/2.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))) of role axiom named satz107
% 1.86/2.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 1.86/2.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))) of role axiom named satz107a
% 1.86/2.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 1.86/2.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))) of role axiom named satz108a
% 1.86/2.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 1.86/2.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))) of role axiom named satz108b
% 1.86/2.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 1.86/2.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))) of role axiom named satz108c
% 1.86/2.44 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 1.86/2.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))) of role axiom named satz108d
% 1.86/2.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 1.86/2.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))) of role axiom named satz109
% 1.86/2.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 1.86/2.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))) of role axiom named satz109a
% 1.86/2.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 1.86/2.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0))))))) of role axiom named satz110a
% 1.86/2.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 1.86/2.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->(((rt_is ((rt_ts X1) X3)) X0)->((rt_is X2) X3))))))))))) of role axiom named satz110b
% 1.86/2.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->(((rt_is ((rt_ts X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 1.86/2.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_one (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0))))))) of role axiom named satz110
% 1.86/2.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_one (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 1.86/2.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))->((d_29_ii X0) X1)))))) of role axiom named satz111a
% 1.86/2.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))->((d_29_ii X0) X1))))))
% 1.95/2.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))->((n_is X0) X1)))))) of role axiom named satz111b
% 1.95/2.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))->((n_is X0) X1))))))
% 1.95/2.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))->((iii X0) X1)))))) of role axiom named satz111c
% 1.95/2.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))->((iii X0) X1))))))
% 1.95/2.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))))))) of role axiom named satz111d
% 1.95/2.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((moref ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 1.95/2.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is X0) X1)->((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))))))) of role axiom named satz111e
% 1.95/2.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is X0) X1)->((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 1.95/2.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))))))) of role axiom named satz111f
% 1.95/2.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 1.95/2.48 FOF formula (<kernel.Constant object at 0x2aefbd942e18>, <kernel.DependentProduct object at 0x2aefbd942ef0>) of role type named typ_natprop
% 1.95/2.48 Using role type
% 1.95/2.48 Declaring natprop:(fofType->(fofType->Prop))
% 1.95/2.48 FOF formula (((eq (fofType->(fofType->Prop))) natprop) (fun (X0:fofType) (X1:fofType)=> ((inf ((n_fr X1) n_1)) (class X0)))) of role definition named def_natprop
% 1.95/2.48 A new definition: (((eq (fofType->(fofType->Prop))) natprop) (fun (X0:fofType) (X1:fofType)=> ((inf ((n_fr X1) n_1)) (class X0))))
% 1.95/2.48 Defined: natprop:=(fun (X0:fofType) (X1:fofType)=> ((inf ((n_fr X1) n_1)) (class X0)))
% 1.95/2.48 FOF formula (<kernel.Constant object at 0x2aefbd942ef0>, <kernel.DependentProduct object at 0x2aefbd942dd0>) of role type named typ_natrt
% 1.95/2.48 Using role type
% 1.95/2.48 Declaring natrt:(fofType->Prop)
% 1.95/2.48 FOF formula (((eq (fofType->Prop)) natrt) (fun (X0:fofType)=> (n_some (natprop X0)))) of role definition named def_natrt
% 1.95/2.48 A new definition: (((eq (fofType->Prop)) natrt) (fun (X0:fofType)=> (n_some (natprop X0))))
% 1.95/2.48 Defined: natrt:=(fun (X0:fofType)=> (n_some (natprop X0)))
% 1.95/2.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->(n_one (natprop X0))))) of role axiom named satz111g
% 1.95/2.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->(n_one (natprop X0)))))
% 1.95/2.48 FOF formula (<kernel.Constant object at 0x2aefbd942cb0>, <kernel.DependentProduct object at 0x2aefbd942e60>) of role type named typ_nofrt
% 1.95/2.48 Using role type
% 1.95/2.48 Declaring nofrt:(fofType->fofType)
% 1.95/2.48 FOF formula (((eq (fofType->fofType)) nofrt) (fun (X0:fofType)=> ((ind nat) (natprop X0)))) of role definition named def_nofrt
% 1.95/2.48 A new definition: (((eq (fofType->fofType)) nofrt) (fun (X0:fofType)=> ((ind nat) (natprop X0))))
% 1.95/2.48 Defined: nofrt:=(fun (X0:fofType)=> ((ind nat) (natprop X0)))
% 1.95/2.48 FOF formula (<kernel.Constant object at 0x2aefbd942e60>, <kernel.DependentProduct object at 0x2aefbd942ab8>) of role type named typ_rtofn
% 1.97/2.51 Using role type
% 1.97/2.51 Declaring rtofn:(fofType->fofType)
% 1.97/2.51 FOF formula (((eq (fofType->fofType)) rtofn) (fun (X0:fofType)=> (ratof ((n_fr X0) n_1)))) of role definition named def_rtofn
% 1.97/2.51 A new definition: (((eq (fofType->fofType)) rtofn) (fun (X0:fofType)=> (ratof ((n_fr X0) n_1))))
% 1.97/2.51 Defined: rtofn:=(fun (X0:fofType)=> (ratof ((n_fr X0) n_1)))
% 1.97/2.51 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_pf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_pl X0) X1)) n_1)))))) of role axiom named satz112a
% 1.97/2.51 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_pf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_pl X0) X1)) n_1))))))
% 1.97/2.51 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_tf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_ts X0) X1)) n_1)))))) of role axiom named satz112b
% 1.97/2.51 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_tf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_ts X0) X1)) n_1))))))
% 1.97/2.51 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_pl (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_pl X0) X1))))))))) of role axiom named satz112c
% 1.97/2.51 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_pl (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_pl X0) X1)))))))))
% 1.97/2.51 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_pl X0) X1)))))))) of role axiom named satz112d
% 1.97/2.51 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_pl X0) X1))))))))
% 1.97/2.51 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_ts (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_ts X0) X1))))))))) of role axiom named satz112e
% 1.97/2.51 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_ts (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_ts X0) X1)))))))))
% 1.97/2.51 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_ts X0) X1)))))))) of role axiom named satz112f
% 1.97/2.51 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_ts X0) X1))))))))
% 1.97/2.51 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(((rt_more X0) X1)->(natrt ((rt_mn X0) X1))))))))) of role axiom named satz112g
% 1.97/2.51 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(((rt_more X0) X1)->(natrt ((rt_mn X0) X1)))))))))
% 1.97/2.51 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_pl (rtofn X0)) (rtofn X1))) (rtofn ((n_pl X0) X1))))))) of role axiom named satz112h
% 1.97/2.51 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_pl (rtofn X0)) (rtofn X1))) (rtofn ((n_pl X0) X1)))))))
% 1.98/2.52 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X0)) (rtofn X1))) (rtofn ((n_ts X0) X1))))))) of role axiom named satz112j
% 1.98/2.52 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X0)) (rtofn X1))) (rtofn ((n_ts X0) X1)))))))
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd942ab8>, <kernel.Single object at 0x2aefbd942e60>) of role type named typ_natt
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring natt:fofType
% 1.98/2.52 FOF formula (((eq fofType) natt) ((d_Sep rat) natrt)) of role definition named def_natt
% 1.98/2.52 A new definition: (((eq fofType) natt) ((d_Sep rat) natrt))
% 1.98/2.52 Defined: natt:=((d_Sep rat) natrt)
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd942e60>, <kernel.DependentProduct object at 0x2aefbd942290>) of role type named typ_ntofrt
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring ntofrt:(fofType->fofType)
% 1.98/2.52 FOF formula (((eq (fofType->fofType)) ntofrt) ((out rat) natrt)) of role definition named def_ntofrt
% 1.98/2.52 A new definition: (((eq (fofType->fofType)) ntofrt) ((out rat) natrt))
% 1.98/2.52 Defined: ntofrt:=((out rat) natrt)
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd942a28>, <kernel.DependentProduct object at 0x2aefbd942290>) of role type named typ_nt_is
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring nt_is:(fofType->(fofType->Prop))
% 1.98/2.52 FOF formula (((eq (fofType->(fofType->Prop))) nt_is) (e_is natt)) of role definition named def_nt_is
% 1.98/2.52 A new definition: (((eq (fofType->(fofType->Prop))) nt_is) (e_is natt))
% 1.98/2.52 Defined: nt_is:=(e_is natt)
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd942cf8>, <kernel.DependentProduct object at 0x2aefbd9463f8>) of role type named typ_nt_nis
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring nt_nis:(fofType->(fofType->Prop))
% 1.98/2.52 FOF formula (((eq (fofType->(fofType->Prop))) nt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((nt_is X0) X1)))) of role definition named def_nt_nis
% 1.98/2.52 A new definition: (((eq (fofType->(fofType->Prop))) nt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((nt_is X0) X1))))
% 1.98/2.52 Defined: nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((nt_is X0) X1)))
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd9429e0>, <kernel.DependentProduct object at 0x2aefbd9460e0>) of role type named typ_nt_all
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring nt_all:((fofType->Prop)->Prop)
% 1.98/2.52 FOF formula (((eq ((fofType->Prop)->Prop)) nt_all) (all natt)) of role definition named def_nt_all
% 1.98/2.52 A new definition: (((eq ((fofType->Prop)->Prop)) nt_all) (all natt))
% 1.98/2.52 Defined: nt_all:=(all natt)
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd9429e0>, <kernel.DependentProduct object at 0x2aefbd9464d0>) of role type named typ_nt_some
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring nt_some:((fofType->Prop)->Prop)
% 1.98/2.52 FOF formula (((eq ((fofType->Prop)->Prop)) nt_some) (l_some natt)) of role definition named def_nt_some
% 1.98/2.52 A new definition: (((eq ((fofType->Prop)->Prop)) nt_some) (l_some natt))
% 1.98/2.52 Defined: nt_some:=(l_some natt)
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd9429e0>, <kernel.DependentProduct object at 0x2aefbd9464d0>) of role type named typ_nt_one
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring nt_one:((fofType->Prop)->Prop)
% 1.98/2.52 FOF formula (((eq ((fofType->Prop)->Prop)) nt_one) (one natt)) of role definition named def_nt_one
% 1.98/2.52 A new definition: (((eq ((fofType->Prop)->Prop)) nt_one) (one natt))
% 1.98/2.52 Defined: nt_one:=(one natt)
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd946368>, <kernel.DependentProduct object at 0x2aefbd946560>) of role type named typ_nt_in
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring nt_in:(fofType->(fofType->Prop))
% 1.98/2.52 FOF formula (((eq (fofType->(fofType->Prop))) nt_in) (esti natt)) of role definition named def_nt_in
% 1.98/2.52 A new definition: (((eq (fofType->(fofType->Prop))) nt_in) (esti natt))
% 1.98/2.52 Defined: nt_in:=(esti natt)
% 1.98/2.52 FOF formula (<kernel.Constant object at 0x2aefbd946098>, <kernel.DependentProduct object at 0x2aefbd946320>) of role type named typ_rtofnt
% 1.98/2.52 Using role type
% 1.98/2.52 Declaring rtofnt:(fofType->fofType)
% 1.98/2.52 FOF formula (((eq (fofType->fofType)) rtofnt) ((e_in rat) natrt)) of role definition named def_rtofnt
% 1.98/2.53 A new definition: (((eq (fofType->fofType)) rtofnt) ((e_in rat) natrt))
% 1.98/2.53 Defined: rtofnt:=((e_in rat) natrt)
% 1.98/2.53 FOF formula (<kernel.Constant object at 0x2aefbd946320>, <kernel.DependentProduct object at 0x2aefbd946170>) of role type named typ_ntofn
% 1.98/2.53 Using role type
% 1.98/2.53 Declaring ntofn:(fofType->fofType)
% 1.98/2.53 FOF formula (((eq (fofType->fofType)) ntofn) (fun (X0:fofType)=> (ntofrt (rtofn X0)))) of role definition named def_ntofn
% 1.98/2.53 A new definition: (((eq (fofType->fofType)) ntofn) (fun (X0:fofType)=> (ntofrt (rtofn X0))))
% 1.98/2.53 Defined: ntofn:=(fun (X0:fofType)=> (ntofrt (rtofn X0)))
% 1.98/2.53 FOF formula (<kernel.Constant object at 0x2aefbd946170>, <kernel.DependentProduct object at 0x2aefbd9460e0>) of role type named typ_nofnt
% 1.98/2.53 Using role type
% 1.98/2.53 Declaring nofnt:(fofType->fofType)
% 1.98/2.53 FOF formula (((eq (fofType->fofType)) nofnt) (fun (X0:fofType)=> (nofrt (rtofnt X0)))) of role definition named def_nofnt
% 1.98/2.53 A new definition: (((eq (fofType->fofType)) nofnt) (fun (X0:fofType)=> (nofrt (rtofnt X0))))
% 1.98/2.53 Defined: nofnt:=(fun (X0:fofType)=> (nofrt (rtofnt X0)))
% 1.98/2.53 FOF formula (<kernel.Constant object at 0x2aefbd9460e0>, <kernel.Single object at 0x2aefbd946170>) of role type named typ_nt_1t
% 1.98/2.53 Using role type
% 1.98/2.53 Declaring nt_1t:fofType
% 1.98/2.53 FOF formula (((eq fofType) nt_1t) (ntofn n_1)) of role definition named def_nt_1t
% 1.98/2.53 A new definition: (((eq fofType) nt_1t) (ntofn n_1))
% 1.98/2.53 Defined: nt_1t:=(ntofn n_1)
% 1.98/2.53 FOF formula (<kernel.Constant object at 0x2aefbd946320>, <kernel.Single object at 0x2aefbd9460e0>) of role type named typ_suct
% 1.98/2.53 Using role type
% 1.98/2.53 Declaring suct:fofType
% 1.98/2.53 FOF formula (((eq fofType) suct) ((d_Sigma natt) (fun (X0:fofType)=> (ntofn (ordsucc (nofnt X0)))))) of role definition named def_suct
% 1.98/2.53 A new definition: (((eq fofType) suct) ((d_Sigma natt) (fun (X0:fofType)=> (ntofn (ordsucc (nofnt X0))))))
% 1.98/2.53 Defined: suct:=((d_Sigma natt) (fun (X0:fofType)=> (ntofn (ordsucc (nofnt X0)))))
% 1.98/2.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((nt_nis ((ap suct) X0)) nt_1t))) of role axiom named satz113a
% 1.98/2.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((nt_nis ((ap suct) X0)) nt_1t)))
% 1.98/2.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_is ((ap suct) X0)) ((ap suct) X1))->((nt_is X0) X1)))))) of role axiom named satz113b
% 1.98/2.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_is ((ap suct) X0)) ((ap suct) X1))->((nt_is X0) X1))))))
% 1.98/2.53 FOF formula (<kernel.Constant object at 0x2aefbd9467e8>, <kernel.DependentProduct object at 0x2aefbd946a28>) of role type named typ_nt_cond1
% 1.98/2.53 Using role type
% 1.98/2.53 Declaring nt_cond1:(fofType->Prop)
% 1.98/2.53 FOF formula (((eq (fofType->Prop)) nt_cond1) (nt_in nt_1t)) of role definition named def_nt_cond1
% 1.98/2.53 A new definition: (((eq (fofType->Prop)) nt_cond1) (nt_in nt_1t))
% 1.98/2.53 Defined: nt_cond1:=(nt_in nt_1t)
% 1.98/2.53 FOF formula (<kernel.Constant object at 0x2aefbd9462d8>, <kernel.DependentProduct object at 0x2aefbd946908>) of role type named typ_nt_cond2
% 1.98/2.53 Using role type
% 1.98/2.53 Declaring nt_cond2:(fofType->Prop)
% 1.98/2.53 FOF formula (((eq (fofType->Prop)) nt_cond2) (fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((imp ((nt_in X1) X0)) ((nt_in ((ap suct) X1)) X0)))))) of role definition named def_nt_cond2
% 1.98/2.53 A new definition: (((eq (fofType->Prop)) nt_cond2) (fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((imp ((nt_in X1) X0)) ((nt_in ((ap suct) X1)) X0))))))
% 1.98/2.53 Defined: nt_cond2:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((imp ((nt_in X1) X0)) ((nt_in ((ap suct) X1)) X0)))))
% 1.98/2.53 FOF formula (<kernel.Constant object at 0x2aefbd946908>, <kernel.DependentProduct object at 0x2aefbd946170>) of role type named typ_d_5113_prop1
% 1.98/2.53 Using role type
% 1.98/2.53 Declaring d_5113_prop1:(fofType->(fofType->Prop))
% 1.98/2.53 FOF formula (((eq (fofType->(fofType->Prop))) d_5113_prop1) (fun (X0:fofType) (X1:fofType)=> ((nt_in (ntofn X1)) X0))) of role definition named def_d_5113_prop1
% 1.98/2.53 A new definition: (((eq (fofType->(fofType->Prop))) d_5113_prop1) (fun (X0:fofType) (X1:fofType)=> ((nt_in (ntofn X1)) X0)))
% 1.98/2.55 Defined: d_5113_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nt_in (ntofn X1)) X0))
% 1.98/2.55 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) (power natt)))) (fun (X0:fofType)=> ((nt_cond1 X0)->((nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((nt_in X1) X0))))))) of role axiom named satz113c
% 1.98/2.55 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) (power natt)))) (fun (X0:fofType)=> ((nt_cond1 X0)->((nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((nt_in X1) X0)))))))
% 1.98/2.55 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_nis X0) X1)->((nt_nis ((ap suct) X0)) ((ap suct) X1))))))) of role axiom named nt_satz1
% 1.98/2.55 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_nis X0) X1)->((nt_nis ((ap suct) X0)) ((ap suct) X1)))))))
% 1.98/2.55 FOF formula (<kernel.Constant object at 0x2aefbd946a28>, <kernel.DependentProduct object at 0x2aefbd946e60>) of role type named typ_prop1t
% 1.98/2.55 Using role type
% 1.98/2.55 Declaring prop1t:(fofType->Prop)
% 1.98/2.55 FOF formula (((eq (fofType->Prop)) prop1t) (fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((nt_is ((ap X0) ((ap suct) X1))) ((ap suct) ((ap X0) X1))))))) of role definition named def_prop1t
% 1.98/2.55 A new definition: (((eq (fofType->Prop)) prop1t) (fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((nt_is ((ap X0) ((ap suct) X1))) ((ap suct) ((ap X0) X1)))))))
% 1.98/2.55 Defined: prop1t:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((nt_is ((ap X0) ((ap suct) X1))) ((ap suct) ((ap X0) X1))))))
% 1.98/2.55 FOF formula (<kernel.Constant object at 0x2aefbd946e60>, <kernel.DependentProduct object at 0x2aefbd946320>) of role type named typ_prop2t
% 1.98/2.55 Using role type
% 1.98/2.55 Declaring prop2t:(fofType->(fofType->Prop))
% 1.98/2.55 FOF formula (((eq (fofType->(fofType->Prop))) prop2t) (fun (X0:fofType) (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (prop1t X1)))) of role definition named def_prop2t
% 1.98/2.55 A new definition: (((eq (fofType->(fofType->Prop))) prop2t) (fun (X0:fofType) (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (prop1t X1))))
% 1.98/2.55 Defined: prop2t:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (prop1t X1)))
% 1.98/2.55 FOF formula (<kernel.Constant object at 0x2aefbd946320>, <kernel.DependentProduct object at 0x2aefbd946488>) of role type named typ_d_54_prop2
% 1.98/2.55 Using role type
% 1.98/2.55 Declaring d_54_prop2:(fofType->(fofType->Prop))
% 1.98/2.55 FOF formula (((eq (fofType->(fofType->Prop))) d_54_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc (nofnt X0)))) (d_24_prop1 X1)))) of role definition named def_d_54_prop2
% 1.98/2.55 A new definition: (((eq (fofType->(fofType->Prop))) d_54_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc (nofnt X0)))) (d_24_prop1 X1))))
% 1.98/2.55 Defined: d_54_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc (nofnt X0)))) (d_24_prop1 X1)))
% 1.98/2.55 FOF formula (<kernel.Constant object at 0x2aefbd946488>, <kernel.DependentProduct object at 0x2aefbd946518>) of role type named typ_d_54_g
% 1.98/2.55 Using role type
% 1.98/2.55 Declaring d_54_g:(fofType->fofType)
% 1.98/2.55 FOF formula (((eq (fofType->fofType)) d_54_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (nofnt ((ap X0) (ntofn X1))))))) of role definition named def_d_54_g
% 1.98/2.55 A new definition: (((eq (fofType->fofType)) d_54_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (nofnt ((ap X0) (ntofn X1)))))))
% 1.98/2.55 Defined: d_54_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (nofnt ((ap X0) (ntofn X1))))))
% 1.98/2.55 FOF formula (<kernel.Constant object at 0x2aefbd946518>, <kernel.DependentProduct object at 0x2aefbd946908>) of role type named typ_d_54_gt
% 1.98/2.55 Using role type
% 1.98/2.55 Declaring d_54_gt:(fofType->fofType)
% 1.98/2.55 FOF formula (((eq (fofType->fofType)) d_54_gt) (fun (X0:fofType)=> ((d_Sigma natt) (fun (X1:fofType)=> (ntofn ((ap X0) (nofnt X1))))))) of role definition named def_d_54_gt
% 1.98/2.55 A new definition: (((eq (fofType->fofType)) d_54_gt) (fun (X0:fofType)=> ((d_Sigma natt) (fun (X1:fofType)=> (ntofn ((ap X0) (nofnt X1)))))))
% 1.98/2.56 Defined: d_54_gt:=(fun (X0:fofType)=> ((d_Sigma natt) (fun (X1:fofType)=> (ntofn ((ap X0) (nofnt X1))))))
% 1.98/2.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((one ((d_Pi natt) (fun (X1:fofType)=> natt))) (fun (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (nt_all (fun (X2:fofType)=> ((nt_is ((ap X1) ((ap suct) X2))) ((ap suct) ((ap X1) X2)))))))))) of role axiom named nt_satz4
% 1.98/2.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((one ((d_Pi natt) (fun (X1:fofType)=> natt))) (fun (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (nt_all (fun (X2:fofType)=> ((nt_is ((ap X1) ((ap suct) X2))) ((ap suct) ((ap X1) X2))))))))))
% 1.98/2.56 FOF formula (<kernel.Constant object at 0x2aefbd946b00>, <kernel.DependentProduct object at 0x2aefbd9467a0>) of role type named typ_nt_pl
% 1.98/2.56 Using role type
% 1.98/2.56 Declaring nt_pl:(fofType->(fofType->fofType))
% 1.98/2.56 FOF formula (((eq (fofType->(fofType->fofType))) nt_pl) (fun (X0:fofType) (X1:fofType)=> (ntofrt ((rt_pl (rtofnt X0)) (rtofnt X1))))) of role definition named def_nt_pl
% 1.98/2.56 A new definition: (((eq (fofType->(fofType->fofType))) nt_pl) (fun (X0:fofType) (X1:fofType)=> (ntofrt ((rt_pl (rtofnt X0)) (rtofnt X1)))))
% 1.98/2.56 Defined: nt_pl:=(fun (X0:fofType) (X1:fofType)=> (ntofrt ((rt_pl (rtofnt X0)) (rtofnt X1))))
% 1.98/2.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((nt_is ((nt_pl ((nt_pl X0) X1)) X2)) ((nt_pl X0) ((nt_pl X1) X2))))))))) of role axiom named nt_satz5
% 1.98/2.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((nt_is ((nt_pl ((nt_pl X0) X1)) X2)) ((nt_pl X0) ((nt_pl X1) X2)))))))))
% 1.98/2.56 FOF formula (<kernel.Constant object at 0x2aefbd9460e0>, <kernel.DependentProduct object at 0x2aefbd946b48>) of role type named typ_nt_diffprop
% 1.98/2.56 Using role type
% 1.98/2.56 Declaring nt_diffprop:(fofType->(fofType->(fofType->Prop)))
% 1.98/2.56 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) nt_diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2)))) of role definition named def_nt_diffprop
% 1.98/2.56 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) nt_diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))))
% 1.98/2.56 Defined: nt_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2)))
% 1.98/2.56 FOF formula (<kernel.Constant object at 0x2aefbd946b48>, <kernel.DependentProduct object at 0x2aefbd946cb0>) of role type named typ_iit
% 1.98/2.56 Using role type
% 1.98/2.56 Declaring iit:(fofType->(fofType->Prop))
% 1.98/2.56 FOF formula (((eq (fofType->(fofType->Prop))) iit) (fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X0) X1)))) of role definition named def_iit
% 1.98/2.56 A new definition: (((eq (fofType->(fofType->Prop))) iit) (fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X0) X1))))
% 1.98/2.56 Defined: iit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X0) X1)))
% 1.98/2.56 FOF formula (<kernel.Constant object at 0x2aefbd946cb0>, <kernel.DependentProduct object at 0x2aefbd946ef0>) of role type named typ_iiit
% 1.98/2.56 Using role type
% 1.98/2.56 Declaring iiit:(fofType->(fofType->Prop))
% 1.98/2.56 FOF formula (((eq (fofType->(fofType->Prop))) iiit) (fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X1) X0)))) of role definition named def_iiit
% 1.98/2.56 A new definition: (((eq (fofType->(fofType->Prop))) iiit) (fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X1) X0))))
% 1.98/2.56 Defined: iiit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X1) X0)))
% 1.98/2.56 FOF formula (<kernel.Constant object at 0x2aefbd946ef0>, <kernel.DependentProduct object at 0x2aefbd946ea8>) of role type named typ_d_59_i
% 1.98/2.56 Using role type
% 1.98/2.56 Declaring d_59_i:(fofType->(fofType->Prop))
% 1.98/2.56 FOF formula (((eq (fofType->(fofType->Prop))) d_59_i) (fun (X0:fofType) (X1:fofType)=> ((n_is (nofnt X0)) (nofnt X1)))) of role definition named def_d_59_i
% 1.98/2.58 A new definition: (((eq (fofType->(fofType->Prop))) d_59_i) (fun (X0:fofType) (X1:fofType)=> ((n_is (nofnt X0)) (nofnt X1))))
% 1.98/2.58 Defined: d_59_i:=(fun (X0:fofType) (X1:fofType)=> ((n_is (nofnt X0)) (nofnt X1)))
% 1.98/2.58 FOF formula (<kernel.Constant object at 0x2aefbd946fc8>, <kernel.DependentProduct object at 0x2aefbd946c68>) of role type named typ_d_59_ii
% 1.98/2.58 Using role type
% 1.98/2.58 Declaring d_59_ii:(fofType->(fofType->Prop))
% 1.98/2.58 FOF formula (((eq (fofType->(fofType->Prop))) d_59_ii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X0)) (nofnt X1))))) of role definition named def_d_59_ii
% 1.98/2.58 A new definition: (((eq (fofType->(fofType->Prop))) d_59_ii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X0)) (nofnt X1)))))
% 1.98/2.58 Defined: d_59_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X0)) (nofnt X1))))
% 1.98/2.58 FOF formula (<kernel.Constant object at 0x2aefbd946b48>, <kernel.DependentProduct object at 0x2aefbd9460e0>) of role type named typ_d_59_iii
% 1.98/2.58 Using role type
% 1.98/2.58 Declaring d_59_iii:(fofType->(fofType->Prop))
% 1.98/2.58 FOF formula (((eq (fofType->(fofType->Prop))) d_59_iii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X1)) (nofnt X0))))) of role definition named def_d_59_iii
% 1.98/2.58 A new definition: (((eq (fofType->(fofType->Prop))) d_59_iii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X1)) (nofnt X0)))))
% 1.98/2.58 Defined: d_59_iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X1)) (nofnt X0))))
% 1.98/2.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((orec3 ((nt_is X0) X1)) (nt_some (fun (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))))) (nt_some (fun (X2:fofType)=> ((nt_is X1) ((nt_pl X0) X2))))))))) of role axiom named nt_satz9
% 1.98/2.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((orec3 ((nt_is X0) X1)) (nt_some (fun (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))))) (nt_some (fun (X2:fofType)=> ((nt_is X1) ((nt_pl X0) X2)))))))))
% 1.98/2.58 FOF formula (<kernel.Constant object at 0x2aefbd9469e0>, <kernel.DependentProduct object at 0x2aefbd9620e0>) of role type named typ_nt_more
% 1.98/2.58 Using role type
% 1.98/2.58 Declaring nt_more:(fofType->(fofType->Prop))
% 1.98/2.58 FOF formula (((eq (fofType->(fofType->Prop))) nt_more) (fun (X0:fofType) (X1:fofType)=> ((rt_more (rtofnt X0)) (rtofnt X1)))) of role definition named def_nt_more
% 1.98/2.58 A new definition: (((eq (fofType->(fofType->Prop))) nt_more) (fun (X0:fofType) (X1:fofType)=> ((rt_more (rtofnt X0)) (rtofnt X1))))
% 1.98/2.58 Defined: nt_more:=(fun (X0:fofType) (X1:fofType)=> ((rt_more (rtofnt X0)) (rtofnt X1)))
% 1.98/2.58 FOF formula (<kernel.Constant object at 0x2aefbd946fc8>, <kernel.DependentProduct object at 0x2aefbd962248>) of role type named typ_nt_less
% 1.98/2.58 Using role type
% 1.98/2.58 Declaring nt_less:(fofType->(fofType->Prop))
% 1.98/2.58 FOF formula (((eq (fofType->(fofType->Prop))) nt_less) (fun (X0:fofType) (X1:fofType)=> ((rt_less (rtofnt X0)) (rtofnt X1)))) of role definition named def_nt_less
% 1.98/2.58 A new definition: (((eq (fofType->(fofType->Prop))) nt_less) (fun (X0:fofType) (X1:fofType)=> ((rt_less (rtofnt X0)) (rtofnt X1))))
% 1.98/2.58 Defined: nt_less:=(fun (X0:fofType) (X1:fofType)=> ((rt_less (rtofnt X0)) (rtofnt X1)))
% 1.98/2.58 FOF formula (<kernel.Constant object at 0x2aefbd946fc8>, <kernel.DependentProduct object at 0x2aefbd962560>) of role type named typ_nt_moreis
% 1.98/2.58 Using role type
% 1.98/2.58 Declaring nt_moreis:(fofType->(fofType->Prop))
% 1.98/2.58 FOF formula (((eq (fofType->(fofType->Prop))) nt_moreis) (fun (X0:fofType) (X1:fofType)=> ((rt_moreis (rtofnt X0)) (rtofnt X1)))) of role definition named def_nt_moreis
% 1.98/2.58 A new definition: (((eq (fofType->(fofType->Prop))) nt_moreis) (fun (X0:fofType) (X1:fofType)=> ((rt_moreis (rtofnt X0)) (rtofnt X1))))
% 1.98/2.58 Defined: nt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((rt_moreis (rtofnt X0)) (rtofnt X1)))
% 1.98/2.58 FOF formula (<kernel.Constant object at 0x2aefbd9460e0>, <kernel.DependentProduct object at 0x2aefbd9624d0>) of role type named typ_nt_lessis
% 1.98/2.58 Using role type
% 1.98/2.58 Declaring nt_lessis:(fofType->(fofType->Prop))
% 1.98/2.58 FOF formula (((eq (fofType->(fofType->Prop))) nt_lessis) (fun (X0:fofType) (X1:fofType)=> ((rt_lessis (rtofnt X0)) (rtofnt X1)))) of role definition named def_nt_lessis
% 1.98/2.59 A new definition: (((eq (fofType->(fofType->Prop))) nt_lessis) (fun (X0:fofType) (X1:fofType)=> ((rt_lessis (rtofnt X0)) (rtofnt X1))))
% 1.98/2.59 Defined: nt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((rt_lessis (rtofnt X0)) (rtofnt X1)))
% 1.98/2.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> (((nt_less X0) X1)->(((nt_less X1) X2)->((nt_less X0) X2))))))))) of role axiom named nt_satz15
% 1.98/2.59 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> (((nt_less X0) X1)->(((nt_less X1) X2)->((nt_less X0) X2)))))))))
% 1.98/2.59 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) natt))) (fun (X3:fofType)=> (((nt_more X0) X1)->(((nt_more X2) X3)->((nt_more ((nt_pl X0) X2)) ((nt_pl X1) X3)))))))))))) of role axiom named nt_satz21
% 1.98/2.60 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) natt))) (fun (X3:fofType)=> (((nt_more X0) X1)->(((nt_more X2) X3)->((nt_more ((nt_pl X0) X2)) ((nt_pl X1) X3))))))))))))
% 1.98/2.60 FOF formula (<kernel.Constant object at 0x2aefbd962638>, <kernel.DependentProduct object at 0x2aefbd9625a8>) of role type named typ_nt_lb
% 1.98/2.60 Using role type
% 1.98/2.60 Declaring nt_lb:((fofType->Prop)->(fofType->Prop))
% 1.98/2.60 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) nt_lb) (fun (X0:(fofType->Prop)) (X1:fofType)=> (nt_all (fun (X2:fofType)=> ((imp (X0 X2)) ((nt_lessis X1) X2)))))) of role definition named def_nt_lb
% 1.98/2.60 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) nt_lb) (fun (X0:(fofType->Prop)) (X1:fofType)=> (nt_all (fun (X2:fofType)=> ((imp (X0 X2)) ((nt_lessis X1) X2))))))
% 1.98/2.60 Defined: nt_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (nt_all (fun (X2:fofType)=> ((imp (X0 X2)) ((nt_lessis X1) X2)))))
% 1.98/2.60 FOF formula (<kernel.Constant object at 0x2aefbd9625a8>, <kernel.DependentProduct object at 0x2aefbd962290>) of role type named typ_nt_min
% 1.98/2.60 Using role type
% 1.98/2.60 Declaring nt_min:((fofType->Prop)->(fofType->Prop))
% 1.98/2.60 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) nt_min) (fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((nt_lb X0) X1)) (X0 X1)))) of role definition named def_nt_min
% 1.98/2.60 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) nt_min) (fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((nt_lb X0) X1)) (X0 X1))))
% 1.98/2.60 Defined: nt_min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((nt_lb X0) X1)) (X0 X1)))
% 1.98/2.60 FOF formula (<kernel.Constant object at 0x2aefbd962290>, <kernel.DependentProduct object at 0x2aefbd962a28>) of role type named typ_d_527_q
% 1.98/2.60 Using role type
% 1.98/2.60 Declaring d_527_q:((fofType->Prop)->(fofType->Prop))
% 1.98/2.60 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) d_527_q) (fun (X0:(fofType->Prop)) (X1:fofType)=> (X0 (ntofn X1)))) of role definition named def_d_527_q
% 1.98/2.60 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) d_527_q) (fun (X0:(fofType->Prop)) (X1:fofType)=> (X0 (ntofn X1))))
% 1.98/2.60 Defined: d_527_q:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (X0 (ntofn X1)))
% 1.98/2.60 FOF formula (forall (X0:(fofType->Prop)), ((nt_some X0)->(nt_some (nt_min X0)))) of role axiom named nt_satz27
% 1.98/2.60 A new axiom: (forall (X0:(fofType->Prop)), ((nt_some X0)->(nt_some (nt_min X0))))
% 1.98/2.60 FOF formula (<kernel.Constant object at 0x2aefbd9621b8>, <kernel.Single object at 0x2aefbd962a28>) of role type named typ_d_1rt
% 1.98/2.60 Using role type
% 1.98/2.60 Declaring d_1rt:fofType
% 1.98/2.60 FOF formula (((eq fofType) d_1rt) (rtofn n_1)) of role definition named def_d_1rt
% 1.98/2.60 A new definition: (((eq fofType) d_1rt) (rtofn n_1))
% 2.08/2.62 Defined: d_1rt:=(rtofn n_1)
% 2.08/2.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((rt_is ((rt_ts (rtofn (den X0))) (ratof X0))) (rtofn (num X0))))) of role axiom named satz114
% 2.08/2.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((rt_is ((rt_ts (rtofn (den X0))) (ratof X0))) (rtofn (num X0)))))
% 2.08/2.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X1)) (ratof ((n_fr X0) X1)))) (rtofn X0)))))) of role axiom named satz114a
% 2.08/2.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X1)) (ratof ((n_fr X0) X1)))) (rtofn X0))))))
% 2.08/2.62 FOF formula (<kernel.Constant object at 0x2aefbd9626c8>, <kernel.DependentProduct object at 0x2aefbd962320>) of role type named typ_rt_ov
% 2.08/2.62 Using role type
% 2.08/2.62 Declaring rt_ov:(fofType->(fofType->fofType))
% 2.08/2.62 FOF formula (((eq (fofType->(fofType->fofType))) rt_ov) (fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0))))) of role definition named def_rt_ov
% 2.08/2.62 A new definition: (((eq (fofType->(fofType->fofType))) rt_ov) (fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))
% 2.08/2.62 Defined: rt_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0))))
% 2.08/2.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X1) ((rt_ov X0) X1))) X0))))) of role axiom named satz110c
% 2.08/2.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X1) ((rt_ov X0) X1))) X0)))))
% 2.08/2.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts X1) ((rt_ov X0) X1))))))) of role axiom named satz110d
% 2.08/2.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts X1) ((rt_ov X0) X1)))))))
% 2.08/2.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov X0) X1)) X1)) X0))))) of role axiom named satz110e
% 2.08/2.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov X0) X1)) X1)) X0)))))
% 2.08/2.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts ((rt_ov X0) X1)) X1)))))) of role axiom named satz110f
% 2.08/2.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts ((rt_ov X0) X1)) X1))))))
% 2.08/2.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->((rt_is X2) ((rt_ov X0) X1))))))))) of role axiom named satz110g
% 2.08/2.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->((rt_is X2) ((rt_ov X0) X1)))))))))
% 2.08/2.62 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is (ratof ((n_fr X0) X1))) ((rt_ov (rtofn X0)) (rtofn X1))))))) of role axiom named satz114b
% 2.08/2.62 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is (ratof ((n_fr X0) X1))) ((rt_ov (rtofn X0)) (rtofn X1)))))))
% 2.08/2.64 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ov (rtofn X0)) (rtofn X1))) (ratof ((n_fr X0) X1))))))) of role axiom named satz114c
% 2.08/2.64 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ov (rtofn X0)) (rtofn X1))) (ratof ((n_fr X0) X1)))))))
% 2.08/2.64 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (n_some (fun (X2:fofType)=> ((rt_more ((rt_ts (rtofn X2)) X0)) X1))))))) of role axiom named satz115
% 2.08/2.64 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (n_some (fun (X2:fofType)=> ((rt_more ((rt_ts (rtofn X2)) X0)) X1)))))))
% 2.08/2.64 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and (natrt X2)) ((rt_more ((rt_ts X2) X0)) X1)))))))) of role axiom named satz115a
% 2.08/2.64 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and (natrt X2)) ((rt_more ((rt_ts X2) X0)) X1))))))))
% 2.08/2.64 FOF formula (<kernel.Constant object at 0x2aefbd962d40>, <kernel.DependentProduct object at 0x2aefbd962050>) of role type named typ_cutprop1a
% 2.08/2.64 Using role type
% 2.08/2.64 Declaring cutprop1a:(fofType->Prop)
% 2.08/2.64 FOF formula (((eq (fofType->Prop)) cutprop1a) (nonempty rat)) of role definition named def_cutprop1a
% 2.08/2.64 A new definition: (((eq (fofType->Prop)) cutprop1a) (nonempty rat))
% 2.08/2.64 Defined: cutprop1a:=(nonempty rat)
% 2.08/2.64 FOF formula (<kernel.Constant object at 0x2aefbd962dd0>, <kernel.DependentProduct object at 0x2aefbd962f38>) of role type named typ_cutprop1b
% 2.08/2.64 Using role type
% 2.08/2.64 Declaring cutprop1b:(fofType->Prop)
% 2.08/2.64 FOF formula (((eq (fofType->Prop)) cutprop1b) (fun (X0:fofType)=> (d_not (rt_all (fun (X1:fofType)=> ((rt_in X1) X0)))))) of role definition named def_cutprop1b
% 2.08/2.64 A new definition: (((eq (fofType->Prop)) cutprop1b) (fun (X0:fofType)=> (d_not (rt_all (fun (X1:fofType)=> ((rt_in X1) X0))))))
% 2.08/2.64 Defined: cutprop1b:=(fun (X0:fofType)=> (d_not (rt_all (fun (X1:fofType)=> ((rt_in X1) X0)))))
% 2.08/2.64 FOF formula (<kernel.Constant object at 0x2aefbd962f38>, <kernel.DependentProduct object at 0x2aefbd962998>) of role type named typ_cutprop1
% 2.08/2.64 Using role type
% 2.08/2.64 Declaring cutprop1:(fofType->Prop)
% 2.08/2.64 FOF formula (((eq (fofType->Prop)) cutprop1) (fun (X0:fofType)=> ((d_and (cutprop1a X0)) (cutprop1b X0)))) of role definition named def_cutprop1
% 2.08/2.64 A new definition: (((eq (fofType->Prop)) cutprop1) (fun (X0:fofType)=> ((d_and (cutprop1a X0)) (cutprop1b X0))))
% 2.08/2.64 Defined: cutprop1:=(fun (X0:fofType)=> ((d_and (cutprop1a X0)) (cutprop1b X0)))
% 2.08/2.64 FOF formula (<kernel.Constant object at 0x2aefbd962998>, <kernel.DependentProduct object at 0x2aefbd9620e0>) of role type named typ_cutprop2a
% 2.08/2.64 Using role type
% 2.08/2.64 Declaring cutprop2a:(fofType->(fofType->Prop))
% 2.08/2.64 FOF formula (((eq (fofType->(fofType->Prop))) cutprop2a) (fun (X0:fofType) (X1:fofType)=> (rt_all (fun (X2:fofType)=> ((imp (d_not ((rt_in X2) X0))) ((rt_less X1) X2)))))) of role definition named def_cutprop2a
% 2.08/2.64 A new definition: (((eq (fofType->(fofType->Prop))) cutprop2a) (fun (X0:fofType) (X1:fofType)=> (rt_all (fun (X2:fofType)=> ((imp (d_not ((rt_in X2) X0))) ((rt_less X1) X2))))))
% 2.08/2.64 Defined: cutprop2a:=(fun (X0:fofType) (X1:fofType)=> (rt_all (fun (X2:fofType)=> ((imp (d_not ((rt_in X2) X0))) ((rt_less X1) X2)))))
% 2.08/2.64 FOF formula (<kernel.Constant object at 0x2aefbd9620e0>, <kernel.DependentProduct object at 0x2aefbd9626c8>) of role type named typ_cutprop2
% 2.08/2.64 Using role type
% 2.08/2.64 Declaring cutprop2:(fofType->Prop)
% 2.08/2.64 FOF formula (((eq (fofType->Prop)) cutprop2) (fun (X0:fofType)=> (rt_all (fun (X1:fofType)=> ((imp ((rt_in X1) X0)) ((cutprop2a X0) X1)))))) of role definition named def_cutprop2
% 2.08/2.64 A new definition: (((eq (fofType->Prop)) cutprop2) (fun (X0:fofType)=> (rt_all (fun (X1:fofType)=> ((imp ((rt_in X1) X0)) ((cutprop2a X0) X1))))))
% 2.08/2.65 Defined: cutprop2:=(fun (X0:fofType)=> (rt_all (fun (X1:fofType)=> ((imp ((rt_in X1) X0)) ((cutprop2a X0) X1)))))
% 2.08/2.65 FOF formula (<kernel.Constant object at 0x2aefbd9626c8>, <kernel.DependentProduct object at 0x2aefbd962320>) of role type named typ_ubprop
% 2.08/2.65 Using role type
% 2.08/2.65 Declaring ubprop:(fofType->(fofType->(fofType->Prop)))
% 2.08/2.65 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) ubprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_moreis X1) X2)))) of role definition named def_ubprop
% 2.08/2.65 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) ubprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_moreis X1) X2))))
% 2.08/2.65 Defined: ubprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_moreis X1) X2)))
% 2.08/2.65 FOF formula (<kernel.Constant object at 0x2aefbd962320>, <kernel.DependentProduct object at 0x2aefbd962fc8>) of role type named typ_rt_ub
% 2.08/2.65 Using role type
% 2.08/2.65 Declaring rt_ub:(fofType->(fofType->Prop))
% 2.08/2.65 FOF formula (((eq (fofType->(fofType->Prop))) rt_ub) (fun (X0:fofType) (X1:fofType)=> (rt_all ((ubprop X0) X1)))) of role definition named def_rt_ub
% 2.08/2.65 A new definition: (((eq (fofType->(fofType->Prop))) rt_ub) (fun (X0:fofType) (X1:fofType)=> (rt_all ((ubprop X0) X1))))
% 2.08/2.65 Defined: rt_ub:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((ubprop X0) X1)))
% 2.08/2.65 FOF formula (<kernel.Constant object at 0x2aefbd962fc8>, <kernel.DependentProduct object at 0x2aefbd962b00>) of role type named typ_max
% 2.08/2.65 Using role type
% 2.08/2.65 Declaring max:(fofType->(fofType->Prop))
% 2.08/2.65 FOF formula (((eq (fofType->(fofType->Prop))) max) (fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_ub X0) X1)) ((rt_in X1) X0)))) of role definition named def_max
% 2.08/2.65 A new definition: (((eq (fofType->(fofType->Prop))) max) (fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_ub X0) X1)) ((rt_in X1) X0))))
% 2.08/2.65 Defined: max:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_ub X0) X1)) ((rt_in X1) X0)))
% 2.08/2.65 FOF formula (<kernel.Constant object at 0x2aefbd962b00>, <kernel.DependentProduct object at 0x2aefbd962e60>) of role type named typ_cutprop3
% 2.08/2.65 Using role type
% 2.08/2.65 Declaring cutprop3:(fofType->Prop)
% 2.08/2.65 FOF formula (((eq (fofType->Prop)) cutprop3) (fun (X0:fofType)=> (d_not (rt_some (max X0))))) of role definition named def_cutprop3
% 2.08/2.65 A new definition: (((eq (fofType->Prop)) cutprop3) (fun (X0:fofType)=> (d_not (rt_some (max X0)))))
% 2.08/2.65 Defined: cutprop3:=(fun (X0:fofType)=> (d_not (rt_some (max X0))))
% 2.08/2.65 FOF formula (<kernel.Constant object at 0x2aefbd962e60>, <kernel.DependentProduct object at 0x2aefbd962878>) of role type named typ_cutprop
% 2.08/2.65 Using role type
% 2.08/2.65 Declaring cutprop:(fofType->Prop)
% 2.08/2.65 FOF formula (((eq (fofType->Prop)) cutprop) (fun (X0:fofType)=> (((and3 (cutprop1 X0)) (cutprop2 X0)) (cutprop3 X0)))) of role definition named def_cutprop
% 2.08/2.65 A new definition: (((eq (fofType->Prop)) cutprop) (fun (X0:fofType)=> (((and3 (cutprop1 X0)) (cutprop2 X0)) (cutprop3 X0))))
% 2.08/2.65 Defined: cutprop:=(fun (X0:fofType)=> (((and3 (cutprop1 X0)) (cutprop2 X0)) (cutprop3 X0)))
% 2.08/2.65 FOF formula (<kernel.Constant object at 0x2aefbd962b00>, <kernel.DependentProduct object at 0x2aefbd962488>) of role type named typ_iii1_lbprop
% 2.08/2.65 Using role type
% 2.08/2.65 Declaring iii1_lbprop:(fofType->(fofType->(fofType->Prop)))
% 2.08/2.65 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) iii1_lbprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_lessis X1) X2)))) of role definition named def_iii1_lbprop
% 2.08/2.65 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) iii1_lbprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_lessis X1) X2))))
% 2.08/2.65 Defined: iii1_lbprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_lessis X1) X2)))
% 2.08/2.65 FOF formula (<kernel.Constant object at 0x2aefbd962878>, <kernel.DependentProduct object at 0x2aefb295f320>) of role type named typ_rt_lb
% 2.08/2.65 Using role type
% 2.08/2.65 Declaring rt_lb:(fofType->(fofType->Prop))
% 2.08/2.65 FOF formula (((eq (fofType->(fofType->Prop))) rt_lb) (fun (X0:fofType) (X1:fofType)=> (rt_all ((iii1_lbprop X0) X1)))) of role definition named def_rt_lb
% 2.08/2.65 A new definition: (((eq (fofType->(fofType->Prop))) rt_lb) (fun (X0:fofType) (X1:fofType)=> (rt_all ((iii1_lbprop X0) X1))))
% 2.08/2.66 Defined: rt_lb:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((iii1_lbprop X0) X1)))
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefbd962b00>, <kernel.DependentProduct object at 0x2aefb295f128>) of role type named typ_rt_min
% 2.08/2.66 Using role type
% 2.08/2.66 Declaring rt_min:(fofType->(fofType->Prop))
% 2.08/2.66 FOF formula (((eq (fofType->(fofType->Prop))) rt_min) (fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_lb X0) X1)) ((rt_in X1) X0)))) of role definition named def_rt_min
% 2.08/2.66 A new definition: (((eq (fofType->(fofType->Prop))) rt_min) (fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_lb X0) X1)) ((rt_in X1) X0))))
% 2.08/2.66 Defined: rt_min:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_lb X0) X1)) ((rt_in X1) X0)))
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefbd962e60>, <kernel.Single object at 0x2aefbd962b00>) of role type named typ_cut
% 2.08/2.66 Using role type
% 2.08/2.66 Declaring cut:fofType
% 2.08/2.66 FOF formula (((eq fofType) cut) ((d_Sep (power rat)) cutprop)) of role definition named def_cut
% 2.08/2.66 A new definition: (((eq fofType) cut) ((d_Sep (power rat)) cutprop))
% 2.08/2.66 Defined: cut:=((d_Sep (power rat)) cutprop)
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefbd962b00>, <kernel.DependentProduct object at 0x2aefb295f098>) of role type named typ_lcl
% 2.08/2.66 Using role type
% 2.08/2.66 Declaring lcl:(fofType->fofType)
% 2.08/2.66 FOF formula (((eq (fofType->fofType)) lcl) ((e_in (power rat)) cutprop)) of role definition named def_lcl
% 2.08/2.66 A new definition: (((eq (fofType->fofType)) lcl) ((e_in (power rat)) cutprop))
% 2.08/2.66 Defined: lcl:=((e_in (power rat)) cutprop)
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefbd962878>, <kernel.DependentProduct object at 0x2aefb295f290>) of role type named typ_lrt
% 2.08/2.66 Using role type
% 2.08/2.66 Declaring lrt:(fofType->(fofType->Prop))
% 2.08/2.66 FOF formula (((eq (fofType->(fofType->Prop))) lrt) (fun (X0:fofType) (X1:fofType)=> ((rt_in X1) (lcl X0)))) of role definition named def_lrt
% 2.08/2.66 A new definition: (((eq (fofType->(fofType->Prop))) lrt) (fun (X0:fofType) (X1:fofType)=> ((rt_in X1) (lcl X0))))
% 2.08/2.66 Defined: lrt:=(fun (X0:fofType) (X1:fofType)=> ((rt_in X1) (lcl X0)))
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefb295f290>, <kernel.DependentProduct object at 0x2aefb295f4d0>) of role type named typ_urt
% 2.08/2.66 Using role type
% 2.08/2.66 Declaring urt:(fofType->(fofType->Prop))
% 2.08/2.66 FOF formula (((eq (fofType->(fofType->Prop))) urt) (fun (X0:fofType) (X1:fofType)=> (d_not ((rt_in X1) (lcl X0))))) of role definition named def_urt
% 2.08/2.66 A new definition: (((eq (fofType->(fofType->Prop))) urt) (fun (X0:fofType) (X1:fofType)=> (d_not ((rt_in X1) (lcl X0)))))
% 2.08/2.66 Defined: urt:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_in X1) (lcl X0))))
% 2.08/2.66 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM007^3.ax, trying next directory
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefba1e0bd8>, <kernel.DependentProduct object at 0x2aefba1e0710>) of role type named typ_rp_is
% 2.08/2.66 Using role type
% 2.08/2.66 Declaring rp_is:(fofType->(fofType->Prop))
% 2.08/2.66 FOF formula (((eq (fofType->(fofType->Prop))) rp_is) (e_is cut)) of role definition named def_rp_is
% 2.08/2.66 A new definition: (((eq (fofType->(fofType->Prop))) rp_is) (e_is cut))
% 2.08/2.66 Defined: rp_is:=(e_is cut)
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefba1e0638>, <kernel.DependentProduct object at 0x2aefba1e0098>) of role type named typ_rp_nis
% 2.08/2.66 Using role type
% 2.08/2.66 Declaring rp_nis:(fofType->(fofType->Prop))
% 2.08/2.66 FOF formula (((eq (fofType->(fofType->Prop))) rp_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rp_is X0) X1)))) of role definition named def_rp_nis
% 2.08/2.66 A new definition: (((eq (fofType->(fofType->Prop))) rp_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rp_is X0) X1))))
% 2.08/2.66 Defined: rp_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_is X0) X1)))
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefba1e0098>, <kernel.DependentProduct object at 0x2aefba1e0bd8>) of role type named typ_cutof
% 2.08/2.66 Using role type
% 2.08/2.66 Declaring cutof:(fofType->fofType)
% 2.08/2.66 FOF formula (((eq (fofType->fofType)) cutof) ((out (power rat)) cutprop)) of role definition named def_cutof
% 2.08/2.66 A new definition: (((eq (fofType->fofType)) cutof) ((out (power rat)) cutprop))
% 2.08/2.66 Defined: cutof:=((out (power rat)) cutprop)
% 2.08/2.66 FOF formula (<kernel.Constant object at 0x2aefba1e0488>, <kernel.DependentProduct object at 0x2aefba1e0638>) of role type named typ_rp_all
% 2.08/2.68 Using role type
% 2.08/2.68 Declaring rp_all:((fofType->Prop)->Prop)
% 2.08/2.68 FOF formula (((eq ((fofType->Prop)->Prop)) rp_all) (all cut)) of role definition named def_rp_all
% 2.08/2.68 A new definition: (((eq ((fofType->Prop)->Prop)) rp_all) (all cut))
% 2.08/2.68 Defined: rp_all:=(all cut)
% 2.08/2.68 FOF formula (<kernel.Constant object at 0x2aefba1e0cf8>, <kernel.DependentProduct object at 0x2aefba1e0638>) of role type named typ_rp_some
% 2.08/2.68 Using role type
% 2.08/2.68 Declaring rp_some:((fofType->Prop)->Prop)
% 2.08/2.68 FOF formula (((eq ((fofType->Prop)->Prop)) rp_some) (l_some cut)) of role definition named def_rp_some
% 2.08/2.68 A new definition: (((eq ((fofType->Prop)->Prop)) rp_some) (l_some cut))
% 2.08/2.68 Defined: rp_some:=(l_some cut)
% 2.08/2.68 FOF formula (<kernel.Constant object at 0x2aefba1e0098>, <kernel.DependentProduct object at 0x2aefba1e0638>) of role type named typ_rp_one
% 2.08/2.68 Using role type
% 2.08/2.68 Declaring rp_one:((fofType->Prop)->Prop)
% 2.08/2.68 FOF formula (((eq ((fofType->Prop)->Prop)) rp_one) (one cut)) of role definition named def_rp_one
% 2.08/2.68 A new definition: (((eq ((fofType->Prop)->Prop)) rp_one) (one cut))
% 2.08/2.68 Defined: rp_one:=(one cut)
% 2.08/2.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) X0))) of role axiom named satz116
% 2.08/2.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) X0)))
% 2.08/2.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_is X0) X1)->((rp_is X1) X0)))))) of role axiom named satz117
% 2.08/2.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_is X0) X1)->((rp_is X1) X0))))))
% 2.08/2.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->(((rp_is X1) X2)->((rp_is X0) X2))))))))) of role axiom named satz118
% 2.08/2.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->(((rp_is X1) X2)->((rp_is X0) X2)))))))))
% 2.08/2.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X2) X1)->((urt X0) X2))))))))) of role axiom named satz119
% 2.08/2.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X2) X1)->((urt X0) X2)))))))))
% 2.08/2.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X1) X2)->((urt X0) X2))))))))) of role axiom named satz119a
% 2.08/2.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X1) X2)->((urt X0) X2)))))))))
% 2.08/2.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X2) X1)->((lrt X0) X2))))))))) of role axiom named satz120
% 2.08/2.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X2) X1)->((lrt X0) X2)))))))))
% 2.08/2.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X1) X2)->((lrt X0) X2))))))))) of role axiom named satz120a
% 2.17/2.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X1) X2)->((lrt X0) X2)))))))))
% 2.17/2.70 FOF formula (<kernel.Constant object at 0x2aefba1e0488>, <kernel.DependentProduct object at 0x2aefba1ddd40>) of role type named typ_rp_more
% 2.17/2.70 Using role type
% 2.17/2.70 Declaring rp_more:(fofType->(fofType->Prop))
% 2.17/2.70 FOF formula (((eq (fofType->(fofType->Prop))) rp_more) (fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((lrt X0) X2)) ((urt X1) X2)))))) of role definition named def_rp_more
% 2.17/2.70 A new definition: (((eq (fofType->(fofType->Prop))) rp_more) (fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((lrt X0) X2)) ((urt X1) X2))))))
% 2.17/2.70 Defined: rp_more:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((lrt X0) X2)) ((urt X1) X2)))))
% 2.17/2.70 FOF formula (<kernel.Constant object at 0x2aefba1ddd40>, <kernel.DependentProduct object at 0x2aefba1dd908>) of role type named typ_rp_less
% 2.17/2.70 Using role type
% 2.17/2.70 Declaring rp_less:(fofType->(fofType->Prop))
% 2.17/2.70 FOF formula (((eq (fofType->(fofType->Prop))) rp_less) (fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((urt X0) X2)) ((lrt X1) X2)))))) of role definition named def_rp_less
% 2.17/2.70 A new definition: (((eq (fofType->(fofType->Prop))) rp_less) (fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((urt X0) X2)) ((lrt X1) X2))))))
% 2.17/2.70 Defined: rp_less:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((urt X0) X2)) ((lrt X1) X2)))))
% 2.17/2.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_less X1) X0)))))) of role axiom named satz121
% 2.17/2.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_less X1) X0))))))
% 2.17/2.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->((rp_more X1) X0)))))) of role axiom named satz122
% 2.17/2.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->((rp_more X1) X0))))))
% 2.17/2.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((orec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1)))))) of role axiom named satz123
% 2.17/2.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((orec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 2.17/2.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((or3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1)))))) of role axiom named k_satz123a
% 2.17/2.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((or3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 2.17/2.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((ec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1)))))) of role axiom named k_satz123b
% 2.17/2.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((ec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 2.17/2.70 FOF formula (<kernel.Constant object at 0x2aefba1dd878>, <kernel.DependentProduct object at 0x2aefba1dd0e0>) of role type named typ_rp_moreis
% 2.17/2.73 Using role type
% 2.17/2.73 Declaring rp_moreis:(fofType->(fofType->Prop))
% 2.17/2.73 FOF formula (((eq (fofType->(fofType->Prop))) rp_moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_more X0) X1)) ((rp_is X0) X1)))) of role definition named def_rp_moreis
% 2.17/2.73 A new definition: (((eq (fofType->(fofType->Prop))) rp_moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_more X0) X1)) ((rp_is X0) X1))))
% 2.17/2.73 Defined: rp_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_more X0) X1)) ((rp_is X0) X1)))
% 2.17/2.73 FOF formula (<kernel.Constant object at 0x2aefba1dd0e0>, <kernel.DependentProduct object at 0x2aefba1dd7a0>) of role type named typ_rp_lessis
% 2.17/2.73 Using role type
% 2.17/2.73 Declaring rp_lessis:(fofType->(fofType->Prop))
% 2.17/2.73 FOF formula (((eq (fofType->(fofType->Prop))) rp_lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_less X0) X1)) ((rp_is X0) X1)))) of role definition named def_rp_lessis
% 2.17/2.73 A new definition: (((eq (fofType->(fofType->Prop))) rp_lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_less X0) X1)) ((rp_is X0) X1))))
% 2.17/2.73 Defined: rp_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_less X0) X1)) ((rp_is X0) X1)))
% 2.17/2.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->((rp_lessis X1) X0)))))) of role axiom named satz124
% 2.17/2.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->((rp_lessis X1) X0))))))
% 2.17/2.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->((rp_moreis X1) X0)))))) of role axiom named satz125
% 2.17/2.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->((rp_moreis X1) X0))))))
% 2.17/2.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->(d_not ((rp_less X0) X1))))))) of role axiom named satz123c
% 2.17/2.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->(d_not ((rp_less X0) X1)))))))
% 2.17/2.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->(d_not ((rp_more X0) X1))))))) of role axiom named satz123d
% 2.17/2.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->(d_not ((rp_more X0) X1)))))))
% 2.17/2.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_more X0) X1))->((rp_lessis X0) X1)))))) of role axiom named satz123e
% 2.17/2.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_more X0) X1))->((rp_lessis X0) X1))))))
% 2.17/2.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_less X0) X1))->((rp_moreis X0) X1)))))) of role axiom named satz123f
% 2.17/2.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_less X0) X1))->((rp_moreis X0) X1))))))
% 2.17/2.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(d_not ((rp_lessis X0) X1))))))) of role axiom named satz123g
% 2.17/2.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(d_not ((rp_lessis X0) X1)))))))
% 2.17/2.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(d_not ((rp_moreis X0) X1))))))) of role axiom named satz123h
% 2.17/2.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(d_not ((rp_moreis X0) X1)))))))
% 2.17/2.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_moreis X0) X1))->((rp_less X0) X1)))))) of role axiom named satz123j
% 2.17/2.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_moreis X0) X1))->((rp_less X0) X1))))))
% 2.17/2.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_lessis X0) X1))->((rp_more X0) X1)))))) of role axiom named satz123k
% 2.17/2.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_lessis X0) X1))->((rp_more X0) X1))))))
% 2.17/2.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2))))))))) of role axiom named satz126
% 2.17/2.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 2.17/2.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2))))))))) of role axiom named satz127a
% 2.17/2.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 2.17/2.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_lessis X1) X2)->((rp_less X0) X2))))))))) of role axiom named satz127b
% 2.17/2.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_lessis X1) X2)->((rp_less X0) X2)))))))))
% 2.17/2.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_moreis X0) X1)->(((rp_more X1) X2)->((rp_more X0) X2))))))))) of role axiom named satz127c
% 2.17/2.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_moreis X0) X1)->(((rp_more X1) X2)->((rp_more X0) X2)))))))))
% 2.17/2.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_moreis X1) X2)->((rp_more X0) X2))))))))) of role axiom named satz127d
% 2.17/2.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_moreis X1) X2)->((rp_more X0) X2)))))))))
% 2.17/2.77 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X1) X2)->((rp_lessis X0) X2))))))))) of role axiom named satz128
% 2.17/2.77 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X1) X2)->((rp_lessis X0) X2)))))))))
% 2.17/2.77 FOF formula (<kernel.Constant object at 0x2aefba2c0200>, <kernel.DependentProduct object at 0x2aefbac97830>) of role type named typ_sumprop1
% 2.17/2.77 Using role type
% 2.17/2.77 Declaring sumprop1:(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 2.17/2.77 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) sumprop1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_pl X3) X4))))) of role definition named def_sumprop1
% 2.17/2.77 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) sumprop1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_pl X3) X4)))))
% 2.17/2.77 Defined: sumprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_pl X3) X4))))
% 2.17/2.77 FOF formula (<kernel.Constant object at 0x2aefba2c0518>, <kernel.DependentProduct object at 0x2aefbac97908>) of role type named typ_sumprop
% 2.17/2.77 Using role type
% 2.17/2.77 Declaring sumprop:(fofType->(fofType->(fofType->Prop)))
% 2.17/2.77 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) sumprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((sumprop1 X0) X1) X2) X3)))))) of role definition named def_sumprop
% 2.17/2.77 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) sumprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((sumprop1 X0) X1) X2) X3))))))
% 2.17/2.77 Defined: sumprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((sumprop1 X0) X1) X2) X3)))))
% 2.17/2.77 FOF formula (<kernel.Constant object at 0x2aefba2c0518>, <kernel.DependentProduct object at 0x2aefbac97cf8>) of role type named typ_sum
% 2.17/2.77 Using role type
% 2.17/2.77 Declaring sum:(fofType->(fofType->fofType))
% 2.17/2.77 FOF formula (((eq (fofType->(fofType->fofType))) sum) (fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((sumprop X0) X1)))) of role definition named def_sum
% 2.17/2.77 A new definition: (((eq (fofType->(fofType->fofType))) sum) (fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((sumprop X0) X1))))
% 2.17/2.77 Defined: sum:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((sumprop X0) X1)))
% 2.17/2.77 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_pl X2) X3)) ((sum X0) X1))))))))))))) of role axiom named satz129a
% 2.17/2.77 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_pl X2) X3)) ((sum X0) X1)))))))))))))
% 2.17/2.77 FOF formula (<kernel.Constant object at 0x2aefbac97b48>, <kernel.DependentProduct object at 0x2aefbac97d88>) of role type named typ_d_3129_z1
% 2.17/2.77 Using role type
% 2.17/2.77 Declaring d_3129_z1:(fofType->(fofType->(fofType->fofType)))
% 2.17/2.77 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) d_3129_z1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X0) ((rt_pl X1) X2)))) of role definition named def_d_3129_z1
% 2.17/2.77 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) d_3129_z1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X0) ((rt_pl X1) X2))))
% 2.25/2.78 Defined: d_3129_z1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X0) ((rt_pl X1) X2)))
% 2.25/2.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((sum X0) X1)))))) of role axiom named satz129
% 2.25/2.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((sum X0) X1))))))
% 2.25/2.78 FOF formula (<kernel.Constant object at 0x2aefbac97368>, <kernel.DependentProduct object at 0x2aefbac978c0>) of role type named typ_rp_pl
% 2.25/2.78 Using role type
% 2.25/2.78 Declaring rp_pl:(fofType->(fofType->fofType))
% 2.25/2.78 FOF formula (((eq (fofType->(fofType->fofType))) rp_pl) (fun (X0:fofType) (X1:fofType)=> (cutof ((sum X0) X1)))) of role definition named def_rp_pl
% 2.25/2.78 A new definition: (((eq (fofType->(fofType->fofType))) rp_pl) (fun (X0:fofType) (X1:fofType)=> (cutof ((sum X0) X1))))
% 2.25/2.78 Defined: rp_pl:=(fun (X0:fofType) (X1:fofType)=> (cutof ((sum X0) X1)))
% 2.25/2.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_pl X0) X1)) ((rp_pl X1) X0)))))) of role axiom named satz130
% 2.25/2.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_pl X0) X1)) ((rp_pl X1) X0))))))
% 2.25/2.78 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_pl ((rp_pl X0) X1)) X2)) ((rp_pl X0) ((rp_pl X1) X2))))))))) of role axiom named satz131
% 2.25/2.78 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_pl ((rp_pl X0) X1)) X2)) ((rp_pl X0) ((rp_pl X1) X2)))))))))
% 2.25/2.78 FOF formula (<kernel.Constant object at 0x2aefbac97d88>, <kernel.DependentProduct object at 0x2aefbac97dd0>) of role type named typ_d_3132_prop1
% 2.25/2.78 Using role type
% 2.25/2.78 Declaring d_3132_prop1:(fofType->(fofType->(fofType->Prop)))
% 2.25/2.78 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_3132_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((lrt X0) X1)) ((urt X0) X2)))) of role definition named def_d_3132_prop1
% 2.25/2.78 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_3132_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((lrt X0) X1)) ((urt X0) X2))))
% 2.25/2.78 Defined: d_3132_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((lrt X0) X1)) ((urt X0) X2)))
% 2.25/2.78 FOF formula (<kernel.Constant object at 0x2aefbac97dd0>, <kernel.DependentProduct object at 0x2aefbac976c8>) of role type named typ_d_3132_prop2
% 2.25/2.78 Using role type
% 2.25/2.78 Declaring d_3132_prop2:(fofType->(fofType->(fofType->(fofType->Prop))))
% 2.25/2.78 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) d_3132_prop2) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((rt_is ((rt_mn X3) X2)) X1))) of role definition named def_d_3132_prop2
% 2.25/2.78 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) d_3132_prop2) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((rt_is ((rt_mn X3) X2)) X1)))
% 2.25/2.78 Defined: d_3132_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((rt_is ((rt_mn X3) X2)) X1))
% 2.25/2.78 FOF formula (<kernel.Constant object at 0x2aefbac976c8>, <kernel.DependentProduct object at 0x2aefbac97518>) of role type named typ_d_3132_prop3
% 2.25/2.78 Using role type
% 2.25/2.78 Declaring d_3132_prop3:(fofType->(fofType->(fofType->(fofType->Prop))))
% 2.25/2.78 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) d_3132_prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((d_3132_prop1 X0) X2) X3)) ((((d_3132_prop1 X0) X2) X3)->((((d_3132_prop2 X0) X1) X2) X3))))) of role definition named def_d_3132_prop3
% 2.25/2.78 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) d_3132_prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((d_3132_prop1 X0) X2) X3)) ((((d_3132_prop1 X0) X2) X3)->((((d_3132_prop2 X0) X1) X2) X3)))))
% 2.27/2.80 Defined: d_3132_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((d_3132_prop1 X0) X2) X3)) ((((d_3132_prop1 X0) X2) X3)->((((d_3132_prop2 X0) X1) X2) X3))))
% 2.27/2.80 FOF formula (<kernel.Constant object at 0x2aefbac97518>, <kernel.DependentProduct object at 0x2aefbac97f80>) of role type named typ_d_3132_prop4
% 2.27/2.80 Using role type
% 2.27/2.80 Declaring d_3132_prop4:(fofType->(fofType->Prop))
% 2.27/2.80 FOF formula (((eq (fofType->(fofType->Prop))) d_3132_prop4) (fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (((d_3132_prop3 X0) X1) X2)))))) of role definition named def_d_3132_prop4
% 2.27/2.80 A new definition: (((eq (fofType->(fofType->Prop))) d_3132_prop4) (fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (((d_3132_prop3 X0) X1) X2))))))
% 2.27/2.80 Defined: d_3132_prop4:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (((d_3132_prop3 X0) X1) X2)))))
% 2.27/2.80 FOF formula (<kernel.Constant object at 0x2aefbac97f80>, <kernel.DependentProduct object at 0x2aefbac97488>) of role type named typ_d_3132_u0
% 2.27/2.80 Using role type
% 2.27/2.80 Declaring d_3132_u0:(fofType->(fofType->fofType))
% 2.27/2.80 FOF formula (((eq (fofType->(fofType->fofType))) d_3132_u0) (fun (X0:fofType) (X1:fofType)=> ((rt_pl X1) X0))) of role definition named def_d_3132_u0
% 2.27/2.80 A new definition: (((eq (fofType->(fofType->fofType))) d_3132_u0) (fun (X0:fofType) (X1:fofType)=> ((rt_pl X1) X0)))
% 2.27/2.80 Defined: d_3132_u0:=(fun (X0:fofType) (X1:fofType)=> ((rt_pl X1) X0))
% 2.27/2.80 FOF formula (<kernel.Constant object at 0x2aefbac97488>, <kernel.DependentProduct object at 0x2aefbac97290>) of role type named typ_um10
% 2.27/2.80 Using role type
% 2.27/2.80 Declaring um10:(fofType->fofType)
% 2.27/2.80 FOF formula (((eq (fofType->fofType)) um10) (fun (X0:fofType)=> ((rt_mn (rtofn X0)) d_1rt))) of role definition named def_um10
% 2.27/2.80 A new definition: (((eq (fofType->fofType)) um10) (fun (X0:fofType)=> ((rt_mn (rtofn X0)) d_1rt)))
% 2.27/2.80 Defined: um10:=(fun (X0:fofType)=> ((rt_mn (rtofn X0)) d_1rt))
% 2.27/2.80 FOF formula (<kernel.Constant object at 0x2aefbac97290>, <kernel.DependentProduct object at 0x2aefbac976c8>) of role type named typ_um1
% 2.27/2.80 Using role type
% 2.27/2.80 Declaring um1:(fofType->fofType)
% 2.27/2.80 FOF formula (((eq (fofType->fofType)) um1) (fun (X0:fofType)=> (nofrt (um10 X0)))) of role definition named def_um1
% 2.27/2.80 A new definition: (((eq (fofType->fofType)) um1) (fun (X0:fofType)=> (nofrt (um10 X0))))
% 2.27/2.80 Defined: um1:=(fun (X0:fofType)=> (nofrt (um10 X0)))
% 2.27/2.80 FOF formula (<kernel.Constant object at 0x2aefbac976c8>, <kernel.DependentProduct object at 0x2aefbac97878>) of role type named typ_d_3132_v0
% 2.27/2.80 Using role type
% 2.27/2.80 Declaring d_3132_v0:(fofType->(fofType->(fofType->fofType)))
% 2.27/2.80 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) d_3132_v0) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (um10 X2)) X0)))) of role definition named def_d_3132_v0
% 2.27/2.80 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) d_3132_v0) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (um10 X2)) X0))))
% 2.27/2.80 Defined: d_3132_v0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (um10 X2)) X0)))
% 2.27/2.80 FOF formula (<kernel.Constant object at 0x2aefbac97878>, <kernel.DependentProduct object at 0x2aefbac974d0>) of role type named typ_d_3132_w0
% 2.27/2.80 Using role type
% 2.27/2.80 Declaring d_3132_w0:(fofType->(fofType->(fofType->fofType)))
% 2.27/2.80 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) d_3132_w0) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (rtofn X2)) X0)))) of role definition named def_d_3132_w0
% 2.27/2.80 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) d_3132_w0) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (rtofn X2)) X0))))
% 2.27/2.80 Defined: d_3132_w0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (rtofn X2)) X0)))
% 2.27/2.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (fun (X3:fofType)=> ((d_and ((d_and ((lrt X0) X2)) ((urt X0) X3))) (((d_and ((lrt X0) X2)) ((urt X0) X3))->((rt_is ((rt_mn X3) X2)) X1))))))))))) of role axiom named satz132
% 2.28/2.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (fun (X3:fofType)=> ((d_and ((d_and ((lrt X0) X2)) ((urt X0) X3))) (((d_and ((lrt X0) X2)) ((urt X0) X3))->((rt_is ((rt_mn X3) X2)) X1)))))))))))
% 2.28/2.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (forall (X1:Prop), ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((lrt X0) X3)->((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((urt X0) X4)->(((rt_is ((rt_mn X4) X3)) X2)->X1)))))))->X1)))))) of role axiom named satz132app
% 2.28/2.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (forall (X1:Prop), ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((lrt X0) X3)->((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((urt X0) X4)->(((rt_is ((rt_mn X4) X3)) X2)->X1)))))))->X1))))))
% 2.28/2.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_more ((rp_pl X0) X1)) X0))))) of role axiom named satz133
% 2.28/2.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_more ((rp_pl X0) X1)) X0)))))
% 2.28/2.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_less X0) ((rp_pl X0) X1)))))) of role axiom named satz133a
% 2.28/2.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_less X0) ((rp_pl X0) X1))))))
% 2.28/2.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))))))))) of role axiom named satz134
% 2.28/2.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 2.28/2.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))))))))) of role axiom named satz135b
% 2.28/2.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 2.28/2.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))))))))) of role axiom named satz135c
% 2.28/2.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 2.28/2.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))))))))) of role axiom named satz135d
% 2.28/2.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 2.28/2.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))))))))) of role axiom named satz135e
% 2.28/2.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 2.28/2.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))))))))) of role axiom named satz135f
% 2.28/2.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 2.28/2.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz135g
% 2.28/2.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.28/2.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X2) X0)) ((rp_pl X3) X1)))))))))))) of role axiom named satz135h
% 2.28/2.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 2.28/2.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz135j
% 2.28/2.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.28/2.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X2) X0)) ((rp_pl X3) X1)))))))))))) of role axiom named satz135k
% 2.28/2.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 2.28/2.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_more X0) X1)))))))) of role axiom named satz136a
% 2.28/2.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_more X0) X1))))))))
% 2.28/2.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_is X0) X1)))))))) of role axiom named satz136b
% 2.28/2.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_is X0) X1))))))))
% 2.28/2.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_less X0) X1)))))))) of role axiom named satz136c
% 2.28/2.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_less X0) X1))))))))
% 2.28/2.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_more X0) X1)))))))) of role axiom named satz136d
% 2.28/2.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_more X0) X1))))))))
% 2.28/2.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_is X0) X1)))))))) of role axiom named satz136e
% 2.28/2.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_is X0) X1))))))))
% 2.28/2.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_less X0) X1)))))))) of role axiom named satz136f
% 2.28/2.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_less X0) X1))))))))
% 2.28/2.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz137
% 2.28/2.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.28/2.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz137a
% 2.28/2.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.28/2.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz138a
% 2.28/2.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.28/2.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz138b
% 2.28/2.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.28/2.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz138c
% 2.28/2.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.28/2.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz138d
% 2.28/2.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.38/2.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz139
% 2.38/2.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.38/2.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))) of role axiom named satz139a
% 2.38/2.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 2.38/2.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_pl X1) X2)) X0)->(((rp_is ((rp_pl X1) X3)) X0)->((rp_is X2) X3))))))))))) of role axiom named satz140b
% 2.38/2.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_pl X1) X2)) X0)->(((rp_is ((rp_pl X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 2.38/2.92 FOF formula (<kernel.Constant object at 0x2aefbd966440>, <kernel.DependentProduct object at 0x2aefbd966560>) of role type named typ_diffprop1
% 2.38/2.92 Using role type
% 2.38/2.92 Declaring diffprop1:(fofType->(fofType->(fofType->Prop)))
% 2.38/2.92 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) diffprop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((rt_more X1) X2)) (((rt_more X1) X2)->((rt_is X0) ((rt_mn X1) X2)))))) of role definition named def_diffprop1
% 2.38/2.92 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) diffprop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((rt_more X1) X2)) (((rt_more X1) X2)->((rt_is X0) ((rt_mn X1) X2))))))
% 2.38/2.92 Defined: diffprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((rt_more X1) X2)) (((rt_more X1) X2)->((rt_is X0) ((rt_mn X1) X2)))))
% 2.38/2.92 FOF formula (<kernel.Constant object at 0x2aefbd966560>, <kernel.DependentProduct object at 0x2aefbd966b00>) of role type named typ_diffprop2
% 2.38/2.92 Using role type
% 2.38/2.92 Declaring diffprop2:(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 2.38/2.92 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) diffprop2) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((urt X1) X4)) (((diffprop1 X2) X3) X4)))) of role definition named def_diffprop2
% 2.38/2.92 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) diffprop2) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((urt X1) X4)) (((diffprop1 X2) X3) X4))))
% 2.38/2.92 Defined: diffprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((urt X1) X4)) (((diffprop1 X2) X3) X4)))
% 2.38/2.94 FOF formula (<kernel.Constant object at 0x2aefbd966b00>, <kernel.DependentProduct object at 0x2aefbd9662d8>) of role type named typ_rp_diffprop
% 2.38/2.94 Using role type
% 2.38/2.94 Declaring rp_diffprop:(fofType->(fofType->(fofType->Prop)))
% 2.38/2.94 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) rp_diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((diffprop2 X0) X1) X2) X3)))))) of role definition named def_rp_diffprop
% 2.38/2.94 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) rp_diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((diffprop2 X0) X1) X2) X3))))))
% 2.38/2.94 Defined: rp_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((diffprop2 X0) X1) X2) X3)))))
% 2.38/2.94 FOF formula (<kernel.Constant object at 0x2aefbd9662d8>, <kernel.DependentProduct object at 0x2aefbd966680>) of role type named typ_diff
% 2.38/2.94 Using role type
% 2.38/2.94 Declaring diff:(fofType->(fofType->fofType))
% 2.38/2.94 FOF formula (((eq (fofType->(fofType->fofType))) diff) (fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((rp_diffprop X0) X1)))) of role definition named def_diff
% 2.38/2.94 A new definition: (((eq (fofType->(fofType->fofType))) diff) (fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((rp_diffprop X0) X1))))
% 2.38/2.94 Defined: diff:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((rp_diffprop X0) X1)))
% 2.38/2.94 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(cutprop ((diff X0) X1))))))) of role axiom named satz140h
% 2.38/2.94 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(cutprop ((diff X0) X1)))))))
% 2.38/2.94 FOF formula (<kernel.Constant object at 0x2aefbd966200>, <kernel.DependentProduct object at 0x2aefbd966bd8>) of role type named typ_chi
% 2.38/2.94 Using role type
% 2.38/2.94 Declaring chi:(fofType->(fofType->fofType))
% 2.38/2.94 FOF formula (((eq (fofType->(fofType->fofType))) chi) (fun (X0:fofType) (X1:fofType)=> (cutof ((diff X0) X1)))) of role definition named def_chi
% 2.38/2.94 A new definition: (((eq (fofType->(fofType->fofType))) chi) (fun (X0:fofType) (X1:fofType)=> (cutof ((diff X0) X1))))
% 2.38/2.94 Defined: chi:=(fun (X0:fofType) (X1:fofType)=> (cutof ((diff X0) X1)))
% 2.38/2.94 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_some (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))))))) of role axiom named satz140a
% 2.38/2.94 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_some (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 2.38/2.94 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_one (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))))))) of role axiom named satz140
% 2.38/2.94 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_one (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 2.38/2.94 FOF formula (<kernel.Constant object at 0x2aefbd966680>, <kernel.DependentProduct object at 0x2aefbd9666c8>) of role type named typ_rp_mn
% 2.38/2.94 Using role type
% 2.38/2.94 Declaring rp_mn:(fofType->(fofType->fofType))
% 2.38/2.94 FOF formula (((eq (fofType->(fofType->fofType))) rp_mn) (fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))) of role definition named def_rp_mn
% 2.38/2.94 A new definition: (((eq (fofType->(fofType->fofType))) rp_mn) (fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))))
% 2.38/2.94 Defined: rp_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))
% 2.38/2.94 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl X1) ((rp_mn X0) X1))) X0)))))) of role axiom named satz140c
% 2.38/2.96 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl X1) ((rp_mn X0) X1))) X0))))))
% 2.38/2.96 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl X1) ((rp_mn X0) X1)))))))) of role axiom named satz140d
% 2.38/2.96 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl X1) ((rp_mn X0) X1))))))))
% 2.38/2.96 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl ((rp_mn X0) X1)) X1)) X0)))))) of role axiom named satz140e
% 2.38/2.96 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl ((rp_mn X0) X1)) X1)) X0))))))
% 2.38/2.96 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl ((rp_mn X0) X1)) X1))))))) of role axiom named satz140f
% 2.38/2.96 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl ((rp_mn X0) X1)) X1)))))))
% 2.38/2.96 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_is ((rp_pl X1) X2)) X0)->((rp_is X2) ((rp_mn X0) X1)))))))))) of role axiom named satz140g
% 2.38/2.96 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_is ((rp_pl X1) X2)) X0)->((rp_is X2) ((rp_mn X0) X1))))))))))
% 2.38/2.96 FOF formula (<kernel.Constant object at 0x2aefbd966518>, <kernel.DependentProduct object at 0x2aefbd9660e0>) of role type named typ_prodprop1
% 2.38/2.96 Using role type
% 2.38/2.96 Declaring prodprop1:(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 2.38/2.96 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) prodprop1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_ts X3) X4))))) of role definition named def_prodprop1
% 2.38/2.96 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) prodprop1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_ts X3) X4)))))
% 2.38/2.96 Defined: prodprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_ts X3) X4))))
% 2.38/2.96 FOF formula (<kernel.Constant object at 0x2aefbd9660e0>, <kernel.DependentProduct object at 0x2aefbd966ea8>) of role type named typ_prodprop
% 2.38/2.96 Using role type
% 2.38/2.96 Declaring prodprop:(fofType->(fofType->(fofType->Prop)))
% 2.38/2.96 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) prodprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((prodprop1 X0) X1) X2) X3)))))) of role definition named def_prodprop
% 2.38/2.96 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) prodprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((prodprop1 X0) X1) X2) X3))))))
% 2.38/2.96 Defined: prodprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((prodprop1 X0) X1) X2) X3)))))
% 2.38/2.96 FOF formula (<kernel.Constant object at 0x2aefbd966ea8>, <kernel.DependentProduct object at 0x2aefbd9661b8>) of role type named typ_prod
% 2.38/2.98 Using role type
% 2.38/2.98 Declaring prod:(fofType->(fofType->fofType))
% 2.38/2.98 FOF formula (((eq (fofType->(fofType->fofType))) prod) (fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((prodprop X0) X1)))) of role definition named def_prod
% 2.38/2.98 A new definition: (((eq (fofType->(fofType->fofType))) prod) (fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((prodprop X0) X1))))
% 2.38/2.98 Defined: prod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((prodprop X0) X1)))
% 2.38/2.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_ts X2) X3)) ((prod X0) X1))))))))))))) of role axiom named satz141a
% 2.38/2.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_ts X2) X3)) ((prod X0) X1)))))))))))))
% 2.38/2.98 FOF formula (<kernel.Constant object at 0x2aefbd966f38>, <kernel.DependentProduct object at 0x2aefbd9663b0>) of role type named typ_d_4141_v0
% 2.38/2.98 Using role type
% 2.38/2.98 Declaring d_4141_v0:(fofType->(fofType->fofType))
% 2.38/2.98 FOF formula (((eq (fofType->(fofType->fofType))) d_4141_v0) (fun (X0:fofType) (X1:fofType)=> ((rt_ts ((rt_ov d_1rt) X1)) X0))) of role definition named def_d_4141_v0
% 2.38/2.98 A new definition: (((eq (fofType->(fofType->fofType))) d_4141_v0) (fun (X0:fofType) (X1:fofType)=> ((rt_ts ((rt_ov d_1rt) X1)) X0)))
% 2.38/2.98 Defined: d_4141_v0:=(fun (X0:fofType) (X1:fofType)=> ((rt_ts ((rt_ov d_1rt) X1)) X0))
% 2.38/2.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov d_1rt) X1)) X0)) ((rt_ov X0) X1)))))) of role axiom named satz141b
% 2.38/2.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov d_1rt) X1)) X0)) ((rt_ov X0) X1))))))
% 2.38/2.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ov X0) X1)) ((rt_ts ((rt_ov d_1rt) X1)) X0)))))) of role axiom named satz141c
% 2.38/2.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ov X0) X1)) ((rt_ts ((rt_ov d_1rt) X1)) X0))))))
% 2.38/2.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((prod X0) X1)))))) of role axiom named satz141
% 2.38/2.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((prod X0) X1))))))
% 2.38/2.98 FOF formula (<kernel.Constant object at 0x2aefbd966878>, <kernel.DependentProduct object at 0x2aefbd9662d8>) of role type named typ_rp_ts
% 2.38/2.98 Using role type
% 2.38/2.98 Declaring rp_ts:(fofType->(fofType->fofType))
% 2.38/2.98 FOF formula (((eq (fofType->(fofType->fofType))) rp_ts) (fun (X0:fofType) (X1:fofType)=> (cutof ((prod X0) X1)))) of role definition named def_rp_ts
% 2.38/2.98 A new definition: (((eq (fofType->(fofType->fofType))) rp_ts) (fun (X0:fofType) (X1:fofType)=> (cutof ((prod X0) X1))))
% 2.38/2.98 Defined: rp_ts:=(fun (X0:fofType) (X1:fofType)=> (cutof ((prod X0) X1)))
% 2.38/2.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) ((rp_ts X1) X0)))))) of role axiom named satz142
% 2.38/2.98 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) ((rp_ts X1) X0))))))
% 2.38/2.98 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts ((rp_ts X0) X1)) X2)) ((rp_ts X0) ((rp_ts X1) X2))))))))) of role axiom named satz143
% 2.47/3.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts ((rp_ts X0) X1)) X2)) ((rp_ts X0) ((rp_ts X1) X2)))))))))
% 2.47/3.00 FOF formula (<kernel.Constant object at 0x2aefbd9663b0>, <kernel.DependentProduct object at 0x2aefbd966ea8>) of role type named typ_d_4144_x2
% 2.47/3.00 Using role type
% 2.47/3.00 Declaring d_4144_x2:(fofType->(fofType->fofType))
% 2.47/3.00 FOF formula (((eq (fofType->(fofType->fofType))) d_4144_x2) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_moreis X0) X1)) rat) X0) X1))) of role definition named def_d_4144_x2
% 2.47/3.00 A new definition: (((eq (fofType->(fofType->fofType))) d_4144_x2) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_moreis X0) X1)) rat) X0) X1)))
% 2.47/3.00 Defined: d_4144_x2:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_moreis X0) X1)) rat) X0) X1))
% 2.47/3.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts X0) ((rp_pl X1) X2))) ((rp_pl ((rp_ts X0) X1)) ((rp_ts X0) X2))))))))) of role axiom named satz144
% 2.47/3.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts X0) ((rp_pl X1) X2))) ((rp_pl ((rp_ts X0) X1)) ((rp_ts X0) X2)))))))))
% 2.47/3.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))))))))) of role axiom named satz145a
% 2.47/3.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 2.47/3.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))))))))) of role axiom named satz145b
% 2.47/3.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 2.47/3.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))))))))) of role axiom named satz145c
% 2.47/3.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 2.47/3.00 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))))))))) of role axiom named satz145d
% 2.47/3.00 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 2.47/3.03 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))))))))) of role axiom named satz145e
% 2.47/3.03 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 2.47/3.03 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))))))))) of role axiom named satz145f
% 2.47/3.03 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 2.47/3.03 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz145g
% 2.47/3.03 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.47/3.03 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X2) X0)) ((rp_ts X3) X1)))))))))))) of role axiom named satz145h
% 2.47/3.03 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 2.47/3.03 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz145j
% 2.47/3.03 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.47/3.03 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X2) X0)) ((rp_ts X3) X1)))))))))))) of role axiom named satz145k
% 2.47/3.03 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 2.47/3.06 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_more X0) X1)))))))) of role axiom named satz146a
% 2.47/3.06 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_more X0) X1))))))))
% 2.47/3.06 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_is X0) X1)))))))) of role axiom named satz146b
% 2.47/3.06 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_is X0) X1))))))))
% 2.47/3.06 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_less X0) X1)))))))) of role axiom named satz146c
% 2.47/3.06 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_less X0) X1))))))))
% 2.47/3.06 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_more X0) X1)))))))) of role axiom named satz146d
% 2.47/3.06 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_more X0) X1))))))))
% 2.47/3.06 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_is X0) X1)))))))) of role axiom named satz146e
% 2.47/3.06 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_is X0) X1))))))))
% 2.47/3.06 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_less X0) X1)))))))) of role axiom named satz146f
% 2.47/3.06 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_less X0) X1))))))))
% 2.47/3.06 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz147
% 2.47/3.06 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.47/3.08 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz147a
% 2.47/3.08 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.47/3.08 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz148a
% 2.47/3.08 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.47/3.08 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz148b
% 2.47/3.08 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.47/3.08 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz148c
% 2.47/3.08 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.47/3.08 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz148d
% 2.47/3.08 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.57/3.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz149
% 2.57/3.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.57/3.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))) of role axiom named satz149a
% 2.57/3.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 2.57/3.10 FOF formula (<kernel.Constant object at 0x2aefbd942878>, <kernel.DependentProduct object at 0x2aefbd9427a0>) of role type named typ_ratset
% 2.57/3.10 Using role type
% 2.57/3.10 Declaring ratset:(fofType->fofType)
% 2.57/3.10 FOF formula (((eq (fofType->fofType)) ratset) (fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rt_less X1) X0))))) of role definition named def_ratset
% 2.57/3.10 A new definition: (((eq (fofType->fofType)) ratset) (fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rt_less X1) X0)))))
% 2.57/3.10 Defined: ratset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rt_less X1) X0))))
% 2.57/3.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (cutprop (ratset X0)))) of role axiom named satz150
% 2.57/3.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (cutprop (ratset X0))))
% 2.57/3.10 FOF formula (<kernel.Constant object at 0x2aefbd942830>, <kernel.DependentProduct object at 0x2aefbd9421b8>) of role type named typ_rpofrt
% 2.57/3.10 Using role type
% 2.57/3.10 Declaring rpofrt:(fofType->fofType)
% 2.57/3.10 FOF formula (((eq (fofType->fofType)) rpofrt) (fun (X0:fofType)=> (cutof (ratset X0)))) of role definition named def_rpofrt
% 2.57/3.10 A new definition: (((eq (fofType->fofType)) rpofrt) (fun (X0:fofType)=> (cutof (ratset X0))))
% 2.57/3.10 Defined: rpofrt:=(fun (X0:fofType)=> (cutof (ratset X0)))
% 2.57/3.10 FOF formula (<kernel.Constant object at 0x2aefbd9421b8>, <kernel.Single object at 0x2aefbd942830>) of role type named typ_d_1rp
% 2.57/3.10 Using role type
% 2.57/3.10 Declaring d_1rp:fofType
% 2.57/3.10 FOF formula (((eq fofType) d_1rp) (rpofrt d_1rt)) of role definition named def_d_1rp
% 2.57/3.10 A new definition: (((eq fofType) d_1rp) (rpofrt d_1rt))
% 2.57/3.10 Defined: d_1rp:=(rpofrt d_1rt)
% 2.57/3.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) d_1rp)) X0))) of role axiom named satz151
% 2.57/3.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) d_1rp)) X0)))
% 2.57/3.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts X0) d_1rp)))) of role axiom named satz151a
% 2.57/3.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts X0) d_1rp))))
% 2.57/3.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts d_1rp) X0)) X0))) of role axiom named satz151b
% 2.57/3.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts d_1rp) X0)) X0)))
% 2.57/3.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts d_1rp) X0)))) of role axiom named satz151c
% 2.57/3.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts d_1rp) X0))))
% 2.58/3.12 FOF formula (<kernel.Constant object at 0x2aefbd942908>, <kernel.DependentProduct object at 0x2aefbd942560>) of role type named typ_invprop1
% 2.58/3.12 Using role type
% 2.58/3.12 Declaring invprop1:(fofType->(fofType->(fofType->Prop)))
% 2.58/3.12 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) invprop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((urt X0) X2)) ((rt_less X2) X1)))) of role definition named def_invprop1
% 2.58/3.12 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) invprop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((urt X0) X2)) ((rt_less X2) X1))))
% 2.58/3.12 Defined: invprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((urt X0) X2)) ((rt_less X2) X1)))
% 2.58/3.12 FOF formula (<kernel.Constant object at 0x2aefbd942560>, <kernel.DependentProduct object at 0x2aefbd942050>) of role type named typ_invprop2
% 2.58/3.12 Using role type
% 2.58/3.12 Declaring invprop2:(fofType->(fofType->(fofType->Prop)))
% 2.58/3.12 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) invprop2) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 ((urt X0) X2)) (rt_some ((invprop1 X0) X2))) ((rt_is X1) ((rt_ov d_1rt) X2))))) of role definition named def_invprop2
% 2.58/3.12 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) invprop2) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 ((urt X0) X2)) (rt_some ((invprop1 X0) X2))) ((rt_is X1) ((rt_ov d_1rt) X2)))))
% 2.58/3.12 Defined: invprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 ((urt X0) X2)) (rt_some ((invprop1 X0) X2))) ((rt_is X1) ((rt_ov d_1rt) X2))))
% 2.58/3.12 FOF formula (<kernel.Constant object at 0x2aefbd942050>, <kernel.DependentProduct object at 0x2aefbd942a28>) of role type named typ_invprop
% 2.58/3.12 Using role type
% 2.58/3.12 Declaring invprop:(fofType->(fofType->Prop))
% 2.58/3.12 FOF formula (((eq (fofType->(fofType->Prop))) invprop) (fun (X0:fofType) (X1:fofType)=> (rt_some ((invprop2 X0) X1)))) of role definition named def_invprop
% 2.58/3.12 A new definition: (((eq (fofType->(fofType->Prop))) invprop) (fun (X0:fofType) (X1:fofType)=> (rt_some ((invprop2 X0) X1))))
% 2.58/3.12 Defined: invprop:=(fun (X0:fofType) (X1:fofType)=> (rt_some ((invprop2 X0) X1)))
% 2.58/3.12 FOF formula (<kernel.Constant object at 0x2aefbd942a28>, <kernel.DependentProduct object at 0x2aefbd942560>) of role type named typ_inv
% 2.58/3.12 Using role type
% 2.58/3.12 Declaring inv:(fofType->fofType)
% 2.58/3.12 FOF formula (((eq (fofType->fofType)) inv) (fun (X0:fofType)=> ((d_Sep rat) (invprop X0)))) of role definition named def_inv
% 2.58/3.12 A new definition: (((eq (fofType->fofType)) inv) (fun (X0:fofType)=> ((d_Sep rat) (invprop X0))))
% 2.58/3.12 Defined: inv:=(fun (X0:fofType)=> ((d_Sep rat) (invprop X0)))
% 2.58/3.12 FOF formula (<kernel.Constant object at 0x2aefbd942560>, <kernel.DependentProduct object at 0x2aefbd942518>) of role type named typ_d_2x0
% 2.58/3.12 Using role type
% 2.58/3.12 Declaring d_2x0:(fofType->fofType)
% 2.58/3.12 FOF formula (((eq (fofType->fofType)) d_2x0) (fun (X0:fofType)=> ((rt_pl X0) X0))) of role definition named def_d_2x0
% 2.58/3.12 A new definition: (((eq (fofType->fofType)) d_2x0) (fun (X0:fofType)=> ((rt_pl X0) X0)))
% 2.58/3.12 Defined: d_2x0:=(fun (X0:fofType)=> ((rt_pl X0) X0))
% 2.58/3.12 FOF formula (<kernel.Constant object at 0x2aefbd942518>, <kernel.DependentProduct object at 0x2aefbd9426c8>) of role type named typ_d_4152_chi
% 2.58/3.12 Using role type
% 2.58/3.12 Declaring d_4152_chi:(fofType->fofType)
% 2.58/3.12 FOF formula (((eq (fofType->fofType)) d_4152_chi) (fun (X0:fofType)=> (cutof (inv X0)))) of role definition named def_d_4152_chi
% 2.58/3.12 A new definition: (((eq (fofType->fofType)) d_4152_chi) (fun (X0:fofType)=> (cutof (inv X0))))
% 2.58/3.12 Defined: d_4152_chi:=(fun (X0:fofType)=> (cutof (inv X0)))
% 2.58/3.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_some (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) d_1rp))))) of role axiom named satz152
% 2.58/3.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_some (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) d_1rp)))))
% 2.58/3.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->(((rp_is ((rp_ts X1) X3)) X0)->((rp_is X2) X3))))))))))) of role axiom named satz153b
% 2.58/3.14 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->(((rp_is ((rp_ts X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 2.58/3.14 FOF formula (<kernel.Constant object at 0x2aefbd942560>, <kernel.DependentProduct object at 0x2aefbd9426c8>) of role type named typ_d_4153_chi
% 2.58/3.14 Using role type
% 2.58/3.14 Declaring d_4153_chi:(fofType->(fofType->fofType))
% 2.58/3.14 FOF formula (((eq (fofType->(fofType->fofType))) d_4153_chi) (fun (X0:fofType) (X1:fofType)=> ((rp_ts X1) X0))) of role definition named def_d_4153_chi
% 2.58/3.14 A new definition: (((eq (fofType->(fofType->fofType))) d_4153_chi) (fun (X0:fofType) (X1:fofType)=> ((rp_ts X1) X0)))
% 2.58/3.14 Defined: d_4153_chi:=(fun (X0:fofType) (X1:fofType)=> ((rp_ts X1) X0))
% 2.58/3.14 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0))))))) of role axiom named satz153a
% 2.58/3.14 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 2.58/3.14 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_one (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0))))))) of role axiom named satz153
% 2.58/3.14 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_one (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 2.58/3.14 FOF formula (<kernel.Constant object at 0x2aefbd9422d8>, <kernel.DependentProduct object at 0x2aefbd942050>) of role type named typ_rp_ov
% 2.58/3.14 Using role type
% 2.58/3.14 Declaring rp_ov:(fofType->(fofType->fofType))
% 2.58/3.14 FOF formula (((eq (fofType->(fofType->fofType))) rp_ov) (fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0))))) of role definition named def_rp_ov
% 2.58/3.14 A new definition: (((eq (fofType->(fofType->fofType))) rp_ov) (fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))
% 2.58/3.14 Defined: rp_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0))))
% 2.58/3.14 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) ((rp_ov X0) X1))) X0))))) of role axiom named satz153c
% 2.58/3.14 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) ((rp_ov X0) X1))) X0)))))
% 2.58/3.14 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts X1) ((rp_ov X0) X1))))))) of role axiom named satz153d
% 2.58/3.14 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts X1) ((rp_ov X0) X1)))))))
% 2.58/3.14 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts ((rp_ov X0) X1)) X1)) X0))))) of role axiom named satz153e
% 2.58/3.14 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts ((rp_ov X0) X1)) X1)) X0)))))
% 2.58/3.14 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts ((rp_ov X0) X1)) X1)))))) of role axiom named satz153f
% 2.58/3.14 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts ((rp_ov X0) X1)) X1))))))
% 2.58/3.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->((rp_is X2) ((rp_ov X0) X1))))))))) of role axiom named satz153g
% 2.58/3.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->((rp_is X2) ((rp_ov X0) X1)))))))))
% 2.58/3.16 FOF formula (<kernel.Constant object at 0x2aefbd9426c8>, <kernel.DependentProduct object at 0x2aefbd9429e0>) of role type named typ_ratrp
% 2.58/3.16 Using role type
% 2.58/3.16 Declaring ratrp:(fofType->Prop)
% 2.58/3.16 FOF formula (((eq (fofType->Prop)) ratrp) (((image rat) cut) ((d_Sigma rat) rpofrt))) of role definition named def_ratrp
% 2.58/3.16 A new definition: (((eq (fofType->Prop)) ratrp) (((image rat) cut) ((d_Sigma rat) rpofrt)))
% 2.58/3.16 Defined: ratrp:=(((image rat) cut) ((d_Sigma rat) rpofrt))
% 2.58/3.16 FOF formula (<kernel.Constant object at 0x2aefbd9429e0>, <kernel.DependentProduct object at 0x2aefb2962320>) of role type named typ_rpofnt
% 2.58/3.16 Using role type
% 2.58/3.16 Declaring rpofnt:(fofType->fofType)
% 2.58/3.16 FOF formula (((eq (fofType->fofType)) rpofnt) (fun (X0:fofType)=> (rpofrt (rtofn X0)))) of role definition named def_rpofnt
% 2.58/3.16 A new definition: (((eq (fofType->fofType)) rpofnt) (fun (X0:fofType)=> (rpofrt (rtofn X0))))
% 2.58/3.16 Defined: rpofnt:=(fun (X0:fofType)=> (rpofrt (rtofn X0)))
% 2.58/3.16 FOF formula (<kernel.Constant object at 0x2aefbd942b48>, <kernel.DependentProduct object at 0x2aefb2962098>) of role type named typ_natrp
% 2.58/3.16 Using role type
% 2.58/3.16 Declaring natrp:(fofType->Prop)
% 2.58/3.16 FOF formula (((eq (fofType->Prop)) natrp) (((image nat) cut) ((d_Sigma nat) rpofnt))) of role definition named def_natrp
% 2.58/3.16 A new definition: (((eq (fofType->Prop)) natrp) (((image nat) cut) ((d_Sigma nat) rpofnt)))
% 2.58/3.16 Defined: natrp:=(((image nat) cut) ((d_Sigma nat) rpofnt))
% 2.58/3.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_more (rpofrt X0)) (rpofrt X1))))))) of role axiom named satz154a
% 2.58/3.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_more (rpofrt X0)) (rpofrt X1)))))))
% 2.58/3.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rp_is (rpofrt X0)) (rpofrt X1))))))) of role axiom named satz154b
% 2.58/3.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rp_is (rpofrt X0)) (rpofrt X1)))))))
% 2.58/3.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rp_less (rpofrt X0)) (rpofrt X1))))))) of role axiom named satz154c
% 2.58/3.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rp_less (rpofrt X0)) (rpofrt X1)))))))
% 2.58/3.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_more (rpofrt X0)) (rpofrt X1))->((rt_more X0) X1)))))) of role axiom named satz154d
% 2.58/3.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_more (rpofrt X0)) (rpofrt X1))->((rt_more X0) X1))))))
% 2.58/3.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_is (rpofrt X0)) (rpofrt X1))->((rt_is X0) X1)))))) of role axiom named satz154e
% 2.58/3.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_is (rpofrt X0)) (rpofrt X1))->((rt_is X0) X1))))))
% 2.58/3.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X0)) (rpofrt X1))->((rt_less X0) X1)))))) of role axiom named satz154f
% 2.58/3.18 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X0)) (rpofrt X1))->((rt_less X0) X1))))))
% 2.58/3.18 FOF formula (<kernel.Constant object at 0x2aefb29623f8>, <kernel.DependentProduct object at 0x2aefb2962680>) of role type named typ_rtofrp
% 2.58/3.18 Using role type
% 2.58/3.18 Declaring rtofrp:(fofType->fofType)
% 2.58/3.18 FOF formula (((eq (fofType->fofType)) rtofrp) (((soft rat) cut) ((d_Sigma rat) rpofrt))) of role definition named def_rtofrp
% 2.58/3.18 A new definition: (((eq (fofType->fofType)) rtofrp) (((soft rat) cut) ((d_Sigma rat) rpofrt)))
% 2.58/3.18 Defined: rtofrp:=(((soft rat) cut) ((d_Sigma rat) rpofrt))
% 2.58/3.18 FOF formula (<kernel.Constant object at 0x2aefb29623b0>, <kernel.DependentProduct object at 0x2aefb2962680>) of role type named typ_ntofrp
% 2.58/3.18 Using role type
% 2.58/3.18 Declaring ntofrp:(fofType->fofType)
% 2.58/3.18 FOF formula (((eq (fofType->fofType)) ntofrp) (((soft nat) cut) ((d_Sigma nat) rpofnt))) of role definition named def_ntofrp
% 2.58/3.18 A new definition: (((eq (fofType->fofType)) ntofrp) (((soft nat) cut) ((d_Sigma nat) rpofnt)))
% 2.58/3.18 Defined: ntofrp:=(((soft nat) cut) ((d_Sigma nat) rpofnt))
% 2.58/3.18 FOF formula (<kernel.Constant object at 0x2aefb29623f8>, <kernel.DependentProduct object at 0x2aefb2962050>) of role type named typ_u01
% 2.58/3.18 Using role type
% 2.58/3.18 Declaring u01:(fofType->(fofType->(fofType->fofType)))
% 2.58/3.18 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) u01) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X2) ((rt_pl X0) X1)))) of role definition named def_u01
% 2.58/3.18 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) u01) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X2) ((rt_pl X0) X1))))
% 2.58/3.18 Defined: u01:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X2) ((rt_pl X0) X1)))
% 2.58/3.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_pl X0) X1))) ((rp_pl (rpofrt X0)) (rpofrt X1))))))) of role axiom named satz155a
% 2.58/3.18 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_pl X0) X1))) ((rp_pl (rpofrt X0)) (rpofrt X1)))))))
% 2.58/3.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_is (rpofrt ((rt_mn X0) X1))) ((rp_mn (rpofrt X0)) (rpofrt X1)))))))) of role axiom named satz155b
% 2.58/3.18 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_is (rpofrt ((rt_mn X0) X1))) ((rp_mn (rpofrt X0)) (rpofrt X1))))))))
% 2.58/3.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ts X0) X1))) ((rp_ts (rpofrt X0)) (rpofrt X1))))))) of role axiom named satz155c
% 2.58/3.18 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ts X0) X1))) ((rp_ts (rpofrt X0)) (rpofrt X1)))))))
% 2.58/3.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ov X0) X1))) ((rp_ov (rpofrt X0)) (rpofrt X1))))))) of role axiom named satz155d
% 2.58/3.18 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ov X0) X1))) ((rp_ov (rpofrt X0)) (rpofrt X1)))))))
% 2.58/3.18 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_pl X0) X1))) ((rp_pl (rpofnt X0)) (rpofnt X1))))))) of role axiom named satz155e
% 2.58/3.19 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_pl X0) X1))) ((rp_pl (rpofnt X0)) (rpofnt X1)))))))
% 2.58/3.19 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_ts X0) X1))) ((rp_ts (rpofnt X0)) (rpofnt X1))))))) of role axiom named satz155f
% 2.58/3.19 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_ts X0) X1))) ((rp_ts (rpofnt X0)) (rpofnt X1)))))))
% 2.58/3.19 FOF formula (<kernel.Constant object at 0x2aefb29625f0>, <kernel.Single object at 0x2aefb29623f8>) of role type named typ_nt_natt
% 2.58/3.19 Using role type
% 2.58/3.19 Declaring nt_natt:fofType
% 2.58/3.19 FOF formula (((eq fofType) nt_natt) ((d_Sep cut) natrp)) of role definition named def_nt_natt
% 2.58/3.19 A new definition: (((eq fofType) nt_natt) ((d_Sep cut) natrp))
% 2.58/3.19 Defined: nt_natt:=((d_Sep cut) natrp)
% 2.58/3.19 FOF formula (<kernel.Constant object at 0x2aefb29623f8>, <kernel.DependentProduct object at 0x2aefb2962ab8>) of role type named typ_nttofrp
% 2.58/3.19 Using role type
% 2.58/3.19 Declaring nttofrp:(fofType->fofType)
% 2.58/3.19 FOF formula (((eq (fofType->fofType)) nttofrp) ((out cut) natrp)) of role definition named def_nttofrp
% 2.58/3.19 A new definition: (((eq (fofType->fofType)) nttofrp) ((out cut) natrp))
% 2.58/3.19 Defined: nttofrp:=((out cut) natrp)
% 2.58/3.19 FOF formula (<kernel.Constant object at 0x2aefb2962ab8>, <kernel.DependentProduct object at 0x2aefb2962680>) of role type named typ_rp_nt_is
% 2.58/3.19 Using role type
% 2.58/3.19 Declaring rp_nt_is:(fofType->(fofType->Prop))
% 2.58/3.19 FOF formula (((eq (fofType->(fofType->Prop))) rp_nt_is) (e_is nt_natt)) of role definition named def_rp_nt_is
% 2.58/3.19 A new definition: (((eq (fofType->(fofType->Prop))) rp_nt_is) (e_is nt_natt))
% 2.58/3.19 Defined: rp_nt_is:=(e_is nt_natt)
% 2.58/3.19 FOF formula (<kernel.Constant object at 0x2aefb2962128>, <kernel.DependentProduct object at 0x2aefb2962b00>) of role type named typ_rp_nt_nis
% 2.58/3.19 Using role type
% 2.58/3.19 Declaring rp_nt_nis:(fofType->(fofType->Prop))
% 2.58/3.19 FOF formula (((eq (fofType->(fofType->Prop))) rp_nt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rp_nt_is X0) X1)))) of role definition named def_rp_nt_nis
% 2.58/3.19 A new definition: (((eq (fofType->(fofType->Prop))) rp_nt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rp_nt_is X0) X1))))
% 2.58/3.19 Defined: rp_nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_nt_is X0) X1)))
% 2.58/3.19 FOF formula (<kernel.Constant object at 0x2aefb2962b00>, <kernel.DependentProduct object at 0x2aefb2962830>) of role type named typ_rp_nt_all
% 2.58/3.19 Using role type
% 2.58/3.19 Declaring rp_nt_all:((fofType->Prop)->Prop)
% 2.58/3.19 FOF formula (((eq ((fofType->Prop)->Prop)) rp_nt_all) (all nt_natt)) of role definition named def_rp_nt_all
% 2.58/3.19 A new definition: (((eq ((fofType->Prop)->Prop)) rp_nt_all) (all nt_natt))
% 2.58/3.19 Defined: rp_nt_all:=(all nt_natt)
% 2.58/3.19 FOF formula (<kernel.Constant object at 0x2aefb29621b8>, <kernel.DependentProduct object at 0x2aefb2962830>) of role type named typ_rp_nt_some
% 2.58/3.19 Using role type
% 2.58/3.19 Declaring rp_nt_some:((fofType->Prop)->Prop)
% 2.58/3.19 FOF formula (((eq ((fofType->Prop)->Prop)) rp_nt_some) (l_some nt_natt)) of role definition named def_rp_nt_some
% 2.58/3.19 A new definition: (((eq ((fofType->Prop)->Prop)) rp_nt_some) (l_some nt_natt))
% 2.58/3.19 Defined: rp_nt_some:=(l_some nt_natt)
% 2.58/3.19 FOF formula (<kernel.Constant object at 0x2aefb2962ab8>, <kernel.DependentProduct object at 0x2aefb2962830>) of role type named typ_rp_nt_one
% 2.58/3.19 Using role type
% 2.58/3.19 Declaring rp_nt_one:((fofType->Prop)->Prop)
% 2.58/3.19 FOF formula (((eq ((fofType->Prop)->Prop)) rp_nt_one) (one nt_natt)) of role definition named def_rp_nt_one
% 2.58/3.19 A new definition: (((eq ((fofType->Prop)->Prop)) rp_nt_one) (one nt_natt))
% 2.58/3.19 Defined: rp_nt_one:=(one nt_natt)
% 2.58/3.19 FOF formula (<kernel.Constant object at 0x2aefb2962128>, <kernel.DependentProduct object at 0x2aefb2962c68>) of role type named typ_rp_nt_in
% 2.58/3.19 Using role type
% 2.58/3.19 Declaring rp_nt_in:(fofType->(fofType->Prop))
% 2.58/3.19 FOF formula (((eq (fofType->(fofType->Prop))) rp_nt_in) (esti nt_natt)) of role definition named def_rp_nt_in
% 2.58/3.20 A new definition: (((eq (fofType->(fofType->Prop))) rp_nt_in) (esti nt_natt))
% 2.58/3.20 Defined: rp_nt_in:=(esti nt_natt)
% 2.58/3.20 FOF formula (<kernel.Constant object at 0x2aefb2962b00>, <kernel.DependentProduct object at 0x2aefb2962098>) of role type named typ_rpofntt
% 2.58/3.20 Using role type
% 2.58/3.20 Declaring rpofntt:(fofType->fofType)
% 2.58/3.20 FOF formula (((eq (fofType->fofType)) rpofntt) ((e_in cut) natrp)) of role definition named def_rpofntt
% 2.58/3.20 A new definition: (((eq (fofType->fofType)) rpofntt) ((e_in cut) natrp))
% 2.58/3.20 Defined: rpofntt:=((e_in cut) natrp)
% 2.58/3.20 FOF formula (<kernel.Constant object at 0x2aefb2962098>, <kernel.DependentProduct object at 0x2aefb2962cb0>) of role type named typ_nttofnt
% 2.58/3.20 Using role type
% 2.58/3.20 Declaring nttofnt:(fofType->fofType)
% 2.58/3.20 FOF formula (((eq (fofType->fofType)) nttofnt) (fun (X0:fofType)=> (nttofrp (rpofnt X0)))) of role definition named def_nttofnt
% 2.58/3.20 A new definition: (((eq (fofType->fofType)) nttofnt) (fun (X0:fofType)=> (nttofrp (rpofnt X0))))
% 2.58/3.20 Defined: nttofnt:=(fun (X0:fofType)=> (nttofrp (rpofnt X0)))
% 2.58/3.20 FOF formula (<kernel.Constant object at 0x2aefb2962cb0>, <kernel.DependentProduct object at 0x2aefb29621b8>) of role type named typ_ntofntt
% 2.58/3.20 Using role type
% 2.58/3.20 Declaring ntofntt:(fofType->fofType)
% 2.58/3.20 FOF formula (((eq (fofType->fofType)) ntofntt) (fun (X0:fofType)=> (ntofrp (rpofntt X0)))) of role definition named def_ntofntt
% 2.58/3.20 A new definition: (((eq (fofType->fofType)) ntofntt) (fun (X0:fofType)=> (ntofrp (rpofntt X0))))
% 2.58/3.20 Defined: ntofntt:=(fun (X0:fofType)=> (ntofrp (rpofntt X0)))
% 2.58/3.20 FOF formula (<kernel.Constant object at 0x2aefb29621b8>, <kernel.Single object at 0x2aefb2962cb0>) of role type named typ_rp_nt_1t
% 2.58/3.20 Using role type
% 2.58/3.20 Declaring rp_nt_1t:fofType
% 2.58/3.20 FOF formula (((eq fofType) rp_nt_1t) (nttofnt n_1)) of role definition named def_rp_nt_1t
% 2.58/3.20 A new definition: (((eq fofType) rp_nt_1t) (nttofnt n_1))
% 2.58/3.20 Defined: rp_nt_1t:=(nttofnt n_1)
% 2.58/3.20 FOF formula (<kernel.Constant object at 0x2aefb2962098>, <kernel.Single object at 0x2aefb29621b8>) of role type named typ_nt_suct
% 2.58/3.20 Using role type
% 2.58/3.20 Declaring nt_suct:fofType
% 2.58/3.20 FOF formula (((eq fofType) nt_suct) ((d_Sigma nt_natt) (fun (X0:fofType)=> (nttofnt (ordsucc (ntofntt X0)))))) of role definition named def_nt_suct
% 2.58/3.20 A new definition: (((eq fofType) nt_suct) ((d_Sigma nt_natt) (fun (X0:fofType)=> (nttofnt (ordsucc (ntofntt X0))))))
% 2.58/3.20 Defined: nt_suct:=((d_Sigma nt_natt) (fun (X0:fofType)=> (nttofnt (ordsucc (ntofntt X0)))))
% 2.58/3.20 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((rp_nt_nis ((ap nt_suct) X0)) rp_nt_1t))) of role axiom named satz156a
% 2.58/3.20 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((rp_nt_nis ((ap nt_suct) X0)) rp_nt_1t)))
% 2.58/3.20 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> (((rp_nt_is ((ap nt_suct) X0)) ((ap nt_suct) X1))->((rp_nt_is X0) X1)))))) of role axiom named satz156b
% 2.58/3.20 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> (((rp_nt_is ((ap nt_suct) X0)) ((ap nt_suct) X1))->((rp_nt_is X0) X1))))))
% 2.58/3.20 FOF formula (<kernel.Constant object at 0x2aefb2962e60>, <kernel.DependentProduct object at 0x2aefb2962cb0>) of role type named typ_rp_nt_cond1
% 2.58/3.20 Using role type
% 2.58/3.20 Declaring rp_nt_cond1:(fofType->Prop)
% 2.58/3.20 FOF formula (((eq (fofType->Prop)) rp_nt_cond1) (rp_nt_in rp_nt_1t)) of role definition named def_rp_nt_cond1
% 2.58/3.20 A new definition: (((eq (fofType->Prop)) rp_nt_cond1) (rp_nt_in rp_nt_1t))
% 2.58/3.20 Defined: rp_nt_cond1:=(rp_nt_in rp_nt_1t)
% 2.58/3.20 FOF formula (<kernel.Constant object at 0x2aefb2962d88>, <kernel.DependentProduct object at 0x2aefb29621b8>) of role type named typ_rp_nt_cond2
% 2.58/3.20 Using role type
% 2.58/3.20 Declaring rp_nt_cond2:(fofType->Prop)
% 2.58/3.20 FOF formula (((eq (fofType->Prop)) rp_nt_cond2) (fun (X0:fofType)=> (rp_nt_all (fun (X1:fofType)=> ((imp ((rp_nt_in X1) X0)) ((rp_nt_in ((ap nt_suct) X1)) X0)))))) of role definition named def_rp_nt_cond2
% 2.58/3.20 A new definition: (((eq (fofType->Prop)) rp_nt_cond2) (fun (X0:fofType)=> (rp_nt_all (fun (X1:fofType)=> ((imp ((rp_nt_in X1) X0)) ((rp_nt_in ((ap nt_suct) X1)) X0))))))
% 2.68/3.21 Defined: rp_nt_cond2:=(fun (X0:fofType)=> (rp_nt_all (fun (X1:fofType)=> ((imp ((rp_nt_in X1) X0)) ((rp_nt_in ((ap nt_suct) X1)) X0)))))
% 2.68/3.21 FOF formula (<kernel.Constant object at 0x2aefb2962e60>, <kernel.DependentProduct object at 0x2aefb2962cf8>) of role type named typ_d_5156_prop1
% 2.68/3.21 Using role type
% 2.68/3.21 Declaring d_5156_prop1:(fofType->(fofType->Prop))
% 2.68/3.21 FOF formula (((eq (fofType->(fofType->Prop))) d_5156_prop1) (fun (X0:fofType) (X1:fofType)=> ((rp_nt_in (nttofnt X1)) X0))) of role definition named def_d_5156_prop1
% 2.68/3.21 A new definition: (((eq (fofType->(fofType->Prop))) d_5156_prop1) (fun (X0:fofType) (X1:fofType)=> ((rp_nt_in (nttofnt X1)) X0)))
% 2.68/3.21 Defined: d_5156_prop1:=(fun (X0:fofType) (X1:fofType)=> ((rp_nt_in (nttofnt X1)) X0))
% 2.68/3.21 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) (power nt_natt)))) (fun (X0:fofType)=> ((rp_nt_cond1 X0)->((rp_nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> ((rp_nt_in X1) X0))))))) of role axiom named satz156c
% 2.68/3.21 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) (power nt_natt)))) (fun (X0:fofType)=> ((rp_nt_cond1 X0)->((rp_nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> ((rp_nt_in X1) X0)))))))
% 2.68/3.21 FOF formula (<kernel.Constant object at 0x2aefb2962d40>, <kernel.Single object at 0x2aefb2962e60>) of role type named typ_ratt
% 2.68/3.21 Using role type
% 2.68/3.21 Declaring ratt:fofType
% 2.68/3.21 FOF formula (((eq fofType) ratt) ((d_Sep cut) ratrp)) of role definition named def_ratt
% 2.68/3.21 A new definition: (((eq fofType) ratt) ((d_Sep cut) ratrp))
% 2.68/3.21 Defined: ratt:=((d_Sep cut) ratrp)
% 2.68/3.21 FOF formula (<kernel.Constant object at 0x2aefb29621b8>, <kernel.DependentProduct object at 0x2aefb296a368>) of role type named typ_rttofrp
% 2.68/3.21 Using role type
% 2.68/3.21 Declaring rttofrp:(fofType->fofType)
% 2.68/3.21 FOF formula (((eq (fofType->fofType)) rttofrp) ((out cut) ratrp)) of role definition named def_rttofrp
% 2.68/3.21 A new definition: (((eq (fofType->fofType)) rttofrp) ((out cut) ratrp))
% 2.68/3.21 Defined: rttofrp:=((out cut) ratrp)
% 2.68/3.21 FOF formula (<kernel.Constant object at 0x2aefb29621b8>, <kernel.DependentProduct object at 0x2aefb296a3f8>) of role type named typ_rtt_is
% 2.68/3.21 Using role type
% 2.68/3.21 Declaring rtt_is:(fofType->(fofType->Prop))
% 2.68/3.21 FOF formula (((eq (fofType->(fofType->Prop))) rtt_is) (e_is ratt)) of role definition named def_rtt_is
% 2.68/3.21 A new definition: (((eq (fofType->(fofType->Prop))) rtt_is) (e_is ratt))
% 2.68/3.21 Defined: rtt_is:=(e_is ratt)
% 2.68/3.21 FOF formula (<kernel.Constant object at 0x2aefb2962d88>, <kernel.DependentProduct object at 0x2aefb296a170>) of role type named typ_rtt_nis
% 2.68/3.21 Using role type
% 2.68/3.21 Declaring rtt_nis:(fofType->(fofType->Prop))
% 2.68/3.21 FOF formula (((eq (fofType->(fofType->Prop))) rtt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rtt_is X0) X1)))) of role definition named def_rtt_nis
% 2.68/3.21 A new definition: (((eq (fofType->(fofType->Prop))) rtt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rtt_is X0) X1))))
% 2.68/3.21 Defined: rtt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rtt_is X0) X1)))
% 2.68/3.21 FOF formula (<kernel.Constant object at 0x2aefb296a170>, <kernel.DependentProduct object at 0x2aefb296a638>) of role type named typ_rtt_all
% 2.68/3.21 Using role type
% 2.68/3.21 Declaring rtt_all:((fofType->Prop)->Prop)
% 2.68/3.21 FOF formula (((eq ((fofType->Prop)->Prop)) rtt_all) (all ratt)) of role definition named def_rtt_all
% 2.68/3.21 A new definition: (((eq ((fofType->Prop)->Prop)) rtt_all) (all ratt))
% 2.68/3.21 Defined: rtt_all:=(all ratt)
% 2.68/3.21 FOF formula (<kernel.Constant object at 0x2aefb296a248>, <kernel.DependentProduct object at 0x2aefb296a638>) of role type named typ_rtt_some
% 2.68/3.21 Using role type
% 2.68/3.21 Declaring rtt_some:((fofType->Prop)->Prop)
% 2.68/3.21 FOF formula (((eq ((fofType->Prop)->Prop)) rtt_some) (l_some ratt)) of role definition named def_rtt_some
% 2.68/3.21 A new definition: (((eq ((fofType->Prop)->Prop)) rtt_some) (l_some ratt))
% 2.68/3.21 Defined: rtt_some:=(l_some ratt)
% 2.68/3.21 FOF formula (<kernel.Constant object at 0x2aefb296a518>, <kernel.DependentProduct object at 0x2aefb296a638>) of role type named typ_rtt_one
% 2.68/3.21 Using role type
% 2.68/3.21 Declaring rtt_one:((fofType->Prop)->Prop)
% 2.68/3.21 FOF formula (((eq ((fofType->Prop)->Prop)) rtt_one) (one ratt)) of role definition named def_rtt_one
% 2.68/3.23 A new definition: (((eq ((fofType->Prop)->Prop)) rtt_one) (one ratt))
% 2.68/3.23 Defined: rtt_one:=(one ratt)
% 2.68/3.23 FOF formula (<kernel.Constant object at 0x2aefb296a3f8>, <kernel.DependentProduct object at 0x2aefb296a248>) of role type named typ_rpofrtt
% 2.68/3.23 Using role type
% 2.68/3.23 Declaring rpofrtt:(fofType->fofType)
% 2.68/3.23 FOF formula (((eq (fofType->fofType)) rpofrtt) ((e_in cut) ratrp)) of role definition named def_rpofrtt
% 2.68/3.23 A new definition: (((eq (fofType->fofType)) rpofrtt) ((e_in cut) ratrp))
% 2.68/3.23 Defined: rpofrtt:=((e_in cut) ratrp)
% 2.68/3.23 FOF formula (<kernel.Constant object at 0x2aefb296a248>, <kernel.DependentProduct object at 0x2aefb296a200>) of role type named typ_rttofrt
% 2.68/3.23 Using role type
% 2.68/3.23 Declaring rttofrt:(fofType->fofType)
% 2.68/3.23 FOF formula (((eq (fofType->fofType)) rttofrt) (fun (X0:fofType)=> (rttofrp (rpofrt X0)))) of role definition named def_rttofrt
% 2.68/3.23 A new definition: (((eq (fofType->fofType)) rttofrt) (fun (X0:fofType)=> (rttofrp (rpofrt X0))))
% 2.68/3.23 Defined: rttofrt:=(fun (X0:fofType)=> (rttofrp (rpofrt X0)))
% 2.68/3.23 FOF formula (<kernel.Constant object at 0x2aefb296a200>, <kernel.DependentProduct object at 0x2aefb296a488>) of role type named typ_rtofrtt
% 2.68/3.23 Using role type
% 2.68/3.23 Declaring rtofrtt:(fofType->fofType)
% 2.68/3.23 FOF formula (((eq (fofType->fofType)) rtofrtt) (fun (X0:fofType)=> (rtofrp (rpofrtt X0)))) of role definition named def_rtofrtt
% 2.68/3.23 A new definition: (((eq (fofType->fofType)) rtofrtt) (fun (X0:fofType)=> (rtofrp (rpofrtt X0))))
% 2.68/3.23 Defined: rtofrtt:=(fun (X0:fofType)=> (rtofrp (rpofrtt X0)))
% 2.68/3.23 FOF formula (<kernel.Constant object at 0x2aefb296a488>, <kernel.DependentProduct object at 0x2aefb296a1b8>) of role type named typ_d_5157_s1
% 2.68/3.23 Using role type
% 2.68/3.23 Declaring d_5157_s1:(fofType->fofType)
% 2.68/3.23 FOF formula (((eq (fofType->fofType)) d_5157_s1) (fun (X0:fofType)=> ((d_Sep rat) (urt X0)))) of role definition named def_d_5157_s1
% 2.68/3.23 A new definition: (((eq (fofType->fofType)) d_5157_s1) (fun (X0:fofType)=> ((d_Sep rat) (urt X0))))
% 2.68/3.23 Defined: d_5157_s1:=(fun (X0:fofType)=> ((d_Sep rat) (urt X0)))
% 2.68/3.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->((rt_min ((d_Sep rat) (urt X0))) (rtofrp X0))))) of role axiom named satz157a
% 2.68/3.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->((rt_min ((d_Sep rat) (urt X0))) (rtofrp X0)))))
% 2.68/3.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->(rt_some (rt_min ((d_Sep rat) (urt X0))))))) of role axiom named satz157b
% 2.68/3.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->(rt_some (rt_min ((d_Sep rat) (urt X0)))))))
% 2.68/3.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_min ((d_Sep rat) (urt X0))) X1)->((rp_is X0) (rpofrt X1))))))) of role axiom named satz157c
% 2.68/3.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_min ((d_Sep rat) (urt X0))) X1)->((rp_is X0) (rpofrt X1)))))))
% 2.68/3.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rt_some (rt_min ((d_Sep rat) (urt X0))))->(ratrp X0)))) of role axiom named satz157d
% 2.68/3.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rt_some (rt_min ((d_Sep rat) (urt X0))))->(ratrp X0))))
% 2.68/3.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((rp_less (rpofrt X1)) X0)))))) of role axiom named satz158a
% 2.68/3.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((rp_less (rpofrt X1)) X0))))))
% 2.68/3.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((rp_moreis (rpofrt X1)) X0)))))) of role axiom named satz158b
% 2.68/3.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((rp_moreis (rpofrt X1)) X0))))))
% 2.68/3.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X1)) X0)->((lrt X0) X1)))))) of role axiom named satz158c
% 2.68/3.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X1)) X0)->((lrt X0) X1))))))
% 2.68/3.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_moreis (rpofrt X1)) X0)->((urt X0) X1)))))) of role axiom named satz158d
% 2.68/3.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_moreis (rpofrt X1)) X0)->((urt X0) X1))))))
% 2.68/3.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rp_less X0) (rpofrt X2))) ((rp_less (rpofrt X2)) X1))))))))) of role axiom named satz159
% 2.68/3.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rp_less X0) (rpofrt X2))) ((rp_less (rpofrt X2)) X1)))))))))
% 2.68/3.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rp_some (fun (X2:fofType)=> (((and3 (ratrp X2)) ((rp_less X0) X2)) ((rp_less X2) X1))))))))) of role axiom named satz159a
% 2.68/3.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rp_some (fun (X2:fofType)=> (((and3 (ratrp X2)) ((rp_less X0) X2)) ((rp_less X2) X1)))))))))
% 2.68/3.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(forall (X2:Prop), (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rp_less X0) (rpofrt X3))->(((rp_less (rpofrt X3)) X1)->X2))))->X2))))))) of role axiom named satz159app
% 2.68/3.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(forall (X2:Prop), (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rp_less X0) (rpofrt X3))->(((rp_less (rpofrt X3)) X1)->X2))))->X2)))))))
% 2.68/3.25 FOF formula (<kernel.Constant object at 0x2aefb296ad88>, <kernel.DependentProduct object at 0x2aefb296aea8>) of role type named typ_d_5160_nm
% 2.68/3.25 Using role type
% 2.68/3.25 Declaring d_5160_nm:(fofType->(fofType->(fofType->fofType)))
% 2.68/3.25 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) d_5160_nm) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_mn (rpofrt X2)) ((rp_ts X0) X1)))) of role definition named def_d_5160_nm
% 2.68/3.25 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) d_5160_nm) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_mn (rpofrt X2)) ((rp_ts X0) X1))))
% 2.68/3.25 Defined: d_5160_nm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_mn (rpofrt X2)) ((rp_ts X0) X1)))
% 2.68/3.25 FOF formula (<kernel.Constant object at 0x2aefb296aea8>, <kernel.DependentProduct object at 0x2aefb296aef0>) of role type named typ_d_5160_dn
% 2.68/3.25 Using role type
% 2.68/3.25 Declaring d_5160_dn:(fofType->(fofType->fofType))
% 2.68/3.25 FOF formula (((eq (fofType->(fofType->fofType))) d_5160_dn) (fun (X0:fofType) (X1:fofType)=> ((rp_pl ((rp_pl X0) X1)) d_1rp))) of role definition named def_d_5160_dn
% 2.68/3.25 A new definition: (((eq (fofType->(fofType->fofType))) d_5160_dn) (fun (X0:fofType) (X1:fofType)=> ((rp_pl ((rp_pl X0) X1)) d_1rp)))
% 2.68/3.25 Defined: d_5160_dn:=(fun (X0:fofType) (X1:fofType)=> ((rp_pl ((rp_pl X0) X1)) d_1rp))
% 2.68/3.25 FOF formula (<kernel.Constant object at 0x2aefb296aef0>, <kernel.DependentProduct object at 0x2aefb296a710>) of role type named typ_d_5160_fr
% 2.68/3.26 Using role type
% 2.68/3.26 Declaring d_5160_fr:(fofType->(fofType->(fofType->fofType)))
% 2.68/3.26 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) d_5160_fr) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_ov (((d_5160_nm X0) X1) X2)) ((d_5160_dn X0) X1)))) of role definition named def_d_5160_fr
% 2.68/3.26 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) d_5160_fr) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_ov (((d_5160_nm X0) X1) X2)) ((d_5160_dn X0) X1))))
% 2.68/3.26 Defined: d_5160_fr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_ov (((d_5160_nm X0) X1) X2)) ((d_5160_dn X0) X1)))
% 2.68/3.26 FOF formula (<kernel.Constant object at 0x2aefb296a710>, <kernel.DependentProduct object at 0x2aefb296af38>) of role type named typ_zeta
% 2.68/3.26 Using role type
% 2.68/3.26 Declaring zeta:(fofType->(fofType->(fofType->fofType)))
% 2.68/3.26 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) zeta) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((((ite ((rp_less (((d_5160_fr X0) X1) X2)) d_1rp)) cut) (((d_5160_fr X0) X1) X2)) d_1rp))) of role definition named def_zeta
% 2.68/3.26 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) zeta) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((((ite ((rp_less (((d_5160_fr X0) X1) X2)) d_1rp)) cut) (((d_5160_fr X0) X1) X2)) d_1rp)))
% 2.68/3.26 Defined: zeta:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((((ite ((rp_less (((d_5160_fr X0) X1) X2)) d_1rp)) cut) (((d_5160_fr X0) X1) X2)) d_1rp))
% 2.68/3.26 FOF formula (<kernel.Constant object at 0x2aefb296af38>, <kernel.DependentProduct object at 0x2aefb296a998>) of role type named typ_d_5160_xr
% 2.68/3.26 Using role type
% 2.68/3.26 Declaring d_5160_xr:(fofType->(fofType->fofType))
% 2.68/3.26 FOF formula (((eq (fofType->(fofType->fofType))) d_5160_xr) (fun (X0:fofType) (X1:fofType)=> (rpofrt ((rt_ov X0) X1)))) of role definition named def_d_5160_xr
% 2.68/3.26 A new definition: (((eq (fofType->(fofType->fofType))) d_5160_xr) (fun (X0:fofType) (X1:fofType)=> (rpofrt ((rt_ov X0) X1))))
% 2.68/3.26 Defined: d_5160_xr:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((rt_ov X0) X1)))
% 2.68/3.26 FOF formula (<kernel.Constant object at 0x2aefb296a998>, <kernel.DependentProduct object at 0x2aefb296a710>) of role type named typ_d_5160_y0
% 2.68/3.26 Using role type
% 2.68/3.26 Declaring d_5160_y0:(fofType->fofType)
% 2.68/3.26 FOF formula (((eq (fofType->fofType)) d_5160_y0) (fun (X0:fofType)=> X0)) of role definition named def_d_5160_y0
% 2.68/3.26 A new definition: (((eq (fofType->fofType)) d_5160_y0) (fun (X0:fofType)=> X0))
% 2.68/3.26 Defined: d_5160_y0:=(fun (X0:fofType)=> X0)
% 2.68/3.26 FOF formula (<kernel.Constant object at 0x2aefb296a710>, <kernel.DependentProduct object at 0x2aefb296a950>) of role type named typ_d_5160_yr
% 2.68/3.26 Using role type
% 2.68/3.26 Declaring d_5160_yr:(fofType->fofType)
% 2.68/3.26 FOF formula (((eq (fofType->fofType)) d_5160_yr) (fun (X0:fofType)=> (rpofrt (d_5160_y0 X0)))) of role definition named def_d_5160_yr
% 2.68/3.26 A new definition: (((eq (fofType->fofType)) d_5160_yr) (fun (X0:fofType)=> (rpofrt (d_5160_y0 X0))))
% 2.68/3.26 Defined: d_5160_yr:=(fun (X0:fofType)=> (rpofrt (d_5160_y0 X0)))
% 2.68/3.26 FOF formula (<kernel.Constant object at 0x2aefb296a950>, <kernel.DependentProduct object at 0x2aefb296a908>) of role type named typ_d_5160_prop1
% 2.68/3.26 Using role type
% 2.68/3.26 Declaring d_5160_prop1:(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 2.68/3.26 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) d_5160_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2)))) of role definition named def_d_5160_prop1
% 2.68/3.26 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) d_5160_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2))))
% 2.68/3.26 Defined: d_5160_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2)))
% 2.68/3.26 FOF formula (<kernel.Constant object at 0x2aefb296af80>, <kernel.DependentProduct object at 0x2aefb296a4d0>) of role type named typ_d_5160_prop2
% 2.68/3.26 Using role type
% 2.68/3.26 Declaring d_5160_prop2:(fofType->(fofType->(fofType->Prop)))
% 2.68/3.28 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_5160_prop2) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((d_5160_prop1 X0) X1) X2) X3)))))) of role definition named def_d_5160_prop2
% 2.68/3.28 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_5160_prop2) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((d_5160_prop1 X0) X1) X2) X3))))))
% 2.68/3.28 Defined: d_5160_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((d_5160_prop1 X0) X1) X2) X3)))))
% 2.68/3.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(rt_some (fun (X3:fofType)=> (rt_some (fun (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2))))))))))))) of role axiom named satz160
% 2.68/3.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(rt_some (fun (X3:fofType)=> (rt_some (fun (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2)))))))))))))
% 2.68/3.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(forall (X3:Prop), (((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((rp_more (rpofrt X4)) X0)->((all_of (fun (X5:fofType)=> ((in X5) rat))) (fun (X5:fofType)=> (((rp_more (rpofrt X5)) X1)->(((rt_is ((rt_ts X4) X5)) X2)->X3)))))))->X3))))))))) of role axiom named satz160app
% 2.68/3.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(forall (X3:Prop), (((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((rp_more (rpofrt X4)) X0)->((all_of (fun (X5:fofType)=> ((in X5) rat))) (fun (X5:fofType)=> (((rp_more (rpofrt X5)) X1)->(((rt_is ((rt_ts X4) X5)) X2)->X3)))))))->X3)))))))))
% 2.68/3.28 FOF formula (<kernel.Constant object at 0x2aefb296a710>, <kernel.DependentProduct object at 0x2aefb296a4d0>) of role type named typ_d_5161_min
% 2.68/3.28 Using role type
% 2.68/3.28 Declaring d_5161_min:(fofType->(fofType->fofType))
% 2.68/3.28 FOF formula (((eq (fofType->(fofType->fofType))) d_5161_min) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_less X0) X1)) cut) X0) X1))) of role definition named def_d_5161_min
% 2.68/3.28 A new definition: (((eq (fofType->(fofType->fofType))) d_5161_min) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_less X0) X1)) cut) X0) X1)))
% 2.68/3.28 Defined: d_5161_min:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_less X0) X1)) cut) X0) X1))
% 2.68/3.28 FOF formula (<kernel.Constant object at 0x2aefb296abd8>, <kernel.DependentProduct object at 0x2aefb2973050>) of role type named typ_d_5161_max
% 2.68/3.28 Using role type
% 2.68/3.28 Declaring d_5161_max:(fofType->(fofType->fofType))
% 2.68/3.28 FOF formula (((eq (fofType->(fofType->fofType))) d_5161_max) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_more X0) X1)) cut) X0) X1))) of role definition named def_d_5161_max
% 2.68/3.28 A new definition: (((eq (fofType->(fofType->fofType))) d_5161_max) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_more X0) X1)) cut) X0) X1)))
% 2.68/3.28 Defined: d_5161_max:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_more X0) X1)) cut) X0) X1))
% 2.68/3.28 FOF formula (<kernel.Constant object at 0x2aefb296a950>, <kernel.DependentProduct object at 0x2aefb29735f0>) of role type named typ_sq1
% 2.68/3.28 Using role type
% 2.68/3.28 Declaring sq1:(fofType->fofType)
% 2.68/3.28 FOF formula (((eq (fofType->fofType)) sq1) (fun (X0:fofType)=> ((rp_ts X0) X0))) of role definition named def_sq1
% 2.68/3.28 A new definition: (((eq (fofType->fofType)) sq1) (fun (X0:fofType)=> ((rp_ts X0) X0)))
% 2.68/3.29 Defined: sq1:=(fun (X0:fofType)=> ((rp_ts X0) X0))
% 2.68/3.29 FOF formula (<kernel.Constant object at 0x2aefb296a950>, <kernel.DependentProduct object at 0x2aefb2973098>) of role type named typ_sqrtset
% 2.68/3.29 Using role type
% 2.68/3.29 Declaring sqrtset:(fofType->fofType)
% 2.68/3.29 FOF formula (((eq (fofType->fofType)) sqrtset) (fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rp_less ((rp_ts (rpofrt X1)) (rpofrt X1))) X0))))) of role definition named def_sqrtset
% 2.68/3.29 A new definition: (((eq (fofType->fofType)) sqrtset) (fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rp_less ((rp_ts (rpofrt X1)) (rpofrt X1))) X0)))))
% 2.68/3.29 Defined: sqrtset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rp_less ((rp_ts (rpofrt X1)) (rpofrt X1))) X0))))
% 2.68/3.29 FOF formula (<kernel.Constant object at 0x2aefb296a950>, <kernel.DependentProduct object at 0x2aefb2973560>) of role type named typ_d_5161_nm
% 2.68/3.29 Using role type
% 2.68/3.29 Declaring d_5161_nm:(fofType->(fofType->fofType))
% 2.68/3.29 FOF formula (((eq (fofType->(fofType->fofType))) d_5161_nm) (fun (X0:fofType) (X1:fofType)=> ((rp_mn X0) ((rp_ts (rpofrt X1)) (rpofrt X1))))) of role definition named def_d_5161_nm
% 2.68/3.29 A new definition: (((eq (fofType->(fofType->fofType))) d_5161_nm) (fun (X0:fofType) (X1:fofType)=> ((rp_mn X0) ((rp_ts (rpofrt X1)) (rpofrt X1)))))
% 2.68/3.29 Defined: d_5161_nm:=(fun (X0:fofType) (X1:fofType)=> ((rp_mn X0) ((rp_ts (rpofrt X1)) (rpofrt X1))))
% 2.68/3.29 FOF formula (<kernel.Constant object at 0x2aefb2973560>, <kernel.DependentProduct object at 0x2aefb2973170>) of role type named typ_d_5161_dn
% 2.68/3.29 Using role type
% 2.68/3.29 Declaring d_5161_dn:(fofType->fofType)
% 2.68/3.29 FOF formula (((eq (fofType->fofType)) d_5161_dn) (fun (X0:fofType)=> ((rp_pl (rpofrt X0)) ((rp_pl (rpofrt X0)) d_1rp)))) of role definition named def_d_5161_dn
% 2.68/3.29 A new definition: (((eq (fofType->fofType)) d_5161_dn) (fun (X0:fofType)=> ((rp_pl (rpofrt X0)) ((rp_pl (rpofrt X0)) d_1rp))))
% 2.68/3.29 Defined: d_5161_dn:=(fun (X0:fofType)=> ((rp_pl (rpofrt X0)) ((rp_pl (rpofrt X0)) d_1rp)))
% 2.68/3.29 FOF formula (<kernel.Constant object at 0x2aefb2973170>, <kernel.DependentProduct object at 0x2aefb2973878>) of role type named typ_d_5161_fr
% 2.68/3.29 Using role type
% 2.68/3.29 Declaring d_5161_fr:(fofType->(fofType->fofType))
% 2.68/3.29 FOF formula (((eq (fofType->(fofType->fofType))) d_5161_fr) (fun (X0:fofType) (X1:fofType)=> ((rp_ov ((d_5161_nm X0) X1)) (d_5161_dn X1)))) of role definition named def_d_5161_fr
% 2.68/3.29 A new definition: (((eq (fofType->(fofType->fofType))) d_5161_fr) (fun (X0:fofType) (X1:fofType)=> ((rp_ov ((d_5161_nm X0) X1)) (d_5161_dn X1))))
% 2.68/3.29 Defined: d_5161_fr:=(fun (X0:fofType) (X1:fofType)=> ((rp_ov ((d_5161_nm X0) X1)) (d_5161_dn X1)))
% 2.68/3.29 FOF formula (<kernel.Constant object at 0x2aefb2973878>, <kernel.DependentProduct object at 0x2aefb29734d0>) of role type named typ_rtc
% 2.68/3.29 Using role type
% 2.68/3.29 Declaring rtc:(fofType->fofType)
% 2.68/3.29 FOF formula (((eq (fofType->fofType)) rtc) (fun (X0:fofType)=> (cutof (sqrtset X0)))) of role definition named def_rtc
% 2.68/3.29 A new definition: (((eq (fofType->fofType)) rtc) (fun (X0:fofType)=> (cutof (sqrtset X0))))
% 2.68/3.29 Defined: rtc:=(fun (X0:fofType)=> (cutof (sqrtset X0)))
% 2.68/3.29 FOF formula (<kernel.Constant object at 0x2aefb29734d0>, <kernel.DependentProduct object at 0x2aefb2973518>) of role type named typ_d_5161_xm
% 2.68/3.29 Using role type
% 2.68/3.29 Declaring d_5161_xm:(fofType->(fofType->fofType))
% 2.68/3.29 FOF formula (((eq (fofType->(fofType->fofType))) d_5161_xm) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_more X0) X1)) rat) X0) X1))) of role definition named def_d_5161_xm
% 2.68/3.29 A new definition: (((eq (fofType->(fofType->fofType))) d_5161_xm) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_more X0) X1)) rat) X0) X1)))
% 2.68/3.29 Defined: d_5161_xm:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_more X0) X1)) rat) X0) X1))
% 2.68/3.29 FOF formula (<kernel.Constant object at 0x2aefb2973518>, <kernel.DependentProduct object at 0x2aefb2973128>) of role type named typ_xrm
% 2.68/3.29 Using role type
% 2.68/3.29 Declaring xrm:(fofType->(fofType->fofType))
% 2.68/3.29 FOF formula (((eq (fofType->(fofType->fofType))) xrm) (fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_xm X0) X1)))) of role definition named def_xrm
% 2.68/3.29 A new definition: (((eq (fofType->(fofType->fofType))) xrm) (fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_xm X0) X1))))
% 2.77/3.31 Defined: xrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_xm X0) X1)))
% 2.77/3.31 FOF formula (<kernel.Constant object at 0x2aefb2973128>, <kernel.DependentProduct object at 0x2aefb2973758>) of role type named typ_d_5161_ym
% 2.77/3.31 Using role type
% 2.77/3.31 Declaring d_5161_ym:(fofType->(fofType->fofType))
% 2.77/3.31 FOF formula (((eq (fofType->(fofType->fofType))) d_5161_ym) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_less X0) X1)) rat) X0) X1))) of role definition named def_d_5161_ym
% 2.77/3.31 A new definition: (((eq (fofType->(fofType->fofType))) d_5161_ym) (fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_less X0) X1)) rat) X0) X1)))
% 2.77/3.31 Defined: d_5161_ym:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_less X0) X1)) rat) X0) X1))
% 2.77/3.31 FOF formula (<kernel.Constant object at 0x2aefb2973758>, <kernel.DependentProduct object at 0x2aefb29734d0>) of role type named typ_yrm
% 2.77/3.31 Using role type
% 2.77/3.31 Declaring yrm:(fofType->(fofType->fofType))
% 2.77/3.31 FOF formula (((eq (fofType->(fofType->fofType))) yrm) (fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_ym X0) X1)))) of role definition named def_yrm
% 2.77/3.31 A new definition: (((eq (fofType->(fofType->fofType))) yrm) (fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_ym X0) X1))))
% 2.77/3.31 Defined: yrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_ym X0) X1)))
% 2.77/3.31 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_one (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0))))) of role axiom named satz161
% 2.77/3.31 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_one (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))))
% 2.77/3.31 FOF formula (<kernel.Constant object at 0x2aefb29733f8>, <kernel.DependentProduct object at 0x2aefb2973560>) of role type named typ_irratrp
% 2.77/3.31 Using role type
% 2.77/3.31 Declaring irratrp:(fofType->Prop)
% 2.77/3.31 FOF formula (((eq (fofType->Prop)) irratrp) (fun (X0:fofType)=> (d_not (ratrp X0)))) of role definition named def_irratrp
% 2.77/3.31 A new definition: (((eq (fofType->Prop)) irratrp) (fun (X0:fofType)=> (d_not (ratrp X0))))
% 2.77/3.31 Defined: irratrp:=(fun (X0:fofType)=> (d_not (ratrp X0)))
% 2.77/3.31 FOF formula (<kernel.Constant object at 0x2aefb2973560>, <kernel.DependentProduct object at 0x2aefb29739e0>) of role type named typ_d_5162_prop1
% 2.77/3.31 Using role type
% 2.77/3.31 Declaring d_5162_prop1:(fofType->(fofType->Prop))
% 2.77/3.31 FOF formula (((eq (fofType->(fofType->Prop))) d_5162_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_eq ((n_tf ((n_fr X1) X0)) ((n_fr X1) X0))) ((n_fr (ordsucc n_1)) n_1)))) of role definition named def_d_5162_prop1
% 2.77/3.31 A new definition: (((eq (fofType->(fofType->Prop))) d_5162_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_eq ((n_tf ((n_fr X1) X0)) ((n_fr X1) X0))) ((n_fr (ordsucc n_1)) n_1))))
% 2.77/3.31 Defined: d_5162_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_eq ((n_tf ((n_fr X1) X0)) ((n_fr X1) X0))) ((n_fr (ordsucc n_1)) n_1)))
% 2.77/3.31 FOF formula (<kernel.Constant object at 0x2aefb29739e0>, <kernel.DependentProduct object at 0x2aefb29734d0>) of role type named typ_d_5162_prop2
% 2.77/3.31 Using role type
% 2.77/3.31 Declaring d_5162_prop2:(fofType->Prop)
% 2.77/3.31 FOF formula (((eq (fofType->Prop)) d_5162_prop2) (fun (X0:fofType)=> (n_some (d_5162_prop1 X0)))) of role definition named def_d_5162_prop2
% 2.77/3.31 A new definition: (((eq (fofType->Prop)) d_5162_prop2) (fun (X0:fofType)=> (n_some (d_5162_prop1 X0))))
% 2.77/3.31 Defined: d_5162_prop2:=(fun (X0:fofType)=> (n_some (d_5162_prop1 X0)))
% 2.77/3.31 FOF formula (<kernel.Constant object at 0x2aefb29734d0>, <kernel.Sort object at 0x2aefb2942518>) of role type named typ_d_5162_prop3
% 2.77/3.31 Using role type
% 2.77/3.31 Declaring d_5162_prop3:Prop
% 2.77/3.31 FOF formula (((eq Prop) d_5162_prop3) (n_some d_5162_prop2)) of role definition named def_d_5162_prop3
% 2.77/3.31 A new definition: (((eq Prop) d_5162_prop3) (n_some d_5162_prop2))
% 2.77/3.31 Defined: d_5162_prop3:=(n_some d_5162_prop2)
% 2.77/3.31 FOF formula (<kernel.Constant object at 0x2aefb2973758>, <kernel.Single object at 0x2aefb29734d0>) of role type named typ_d_5162_y
% 2.77/3.31 Using role type
% 2.77/3.31 Declaring d_5162_y:fofType
% 2.77/3.31 FOF formula (((eq fofType) d_5162_y) ((ind nat) (min d_5162_prop2))) of role definition named def_d_5162_y
% 2.77/3.31 A new definition: (((eq fofType) d_5162_y) ((ind nat) (min d_5162_prop2)))
% 2.77/3.31 Defined: d_5162_y:=((ind nat) (min d_5162_prop2))
% 2.77/3.32 FOF formula (<kernel.Constant object at 0x2aefb29734d0>, <kernel.Single object at 0x2aefb2973758>) of role type named typ_ksi
% 2.77/3.32 Using role type
% 2.77/3.32 Declaring ksi:fofType
% 2.77/3.32 FOF formula (((eq fofType) ksi) ((ind cut) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) X0)) (rpofnt (ordsucc n_1)))))) of role definition named def_ksi
% 2.77/3.32 A new definition: (((eq fofType) ksi) ((ind cut) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) X0)) (rpofnt (ordsucc n_1))))))
% 2.77/3.32 Defined: ksi:=((ind cut) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) X0)) (rpofnt (ordsucc n_1)))))
% 2.77/3.32 FOF formula (<kernel.Constant object at 0x2aefb2973758>, <kernel.Single object at 0x2aefb29734d0>) of role type named typ_d_5162_x0
% 2.77/3.32 Using role type
% 2.77/3.32 Declaring d_5162_x0:fofType
% 2.77/3.32 FOF formula (((eq fofType) d_5162_x0) (rtofrp ksi)) of role definition named def_d_5162_x0
% 2.77/3.32 A new definition: (((eq fofType) d_5162_x0) (rtofrp ksi))
% 2.77/3.32 Defined: d_5162_x0:=(rtofrp ksi)
% 2.77/3.32 FOF formula (rp_some irratrp) of role axiom named satz162
% 2.77/3.32 A new axiom: (rp_some irratrp)
% 2.77/3.32 FOF formula (<kernel.Constant object at 0x2aefb29736c8>, <kernel.DependentProduct object at 0x2aefb2973560>) of role type named typ_sqrt
% 2.77/3.32 Using role type
% 2.77/3.32 Declaring sqrt:(fofType->fofType)
% 2.77/3.32 FOF formula (((eq (fofType->fofType)) sqrt) (fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0))))) of role definition named def_sqrt
% 2.77/3.32 A new definition: (((eq (fofType->fofType)) sqrt) (fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))))
% 2.77/3.32 Defined: sqrt:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0))))
% 2.77/3.32 FOF formula (<kernel.Constant object at 0x2aefb2973560>, <kernel.DependentProduct object at 0x2aefb29737a0>) of role type named typ_iiia_x0
% 2.77/3.32 Using role type
% 2.77/3.32 Declaring iiia_x0:(fofType->fofType)
% 2.77/3.32 FOF formula (((eq (fofType->fofType)) iiia_x0) (fun (X0:fofType)=> (rtofn (ntofrp X0)))) of role definition named def_iiia_x0
% 2.77/3.32 A new definition: (((eq (fofType->fofType)) iiia_x0) (fun (X0:fofType)=> (rtofn (ntofrp X0))))
% 2.77/3.32 Defined: iiia_x0:=(fun (X0:fofType)=> (rtofn (ntofrp X0)))
% 2.77/3.32 FOF formula (<kernel.Constant object at 0x2aefb29737a0>, <kernel.DependentProduct object at 0x2aefb29737e8>) of role type named typ_xpy
% 2.77/3.32 Using role type
% 2.77/3.32 Declaring xpy:(fofType->(fofType->fofType))
% 2.77/3.32 FOF formula (((eq (fofType->(fofType->fofType))) xpy) (fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_pl (iiia_x0 X0)) (iiia_x0 X1))))) of role definition named def_xpy
% 2.77/3.32 A new definition: (((eq (fofType->(fofType->fofType))) xpy) (fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_pl (iiia_x0 X0)) (iiia_x0 X1)))))
% 2.77/3.32 Defined: xpy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_pl (iiia_x0 X0)) (iiia_x0 X1))))
% 2.77/3.32 FOF formula (<kernel.Constant object at 0x2aefb29737e8>, <kernel.DependentProduct object at 0x2aefb2973c68>) of role type named typ_xty
% 2.77/3.32 Using role type
% 2.77/3.32 Declaring xty:(fofType->(fofType->fofType))
% 2.77/3.32 FOF formula (((eq (fofType->(fofType->fofType))) xty) (fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_ts (iiia_x0 X0)) (iiia_x0 X1))))) of role definition named def_xty
% 2.77/3.32 A new definition: (((eq (fofType->(fofType->fofType))) xty) (fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_ts (iiia_x0 X0)) (iiia_x0 X1)))))
% 2.77/3.32 Defined: xty:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_ts (iiia_x0 X0)) (iiia_x0 X1))))
% 2.77/3.32 FOF formula (<kernel.Constant object at 0x2aefb2973c68>, <kernel.DependentProduct object at 0x2aefb2973560>) of role type named typ_xmy
% 2.77/3.32 Using role type
% 2.77/3.32 Declaring xmy:(fofType->(fofType->fofType))
% 2.77/3.32 FOF formula (((eq (fofType->(fofType->fofType))) xmy) (fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_mn (iiia_x0 X0)) (iiia_x0 X1))))) of role definition named def_xmy
% 2.77/3.32 A new definition: (((eq (fofType->(fofType->fofType))) xmy) (fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_mn (iiia_x0 X0)) (iiia_x0 X1)))))
% 2.77/3.32 Defined: xmy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_mn (iiia_x0 X0)) (iiia_x0 X1))))
% 2.77/3.32 FOF formula (<kernel.Constant object at 0x2aefb2973560>, <kernel.Single object at 0x2aefb2973c68>) of role type named typ_dif
% 2.77/3.32 Using role type
% 2.77/3.32 Declaring dif:fofType
% 2.77/3.32 FOF formula (((eq fofType) dif) (pair1type cut)) of role definition named def_dif
% 2.77/3.32 A new definition: (((eq fofType) dif) (pair1type cut))
% 2.77/3.33 Defined: dif:=(pair1type cut)
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefb2973e18>, <kernel.DependentProduct object at 0x2aefb2973ab8>) of role type named typ_rp_df
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring rp_df:(fofType->(fofType->fofType))
% 2.77/3.33 FOF formula (((eq (fofType->(fofType->fofType))) rp_df) (pair1 cut)) of role definition named def_rp_df
% 2.77/3.33 A new definition: (((eq (fofType->(fofType->fofType))) rp_df) (pair1 cut))
% 2.77/3.33 Defined: rp_df:=(pair1 cut)
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefb29737e8>, <kernel.DependentProduct object at 0x2aefb2973cf8>) of role type named typ_stm
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring stm:(fofType->fofType)
% 2.77/3.33 FOF formula (((eq (fofType->fofType)) stm) (first1 cut)) of role definition named def_stm
% 2.77/3.33 A new definition: (((eq (fofType->fofType)) stm) (first1 cut))
% 2.77/3.33 Defined: stm:=(first1 cut)
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefb2973c68>, <kernel.DependentProduct object at 0x2aefb29761b8>) of role type named typ_std
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring std:(fofType->fofType)
% 2.77/3.33 FOF formula (((eq (fofType->fofType)) std) (second1 cut)) of role definition named def_std
% 2.77/3.33 A new definition: (((eq (fofType->fofType)) std) (second1 cut))
% 2.77/3.33 Defined: std:=(second1 cut)
% 2.77/3.33 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM007^4.ax, trying next directory
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefba1e0d40>, <kernel.DependentProduct object at 0x2aefba1e0bd8>) of role type named typ_rp_eq
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring rp_eq:(fofType->(fofType->Prop))
% 2.77/3.33 FOF formula (((eq (fofType->(fofType->Prop))) rp_eq) (fun (X0:fofType) (X1:fofType)=> ((rp_is ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0))))) of role definition named def_rp_eq
% 2.77/3.33 A new definition: (((eq (fofType->(fofType->Prop))) rp_eq) (fun (X0:fofType) (X1:fofType)=> ((rp_is ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))))
% 2.77/3.33 Defined: rp_eq:=(fun (X0:fofType) (X1:fofType)=> ((rp_is ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0))))
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefba1e0bd8>, <kernel.DependentProduct object at 0x2aefba1e0098>) of role type named typ_posd
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring posd:(fofType->Prop)
% 2.77/3.33 FOF formula (((eq (fofType->Prop)) posd) (fun (X0:fofType)=> ((rp_more (stm X0)) (std X0)))) of role definition named def_posd
% 2.77/3.33 A new definition: (((eq (fofType->Prop)) posd) (fun (X0:fofType)=> ((rp_more (stm X0)) (std X0))))
% 2.77/3.33 Defined: posd:=(fun (X0:fofType)=> ((rp_more (stm X0)) (std X0)))
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefba1e0098>, <kernel.DependentProduct object at 0x2aefba1e0128>) of role type named typ_zero
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring zero:(fofType->Prop)
% 2.77/3.33 FOF formula (((eq (fofType->Prop)) zero) (fun (X0:fofType)=> ((rp_is (stm X0)) (std X0)))) of role definition named def_zero
% 2.77/3.33 A new definition: (((eq (fofType->Prop)) zero) (fun (X0:fofType)=> ((rp_is (stm X0)) (std X0))))
% 2.77/3.33 Defined: zero:=(fun (X0:fofType)=> ((rp_is (stm X0)) (std X0)))
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefba1e0bd8>, <kernel.DependentProduct object at 0x2aefba1e0d40>) of role type named typ_negd
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring negd:(fofType->Prop)
% 2.77/3.33 FOF formula (((eq (fofType->Prop)) negd) (fun (X0:fofType)=> ((rp_less (stm X0)) (std X0)))) of role definition named def_negd
% 2.77/3.33 A new definition: (((eq (fofType->Prop)) negd) (fun (X0:fofType)=> ((rp_less (stm X0)) (std X0))))
% 2.77/3.33 Defined: negd:=(fun (X0:fofType)=> ((rp_less (stm X0)) (std X0)))
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefba1e0098>, <kernel.DependentProduct object at 0x2aefba1e0638>) of role type named typ_pdofrp
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring pdofrp:(fofType->fofType)
% 2.77/3.33 FOF formula (((eq (fofType->fofType)) pdofrp) (fun (X0:fofType)=> ((rp_df ((rp_pl X0) d_1rp)) d_1rp))) of role definition named def_pdofrp
% 2.77/3.33 A new definition: (((eq (fofType->fofType)) pdofrp) (fun (X0:fofType)=> ((rp_df ((rp_pl X0) d_1rp)) d_1rp)))
% 2.77/3.33 Defined: pdofrp:=(fun (X0:fofType)=> ((rp_df ((rp_pl X0) d_1rp)) d_1rp))
% 2.77/3.33 FOF formula (<kernel.Constant object at 0x2aefba1e03f8>, <kernel.DependentProduct object at 0x2aefba1dde60>) of role type named typ_ndofrp
% 2.77/3.33 Using role type
% 2.77/3.33 Declaring ndofrp:(fofType->fofType)
% 2.77/3.33 FOF formula (((eq (fofType->fofType)) ndofrp) (fun (X0:fofType)=> ((rp_df d_1rp) ((rp_pl X0) d_1rp)))) of role definition named def_ndofrp
% 2.77/3.34 A new definition: (((eq (fofType->fofType)) ndofrp) (fun (X0:fofType)=> ((rp_df d_1rp) ((rp_pl X0) d_1rp))))
% 2.77/3.34 Defined: ndofrp:=(fun (X0:fofType)=> ((rp_df d_1rp) ((rp_pl X0) d_1rp)))
% 2.77/3.34 FOF formula (<kernel.Constant object at 0x2aefba1e0098>, <kernel.DependentProduct object at 0x2aefba1ddc20>) of role type named typ_rpofpd
% 2.77/3.34 Using role type
% 2.77/3.34 Declaring rpofpd:(fofType->fofType)
% 2.77/3.34 FOF formula (((eq (fofType->fofType)) rpofpd) (fun (X0:fofType)=> ((rp_mn (stm X0)) (std X0)))) of role definition named def_rpofpd
% 2.77/3.34 A new definition: (((eq (fofType->fofType)) rpofpd) (fun (X0:fofType)=> ((rp_mn (stm X0)) (std X0))))
% 2.77/3.34 Defined: rpofpd:=(fun (X0:fofType)=> ((rp_mn (stm X0)) (std X0)))
% 2.77/3.34 FOF formula (<kernel.Constant object at 0x2aefba1e0638>, <kernel.DependentProduct object at 0x2aefba1ddfc8>) of role type named typ_rpofnd
% 2.77/3.34 Using role type
% 2.77/3.34 Declaring rpofnd:(fofType->fofType)
% 2.77/3.34 FOF formula (((eq (fofType->fofType)) rpofnd) (fun (X0:fofType)=> ((rp_mn (std X0)) (stm X0)))) of role definition named def_rpofnd
% 2.77/3.34 A new definition: (((eq (fofType->fofType)) rpofnd) (fun (X0:fofType)=> ((rp_mn (std X0)) (stm X0))))
% 2.77/3.34 Defined: rpofnd:=(fun (X0:fofType)=> ((rp_mn (std X0)) (stm X0)))
% 2.77/3.34 FOF formula (<kernel.Constant object at 0x2aefba1e0638>, <kernel.DependentProduct object at 0x2aefba1dd7e8>) of role type named typ_absd
% 2.77/3.34 Using role type
% 2.77/3.34 Declaring absd:(fofType->fofType)
% 2.77/3.34 FOF formula (((eq (fofType->fofType)) absd) (fun (X0:fofType)=> ((((ite (negd X0)) dif) ((rp_df (std X0)) (stm X0))) X0))) of role definition named def_absd
% 2.77/3.34 A new definition: (((eq (fofType->fofType)) absd) (fun (X0:fofType)=> ((((ite (negd X0)) dif) ((rp_df (std X0)) (stm X0))) X0)))
% 2.77/3.34 Defined: absd:=(fun (X0:fofType)=> ((((ite (negd X0)) dif) ((rp_df (std X0)) (stm X0))) X0))
% 2.77/3.34 FOF formula (<kernel.Constant object at 0x2aefba1e03f8>, <kernel.DependentProduct object at 0x2aefba1dde60>) of role type named typ_mored
% 2.77/3.34 Using role type
% 2.77/3.34 Declaring mored:(fofType->(fofType->Prop))
% 2.77/3.34 FOF formula (((eq (fofType->(fofType->Prop))) mored) (fun (X0:fofType) (X1:fofType)=> ((rp_more ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0))))) of role definition named def_mored
% 2.77/3.34 A new definition: (((eq (fofType->(fofType->Prop))) mored) (fun (X0:fofType) (X1:fofType)=> ((rp_more ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))))
% 2.77/3.34 Defined: mored:=(fun (X0:fofType) (X1:fofType)=> ((rp_more ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0))))
% 2.77/3.34 FOF formula (<kernel.Constant object at 0x2aefba1dde60>, <kernel.DependentProduct object at 0x2aefba1dd7e8>) of role type named typ_lessd
% 2.77/3.34 Using role type
% 2.77/3.34 Declaring lessd:(fofType->(fofType->Prop))
% 2.77/3.34 FOF formula (((eq (fofType->(fofType->Prop))) lessd) (fun (X0:fofType) (X1:fofType)=> ((rp_less ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0))))) of role definition named def_lessd
% 2.77/3.34 A new definition: (((eq (fofType->(fofType->Prop))) lessd) (fun (X0:fofType) (X1:fofType)=> ((rp_less ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))))
% 2.77/3.34 Defined: lessd:=(fun (X0:fofType) (X1:fofType)=> ((rp_less ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0))))
% 2.77/3.34 FOF formula (<kernel.Constant object at 0x2aefba1dd7e8>, <kernel.DependentProduct object at 0x2aefba1dd518>) of role type named typ_rp_moreq
% 2.77/3.34 Using role type
% 2.77/3.34 Declaring rp_moreq:(fofType->(fofType->Prop))
% 2.77/3.34 FOF formula (((eq (fofType->(fofType->Prop))) rp_moreq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((mored X0) X1)) ((rp_eq X0) X1)))) of role definition named def_rp_moreq
% 2.77/3.34 A new definition: (((eq (fofType->(fofType->Prop))) rp_moreq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((mored X0) X1)) ((rp_eq X0) X1))))
% 2.77/3.34 Defined: rp_moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((mored X0) X1)) ((rp_eq X0) X1)))
% 2.77/3.34 FOF formula (<kernel.Constant object at 0x2aefba1dd518>, <kernel.DependentProduct object at 0x2aefba1dd560>) of role type named typ_rp_lesseq
% 2.77/3.34 Using role type
% 2.77/3.34 Declaring rp_lesseq:(fofType->(fofType->Prop))
% 2.77/3.34 FOF formula (((eq (fofType->(fofType->Prop))) rp_lesseq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((lessd X0) X1)) ((rp_eq X0) X1)))) of role definition named def_rp_lesseq
% 2.77/3.36 A new definition: (((eq (fofType->(fofType->Prop))) rp_lesseq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((lessd X0) X1)) ((rp_eq X0) X1))))
% 2.77/3.36 Defined: rp_lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessd X0) X1)) ((rp_eq X0) X1)))
% 2.77/3.36 FOF formula (<kernel.Constant object at 0x2aefba1dd560>, <kernel.DependentProduct object at 0x2aefba1dd9e0>) of role type named typ_ratd
% 2.77/3.36 Using role type
% 2.77/3.36 Declaring ratd:(fofType->Prop)
% 2.77/3.36 FOF formula (((eq (fofType->Prop)) ratd) (fun (X0:fofType)=> ((d_not (zero X0))->(ratrp (rpofpd (absd X0)))))) of role definition named def_ratd
% 2.77/3.36 A new definition: (((eq (fofType->Prop)) ratd) (fun (X0:fofType)=> ((d_not (zero X0))->(ratrp (rpofpd (absd X0))))))
% 2.77/3.36 Defined: ratd:=(fun (X0:fofType)=> ((d_not (zero X0))->(ratrp (rpofpd (absd X0)))))
% 2.77/3.36 FOF formula (<kernel.Constant object at 0x2aefba1dd9e0>, <kernel.DependentProduct object at 0x2aefba1ddc20>) of role type named typ_irratd
% 2.77/3.36 Using role type
% 2.77/3.36 Declaring irratd:(fofType->Prop)
% 2.77/3.36 FOF formula (((eq (fofType->Prop)) irratd) (fun (X0:fofType)=> (d_not (ratd X0)))) of role definition named def_irratd
% 2.77/3.36 A new definition: (((eq (fofType->Prop)) irratd) (fun (X0:fofType)=> (d_not (ratd X0))))
% 2.77/3.36 Defined: irratd:=(fun (X0:fofType)=> (d_not (ratd X0)))
% 2.77/3.36 FOF formula (<kernel.Constant object at 0x2aefba1ddc20>, <kernel.DependentProduct object at 0x2aefba1dd518>) of role type named typ_natd
% 2.77/3.36 Using role type
% 2.77/3.36 Declaring natd:(fofType->Prop)
% 2.77/3.36 FOF formula (((eq (fofType->Prop)) natd) (fun (X0:fofType)=> ((d_and (posd X0)) ((posd X0)->(natrp (rpofpd X0)))))) of role definition named def_natd
% 2.77/3.36 A new definition: (((eq (fofType->Prop)) natd) (fun (X0:fofType)=> ((d_and (posd X0)) ((posd X0)->(natrp (rpofpd X0))))))
% 2.77/3.36 Defined: natd:=(fun (X0:fofType)=> ((d_and (posd X0)) ((posd X0)->(natrp (rpofpd X0)))))
% 2.77/3.36 FOF formula (<kernel.Constant object at 0x2aefba1dd518>, <kernel.DependentProduct object at 0x2aefba1dd8c0>) of role type named typ_pdofnt
% 2.77/3.36 Using role type
% 2.77/3.36 Declaring pdofnt:(fofType->fofType)
% 2.77/3.36 FOF formula (((eq (fofType->fofType)) pdofnt) (fun (X0:fofType)=> (pdofrp (rpofnt X0)))) of role definition named def_pdofnt
% 2.77/3.36 A new definition: (((eq (fofType->fofType)) pdofnt) (fun (X0:fofType)=> (pdofrp (rpofnt X0))))
% 2.77/3.36 Defined: pdofnt:=(fun (X0:fofType)=> (pdofrp (rpofnt X0)))
% 2.77/3.36 FOF formula (<kernel.Constant object at 0x2aefba1ddc20>, <kernel.DependentProduct object at 0x2aefba1dd9e0>) of role type named typ_intd
% 2.77/3.36 Using role type
% 2.77/3.36 Declaring intd:(fofType->Prop)
% 2.77/3.36 FOF formula (((eq (fofType->Prop)) intd) (fun (X0:fofType)=> ((l_or (zero X0)) (natd (absd X0))))) of role definition named def_intd
% 2.77/3.36 A new definition: (((eq (fofType->Prop)) intd) (fun (X0:fofType)=> ((l_or (zero X0)) (natd (absd X0)))))
% 2.77/3.36 Defined: intd:=(fun (X0:fofType)=> ((l_or (zero X0)) (natd (absd X0))))
% 2.77/3.36 FOF formula (<kernel.Constant object at 0x2aefba1dd518>, <kernel.DependentProduct object at 0x2aefba1dd5f0>) of role type named typ_rp_pd
% 2.77/3.36 Using role type
% 2.77/3.36 Declaring rp_pd:(fofType->(fofType->fofType))
% 2.77/3.36 FOF formula (((eq (fofType->(fofType->fofType))) rp_pd) (fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl (stm X0)) (stm X1))) ((rp_pl (std X0)) (std X1))))) of role definition named def_rp_pd
% 2.77/3.36 A new definition: (((eq (fofType->(fofType->fofType))) rp_pd) (fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl (stm X0)) (stm X1))) ((rp_pl (std X0)) (std X1)))))
% 2.77/3.36 Defined: rp_pd:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl (stm X0)) (stm X1))) ((rp_pl (std X0)) (std X1))))
% 2.77/3.36 FOF formula (<kernel.Constant object at 0x2aefba2c0128>, <kernel.DependentProduct object at 0x2aefba1ddd40>) of role type named typ_m0d
% 2.77/3.36 Using role type
% 2.77/3.36 Declaring m0d:(fofType->fofType)
% 2.77/3.36 FOF formula (((eq (fofType->fofType)) m0d) (fun (X0:fofType)=> ((rp_df (std X0)) (stm X0)))) of role definition named def_m0d
% 2.77/3.36 A new definition: (((eq (fofType->fofType)) m0d) (fun (X0:fofType)=> ((rp_df (std X0)) (stm X0))))
% 2.77/3.36 Defined: m0d:=(fun (X0:fofType)=> ((rp_df (std X0)) (stm X0)))
% 2.77/3.36 FOF formula (<kernel.Constant object at 0x2aefba2c0518>, <kernel.DependentProduct object at 0x2aefba1dd5f0>) of role type named typ_rp_md
% 2.77/3.37 Using role type
% 2.77/3.37 Declaring rp_md:(fofType->(fofType->fofType))
% 2.77/3.37 FOF formula (((eq (fofType->(fofType->fofType))) rp_md) (fun (X0:fofType) (X1:fofType)=> ((rp_pd X0) (m0d X1)))) of role definition named def_rp_md
% 2.77/3.37 A new definition: (((eq (fofType->(fofType->fofType))) rp_md) (fun (X0:fofType) (X1:fofType)=> ((rp_pd X0) (m0d X1))))
% 2.77/3.37 Defined: rp_md:=(fun (X0:fofType) (X1:fofType)=> ((rp_pd X0) (m0d X1)))
% 2.77/3.37 FOF formula (<kernel.Constant object at 0x2aefba2c0518>, <kernel.DependentProduct object at 0x2aefba1ddd40>) of role type named typ_rp_td
% 2.77/3.37 Using role type
% 2.77/3.37 Declaring rp_td:(fofType->(fofType->fofType))
% 2.77/3.37 FOF formula (((eq (fofType->(fofType->fofType))) rp_td) (fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl ((rp_ts (stm X0)) (stm X1))) ((rp_ts (std X0)) (std X1)))) ((rp_pl ((rp_ts (stm X0)) (std X1))) ((rp_ts (std X0)) (stm X1)))))) of role definition named def_rp_td
% 2.77/3.37 A new definition: (((eq (fofType->(fofType->fofType))) rp_td) (fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl ((rp_ts (stm X0)) (stm X1))) ((rp_ts (std X0)) (std X1)))) ((rp_pl ((rp_ts (stm X0)) (std X1))) ((rp_ts (std X0)) (stm X1))))))
% 2.77/3.37 Defined: rp_td:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl ((rp_ts (stm X0)) (stm X1))) ((rp_ts (std X0)) (std X1)))) ((rp_pl ((rp_ts (stm X0)) (std X1))) ((rp_ts (std X0)) (stm X1)))))
% 2.77/3.37 FOF formula (<kernel.Constant object at 0x2aefba2c0200>, <kernel.Single object at 0x2aefba1dd560>) of role type named typ_d_1df
% 2.77/3.37 Using role type
% 2.77/3.37 Declaring d_1df:fofType
% 2.77/3.37 FOF formula (((eq fofType) d_1df) (pdofrp d_1rp)) of role definition named def_d_1df
% 2.77/3.37 A new definition: (((eq fofType) d_1df) (pdofrp d_1rp))
% 2.77/3.37 Defined: d_1df:=(pdofrp d_1rp)
% 2.77/3.37 FOF formula (<kernel.Constant object at 0x2aefba1dd5f0>, <kernel.DependentProduct object at 0x2aefbac97c20>) of role type named typ_p1p2
% 2.77/3.37 Using role type
% 2.77/3.37 Declaring p1p2:(fofType->(fofType->Prop))
% 2.77/3.37 FOF formula (((eq (fofType->(fofType->Prop))) p1p2) (fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (posd X1)))) of role definition named def_p1p2
% 2.77/3.37 A new definition: (((eq (fofType->(fofType->Prop))) p1p2) (fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (posd X1))))
% 2.77/3.37 Defined: p1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (posd X1)))
% 2.77/3.37 FOF formula (<kernel.Constant object at 0x2aefba1dd8c0>, <kernel.DependentProduct object at 0x2aefbac979e0>) of role type named typ_p1n2
% 2.77/3.37 Using role type
% 2.77/3.37 Declaring p1n2:(fofType->(fofType->Prop))
% 2.77/3.37 FOF formula (((eq (fofType->(fofType->Prop))) p1n2) (fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (negd X1)))) of role definition named def_p1n2
% 2.77/3.37 A new definition: (((eq (fofType->(fofType->Prop))) p1n2) (fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (negd X1))))
% 2.77/3.37 Defined: p1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (negd X1)))
% 2.77/3.37 FOF formula (<kernel.Constant object at 0x2aefba1dd8c0>, <kernel.DependentProduct object at 0x2aefbac97cf8>) of role type named typ_n1p2
% 2.77/3.37 Using role type
% 2.77/3.37 Declaring n1p2:(fofType->(fofType->Prop))
% 2.77/3.37 FOF formula (((eq (fofType->(fofType->Prop))) n1p2) (fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (posd X1)))) of role definition named def_n1p2
% 2.77/3.37 A new definition: (((eq (fofType->(fofType->Prop))) n1p2) (fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (posd X1))))
% 2.77/3.37 Defined: n1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (posd X1)))
% 2.77/3.37 FOF formula (<kernel.Constant object at 0x2aefba1dd8c0>, <kernel.DependentProduct object at 0x2aefbac973f8>) of role type named typ_n1n2
% 2.77/3.37 Using role type
% 2.77/3.37 Declaring n1n2:(fofType->(fofType->Prop))
% 2.77/3.37 FOF formula (((eq (fofType->(fofType->Prop))) n1n2) (fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (negd X1)))) of role definition named def_n1n2
% 2.77/3.37 A new definition: (((eq (fofType->(fofType->Prop))) n1n2) (fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (negd X1))))
% 2.77/3.37 Defined: n1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (negd X1)))
% 2.77/3.37 FOF formula (<kernel.Constant object at 0x2aefbac973f8>, <kernel.DependentProduct object at 0x2aefbac97680>) of role type named typ_arpi
% 2.77/3.37 Using role type
% 2.77/3.37 Declaring arpi:(fofType->fofType)
% 2.77/3.37 FOF formula (((eq (fofType->fofType)) arpi) (fun (X0:fofType)=> ((rp_ov d_1rp) (rpofpd X0)))) of role definition named def_arpi
% 2.77/3.38 A new definition: (((eq (fofType->fofType)) arpi) (fun (X0:fofType)=> ((rp_ov d_1rp) (rpofpd X0))))
% 2.77/3.38 Defined: arpi:=(fun (X0:fofType)=> ((rp_ov d_1rp) (rpofpd X0)))
% 2.77/3.38 FOF formula (<kernel.Constant object at 0x2aefbac97680>, <kernel.DependentProduct object at 0x2aefbac979e0>) of role type named typ_iv4d_ai
% 2.77/3.38 Using role type
% 2.77/3.38 Declaring iv4d_ai:(fofType->fofType)
% 2.77/3.38 FOF formula (((eq (fofType->fofType)) iv4d_ai) (fun (X0:fofType)=> (pdofrp (arpi X0)))) of role definition named def_iv4d_ai
% 2.77/3.38 A new definition: (((eq (fofType->fofType)) iv4d_ai) (fun (X0:fofType)=> (pdofrp (arpi X0))))
% 2.77/3.38 Defined: iv4d_ai:=(fun (X0:fofType)=> (pdofrp (arpi X0)))
% 2.77/3.38 FOF formula (<kernel.Constant object at 0x2aefbac979e0>, <kernel.Single object at 0x2aefbac97680>) of role type named typ_iv5d_2
% 2.77/3.38 Using role type
% 2.77/3.38 Declaring iv5d_2:fofType
% 2.77/3.38 FOF formula (((eq fofType) iv5d_2) ((rp_pl d_1rp) d_1rp)) of role definition named def_iv5d_2
% 2.77/3.38 A new definition: (((eq fofType) iv5d_2) ((rp_pl d_1rp) d_1rp))
% 2.77/3.38 Defined: iv5d_2:=((rp_pl d_1rp) d_1rp)
% 2.77/3.38 FOF formula (<kernel.Constant object at 0x2aefbac97680>, <kernel.DependentProduct object at 0x2aefbac97a70>) of role type named typ_rp1
% 2.77/3.38 Using role type
% 2.77/3.38 Declaring rp1:(fofType->fofType)
% 2.77/3.38 FOF formula (((eq (fofType->fofType)) rp1) (fun (X0:fofType)=> ((rp_pl X0) d_1rp))) of role definition named def_rp1
% 2.77/3.38 A new definition: (((eq (fofType->fofType)) rp1) (fun (X0:fofType)=> ((rp_pl X0) d_1rp)))
% 2.77/3.38 Defined: rp1:=(fun (X0:fofType)=> ((rp_pl X0) d_1rp))
% 2.77/3.38 FOF formula (<kernel.Constant object at 0x2aefbac97a70>, <kernel.DependentProduct object at 0x2aefbac976c8>) of role type named typ_rp_in
% 2.77/3.38 Using role type
% 2.77/3.38 Declaring rp_in:(fofType->(fofType->Prop))
% 2.77/3.38 FOF formula (((eq (fofType->(fofType->Prop))) rp_in) (esti cut)) of role definition named def_rp_in
% 2.77/3.38 A new definition: (((eq (fofType->(fofType->Prop))) rp_in) (esti cut))
% 2.77/3.38 Defined: rp_in:=(esti cut)
% 2.77/3.38 FOF formula (<kernel.Constant object at 0x2aefbac979e0>, <kernel.DependentProduct object at 0x2aefbac978c0>) of role type named typ_d_5p205_prop1
% 2.77/3.38 Using role type
% 2.77/3.38 Declaring d_5p205_prop1:(fofType->(fofType->Prop))
% 2.77/3.38 FOF formula (((eq (fofType->(fofType->Prop))) d_5p205_prop1) (fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_less X2) X1)->((rp_in X2) X0)))))) of role definition named def_d_5p205_prop1
% 2.77/3.38 A new definition: (((eq (fofType->(fofType->Prop))) d_5p205_prop1) (fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_less X2) X1)->((rp_in X2) X0))))))
% 2.77/3.38 Defined: d_5p205_prop1:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_less X2) X1)->((rp_in X2) X0)))))
% 2.77/3.38 FOF formula (<kernel.Constant object at 0x2aefbac978c0>, <kernel.DependentProduct object at 0x2aefbac976c8>) of role type named typ_d_5p205_prop2
% 2.77/3.38 Using role type
% 2.77/3.38 Declaring d_5p205_prop2:(fofType->(fofType->Prop))
% 2.77/3.38 FOF formula (((eq (fofType->(fofType->Prop))) d_5p205_prop2) (fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_more X2) X1)->((rp_in X2) X0)))))) of role definition named def_d_5p205_prop2
% 2.77/3.38 A new definition: (((eq (fofType->(fofType->Prop))) d_5p205_prop2) (fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_more X2) X1)->((rp_in X2) X0))))))
% 2.77/3.38 Defined: d_5p205_prop2:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_more X2) X1)->((rp_in X2) X0)))))
% 2.77/3.38 FOF formula (<kernel.Constant object at 0x2aefbac976c8>, <kernel.DependentProduct object at 0x2aefbac97d40>) of role type named typ_d_5p205_prop3
% 2.77/3.38 Using role type
% 2.77/3.38 Declaring d_5p205_prop3:(fofType->(fofType->(fofType->Prop)))
% 2.77/3.38 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_5p205_prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5p205_prop1 X0) X2)) ((d_5p205_prop2 X1) X2)))) of role definition named def_d_5p205_prop3
% 2.77/3.38 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_5p205_prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5p205_prop1 X0) X2)) ((d_5p205_prop2 X1) X2))))
% 2.77/3.38 Defined: d_5p205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5p205_prop1 X0) X2)) ((d_5p205_prop2 X1) X2)))
% 2.77/3.38 FOF formula (<kernel.Constant object at 0x2aefbac97d40>, <kernel.DependentProduct object at 0x2aefbac97a70>) of role type named typ_schnittprop
% 2.86/3.39 Using role type
% 2.86/3.39 Declaring schnittprop:(fofType->(fofType->Prop))
% 2.86/3.39 FOF formula (((eq (fofType->(fofType->Prop))) schnittprop) (fun (X0:fofType) (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((d_and ((rp_in X2) X0)) ((lrt X2) X1)))))) of role definition named def_schnittprop
% 2.86/3.39 A new definition: (((eq (fofType->(fofType->Prop))) schnittprop) (fun (X0:fofType) (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((d_and ((rp_in X2) X0)) ((lrt X2) X1))))))
% 2.86/3.39 Defined: schnittprop:=(fun (X0:fofType) (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((d_and ((rp_in X2) X0)) ((lrt X2) X1)))))
% 2.86/3.39 FOF formula (<kernel.Constant object at 0x2aefbac97a70>, <kernel.DependentProduct object at 0x2aefbac976c8>) of role type named typ_schnittset
% 2.86/3.39 Using role type
% 2.86/3.39 Declaring schnittset:(fofType->fofType)
% 2.86/3.39 FOF formula (((eq (fofType->fofType)) schnittset) (fun (X0:fofType)=> ((d_Sep rat) (schnittprop X0)))) of role definition named def_schnittset
% 2.86/3.39 A new definition: (((eq (fofType->fofType)) schnittset) (fun (X0:fofType)=> ((d_Sep rat) (schnittprop X0))))
% 2.86/3.39 Defined: schnittset:=(fun (X0:fofType)=> ((d_Sep rat) (schnittprop X0)))
% 2.86/3.39 FOF formula (<kernel.Constant object at 0x2aefbac976c8>, <kernel.DependentProduct object at 0x2aefbac97320>) of role type named typ_snt
% 2.86/3.39 Using role type
% 2.86/3.39 Declaring snt:(fofType->(fofType->fofType))
% 2.86/3.39 FOF formula (((eq (fofType->(fofType->fofType))) snt) (fun (X0:fofType) (X1:fofType)=> (cutof (schnittset X0)))) of role definition named def_snt
% 2.86/3.39 A new definition: (((eq (fofType->(fofType->fofType))) snt) (fun (X0:fofType) (X1:fofType)=> (cutof (schnittset X0))))
% 2.86/3.39 Defined: snt:=(fun (X0:fofType) (X1:fofType)=> (cutof (schnittset X0)))
% 2.86/3.39 FOF formula (<kernel.Constant object at 0x2aefbac97320>, <kernel.DependentProduct object at 0x2aefbac97bd8>) of role type named typ_schnitt
% 2.86/3.39 Using role type
% 2.86/3.39 Declaring schnitt:(fofType->(fofType->fofType))
% 2.86/3.39 FOF formula (((eq (fofType->(fofType->fofType))) schnitt) (fun (X0:fofType) (X1:fofType)=> ((ind cut) ((d_5p205_prop3 X0) X1)))) of role definition named def_schnitt
% 2.86/3.39 A new definition: (((eq (fofType->(fofType->fofType))) schnitt) (fun (X0:fofType) (X1:fofType)=> ((ind cut) ((d_5p205_prop3 X0) X1))))
% 2.86/3.39 Defined: schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) ((d_5p205_prop3 X0) X1)))
% 2.86/3.39 FOF formula (<kernel.Constant object at 0x2aefbac97bd8>, <kernel.DependentProduct object at 0x2aefbac97d88>) of role type named typ_srp
% 2.86/3.39 Using role type
% 2.86/3.39 Declaring srp:(fofType->fofType)
% 2.86/3.39 FOF formula (((eq (fofType->fofType)) srp) (fun (X0:fofType)=> (sqrt (rpofpd X0)))) of role definition named def_srp
% 2.86/3.39 A new definition: (((eq (fofType->fofType)) srp) (fun (X0:fofType)=> (sqrt (rpofpd X0))))
% 2.86/3.39 Defined: srp:=(fun (X0:fofType)=> (sqrt (rpofpd X0)))
% 2.86/3.39 FOF formula (<kernel.Constant object at 0x2aefbac97d88>, <kernel.DependentProduct object at 0x2aefbac97a70>) of role type named typ_d161_s
% 2.86/3.39 Using role type
% 2.86/3.39 Declaring d161_s:(fofType->fofType)
% 2.86/3.39 FOF formula (((eq (fofType->fofType)) d161_s) (fun (X0:fofType)=> (pdofrp (srp X0)))) of role definition named def_d161_s
% 2.86/3.39 A new definition: (((eq (fofType->fofType)) d161_s) (fun (X0:fofType)=> (pdofrp (srp X0))))
% 2.86/3.39 Defined: d161_s:=(fun (X0:fofType)=> (pdofrp (srp X0)))
% 2.86/3.39 FOF formula (<kernel.Constant object at 0x2aefbac97a70>, <kernel.DependentProduct object at 0x2aefbac97638>) of role type named typ_apb1
% 2.86/3.39 Using role type
% 2.86/3.39 Declaring apb1:(fofType->(fofType->fofType))
% 2.86/3.39 FOF formula (((eq (fofType->(fofType->fofType))) apb1) (fun (X0:fofType) (X1:fofType)=> (rpofpd ((rp_pd X0) X1)))) of role definition named def_apb1
% 2.86/3.39 A new definition: (((eq (fofType->(fofType->fofType))) apb1) (fun (X0:fofType) (X1:fofType)=> (rpofpd ((rp_pd X0) X1))))
% 2.86/3.39 Defined: apb1:=(fun (X0:fofType) (X1:fofType)=> (rpofpd ((rp_pd X0) X1)))
% 2.86/3.39 FOF formula (<kernel.Constant object at 0x2aefbac97638>, <kernel.DependentProduct object at 0x2aefbac97d88>) of role type named typ_intd_b2
% 2.86/3.39 Using role type
% 2.86/3.39 Declaring intd_b2:(fofType->fofType)
% 2.86/3.39 FOF formula (((eq (fofType->fofType)) intd_b2) (fun (X0:fofType)=> (rpofpd (m0d X0)))) of role definition named def_intd_b2
% 2.87/3.40 A new definition: (((eq (fofType->fofType)) intd_b2) (fun (X0:fofType)=> (rpofpd (m0d X0))))
% 2.87/3.40 Defined: intd_b2:=(fun (X0:fofType)=> (rpofpd (m0d X0)))
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac97d88>, <kernel.DependentProduct object at 0x2aefbac97248>) of role type named typ_intd_a3
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring intd_a3:(fofType->(fofType->fofType))
% 2.87/3.40 FOF formula (((eq (fofType->(fofType->fofType))) intd_a3) (fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X0)))) of role definition named def_intd_a3
% 2.87/3.40 A new definition: (((eq (fofType->(fofType->fofType))) intd_a3) (fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X0))))
% 2.87/3.40 Defined: intd_a3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X0)))
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac97248>, <kernel.DependentProduct object at 0x2aefbac97d40>) of role type named typ_intd_b3
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring intd_b3:(fofType->(fofType->fofType))
% 2.87/3.40 FOF formula (((eq (fofType->(fofType->fofType))) intd_b3) (fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X1)))) of role definition named def_intd_b3
% 2.87/3.40 A new definition: (((eq (fofType->(fofType->fofType))) intd_b3) (fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X1))))
% 2.87/3.40 Defined: intd_b3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X1)))
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac97d40>, <kernel.DependentProduct object at 0x2aefbac97638>) of role type named typ_atb3
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring atb3:(fofType->(fofType->fofType))
% 2.87/3.40 FOF formula (((eq (fofType->(fofType->fofType))) atb3) (fun (X0:fofType) (X1:fofType)=> (rpofpd (absd ((rp_td X0) X1))))) of role definition named def_atb3
% 2.87/3.40 A new definition: (((eq (fofType->(fofType->fofType))) atb3) (fun (X0:fofType) (X1:fofType)=> (rpofpd (absd ((rp_td X0) X1)))))
% 2.87/3.40 Defined: atb3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd ((rp_td X0) X1))))
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac97638>, <kernel.DependentProduct object at 0x2aefbac97d88>) of role type named typ_r_inn
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring r_inn:(fofType->(fofType->Prop))
% 2.87/3.40 FOF formula (((eq (fofType->(fofType->Prop))) r_inn) (esti dif)) of role definition named def_r_inn
% 2.87/3.40 A new definition: (((eq (fofType->(fofType->Prop))) r_inn) (esti dif))
% 2.87/3.40 Defined: r_inn:=(esti dif)
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac97b48>, <kernel.Single object at 0x2aefbac97638>) of role type named typ_real
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring real:fofType
% 2.87/3.40 FOF formula (((eq fofType) real) ((ect dif) rp_eq)) of role definition named def_real
% 2.87/3.40 A new definition: (((eq fofType) real) ((ect dif) rp_eq))
% 2.87/3.40 Defined: real:=((ect dif) rp_eq)
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac97dd0>, <kernel.DependentProduct object at 0x2aefbd942368>) of role type named typ_r_is
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring r_is:(fofType->(fofType->Prop))
% 2.87/3.40 FOF formula (((eq (fofType->(fofType->Prop))) r_is) (e_is real)) of role definition named def_r_is
% 2.87/3.40 A new definition: (((eq (fofType->(fofType->Prop))) r_is) (e_is real))
% 2.87/3.40 Defined: r_is:=(e_is real)
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac97b48>, <kernel.DependentProduct object at 0x2aefbd942638>) of role type named typ_r_nis
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring r_nis:(fofType->(fofType->Prop))
% 2.87/3.40 FOF formula (((eq (fofType->(fofType->Prop))) r_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((r_is X0) X1)))) of role definition named def_r_nis
% 2.87/3.40 A new definition: (((eq (fofType->(fofType->Prop))) r_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((r_is X0) X1))))
% 2.87/3.40 Defined: r_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((r_is X0) X1)))
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac975a8>, <kernel.DependentProduct object at 0x2aefbd942638>) of role type named typ_r_some
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring r_some:((fofType->Prop)->Prop)
% 2.87/3.40 FOF formula (((eq ((fofType->Prop)->Prop)) r_some) (l_some real)) of role definition named def_r_some
% 2.87/3.40 A new definition: (((eq ((fofType->Prop)->Prop)) r_some) (l_some real))
% 2.87/3.40 Defined: r_some:=(l_some real)
% 2.87/3.40 FOF formula (<kernel.Constant object at 0x2aefbac975a8>, <kernel.DependentProduct object at 0x2aefbd942320>) of role type named typ_r_all
% 2.87/3.40 Using role type
% 2.87/3.40 Declaring r_all:((fofType->Prop)->Prop)
% 2.87/3.40 FOF formula (((eq ((fofType->Prop)->Prop)) r_all) (all real)) of role definition named def_r_all
% 2.88/3.41 A new definition: (((eq ((fofType->Prop)->Prop)) r_all) (all real))
% 2.88/3.41 Defined: r_all:=(all real)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbac97dd0>, <kernel.DependentProduct object at 0x2aefbd942320>) of role type named typ_r_one
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring r_one:((fofType->Prop)->Prop)
% 2.88/3.41 FOF formula (((eq ((fofType->Prop)->Prop)) r_one) (one real)) of role definition named def_r_one
% 2.88/3.41 A new definition: (((eq ((fofType->Prop)->Prop)) r_one) (one real))
% 2.88/3.41 Defined: r_one:=(one real)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd9427e8>, <kernel.DependentProduct object at 0x2aefbd9425f0>) of role type named typ_r_in
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring r_in:(fofType->(fofType->Prop))
% 2.88/3.41 FOF formula (((eq (fofType->(fofType->Prop))) r_in) (esti real)) of role definition named def_r_in
% 2.88/3.41 A new definition: (((eq (fofType->(fofType->Prop))) r_in) (esti real))
% 2.88/3.41 Defined: r_in:=(esti real)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd942b00>, <kernel.DependentProduct object at 0x2aefbd942710>) of role type named typ_realof
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring realof:(fofType->fofType)
% 2.88/3.41 FOF formula (((eq (fofType->fofType)) realof) ((ectelt dif) rp_eq)) of role definition named def_realof
% 2.88/3.41 A new definition: (((eq (fofType->fofType)) realof) ((ectelt dif) rp_eq))
% 2.88/3.41 Defined: realof:=((ectelt dif) rp_eq)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd942710>, <kernel.DependentProduct object at 0x2aefbd942cf8>) of role type named typ_r_class
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring r_class:(fofType->fofType)
% 2.88/3.41 FOF formula (((eq (fofType->fofType)) r_class) ((ecect dif) rp_eq)) of role definition named def_r_class
% 2.88/3.41 A new definition: (((eq (fofType->fofType)) r_class) ((ecect dif) rp_eq))
% 2.88/3.41 Defined: r_class:=((ecect dif) rp_eq)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd942cf8>, <kernel.DependentProduct object at 0x2aefbd942170>) of role type named typ_r_fixf
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring r_fixf:(fofType->(fofType->Prop))
% 2.88/3.41 FOF formula (((eq (fofType->(fofType->Prop))) r_fixf) ((fixfu dif) rp_eq)) of role definition named def_r_fixf
% 2.88/3.41 A new definition: (((eq (fofType->(fofType->Prop))) r_fixf) ((fixfu dif) rp_eq))
% 2.88/3.41 Defined: r_fixf:=((fixfu dif) rp_eq)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd942170>, <kernel.DependentProduct object at 0x2aefbd942200>) of role type named typ_indreal
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring indreal:(fofType->(fofType->(fofType->fofType)))
% 2.88/3.41 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) indreal) ((indeq dif) rp_eq)) of role definition named def_indreal
% 2.88/3.41 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) indreal) ((indeq dif) rp_eq))
% 2.88/3.41 Defined: indreal:=((indeq dif) rp_eq)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd942200>, <kernel.DependentProduct object at 0x2aefbd942f80>) of role type named typ_fixf2
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring fixf2:(fofType->(fofType->Prop))
% 2.88/3.41 FOF formula (((eq (fofType->(fofType->Prop))) fixf2) ((fixfu2 dif) rp_eq)) of role definition named def_fixf2
% 2.88/3.41 A new definition: (((eq (fofType->(fofType->Prop))) fixf2) ((fixfu2 dif) rp_eq))
% 2.88/3.41 Defined: fixf2:=((fixfu2 dif) rp_eq)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd942f80>, <kernel.DependentProduct object at 0x2aefbd9420e0>) of role type named typ_indreal2
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring indreal2:(fofType->(fofType->(fofType->(fofType->fofType))))
% 2.88/3.41 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) indreal2) ((indeq2 dif) rp_eq)) of role definition named def_indreal2
% 2.88/3.41 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) indreal2) ((indeq2 dif) rp_eq))
% 2.88/3.41 Defined: indreal2:=((indeq2 dif) rp_eq)
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd9420e0>, <kernel.Single object at 0x2aefbd942f80>) of role type named typ_r_0
% 2.88/3.41 Using role type
% 2.88/3.41 Declaring r_0:fofType
% 2.88/3.41 FOF formula (((eq fofType) r_0) (realof ((rp_df d_1rp) d_1rp))) of role definition named def_r_0
% 2.88/3.41 A new definition: (((eq fofType) r_0) (realof ((rp_df d_1rp) d_1rp)))
% 2.88/3.41 Defined: r_0:=(realof ((rp_df d_1rp) d_1rp))
% 2.88/3.41 FOF formula (<kernel.Constant object at 0x2aefbd942a70>, <kernel.DependentProduct object at 0x2aefbd942f80>) of role type named typ_propp
% 2.88/3.42 Using role type
% 2.88/3.42 Declaring propp:(fofType->(fofType->Prop))
% 2.88/3.42 FOF formula (((eq (fofType->(fofType->Prop))) propp) (fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (posd X1)))) of role definition named def_propp
% 2.88/3.42 A new definition: (((eq (fofType->(fofType->Prop))) propp) (fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (posd X1))))
% 2.88/3.42 Defined: propp:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (posd X1)))
% 2.88/3.42 FOF formula (<kernel.Constant object at 0x2aefbd942f80>, <kernel.DependentProduct object at 0x2aefbd942170>) of role type named typ_pos
% 2.88/3.42 Using role type
% 2.88/3.42 Declaring pos:(fofType->Prop)
% 2.88/3.42 FOF formula (((eq (fofType->Prop)) pos) (fun (X0:fofType)=> ((l_some dif) (propp X0)))) of role definition named def_pos
% 2.88/3.42 A new definition: (((eq (fofType->Prop)) pos) (fun (X0:fofType)=> ((l_some dif) (propp X0))))
% 2.88/3.42 Defined: pos:=(fun (X0:fofType)=> ((l_some dif) (propp X0)))
% 2.88/3.42 FOF formula (<kernel.Constant object at 0x2aefbd942170>, <kernel.DependentProduct object at 0x2aefbd942fc8>) of role type named typ_propn
% 2.88/3.42 Using role type
% 2.88/3.42 Declaring propn:(fofType->(fofType->Prop))
% 2.88/3.42 FOF formula (((eq (fofType->(fofType->Prop))) propn) (fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (negd X1)))) of role definition named def_propn
% 2.88/3.42 A new definition: (((eq (fofType->(fofType->Prop))) propn) (fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (negd X1))))
% 2.88/3.42 Defined: propn:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (negd X1)))
% 2.88/3.42 FOF formula (<kernel.Constant object at 0x2aefbd942fc8>, <kernel.DependentProduct object at 0x2aefbd942ef0>) of role type named typ_neg
% 2.88/3.42 Using role type
% 2.88/3.42 Declaring neg:(fofType->Prop)
% 2.88/3.42 FOF formula (((eq (fofType->Prop)) neg) (fun (X0:fofType)=> ((l_some dif) (propn X0)))) of role definition named def_neg
% 2.88/3.42 A new definition: (((eq (fofType->Prop)) neg) (fun (X0:fofType)=> ((l_some dif) (propn X0))))
% 2.88/3.42 Defined: neg:=(fun (X0:fofType)=> ((l_some dif) (propn X0)))
% 2.88/3.42 FOF formula (<kernel.Constant object at 0x2aefbd942ef0>, <kernel.DependentProduct object at 0x2aefbd9423f8>) of role type named typ_pofrp
% 2.88/3.42 Using role type
% 2.88/3.42 Declaring pofrp:(fofType->fofType)
% 2.88/3.42 FOF formula (((eq (fofType->fofType)) pofrp) (fun (X0:fofType)=> (realof (pdofrp X0)))) of role definition named def_pofrp
% 2.88/3.42 A new definition: (((eq (fofType->fofType)) pofrp) (fun (X0:fofType)=> (realof (pdofrp X0))))
% 2.88/3.42 Defined: pofrp:=(fun (X0:fofType)=> (realof (pdofrp X0)))
% 2.88/3.42 FOF formula (<kernel.Constant object at 0x2aefbd9423f8>, <kernel.DependentProduct object at 0x2aefbd942a28>) of role type named typ_nofrp
% 2.88/3.42 Using role type
% 2.88/3.42 Declaring nofrp:(fofType->fofType)
% 2.88/3.42 FOF formula (((eq (fofType->fofType)) nofrp) (fun (X0:fofType)=> (realof (ndofrp X0)))) of role definition named def_nofrp
% 2.88/3.42 A new definition: (((eq (fofType->fofType)) nofrp) (fun (X0:fofType)=> (realof (ndofrp X0))))
% 2.88/3.42 Defined: nofrp:=(fun (X0:fofType)=> (realof (ndofrp X0)))
% 2.88/3.42 FOF formula (<kernel.Constant object at 0x2aefbd942a28>, <kernel.DependentProduct object at 0x2aefbd942b90>) of role type named typ_ivr1_pr
% 2.88/3.42 Using role type
% 2.88/3.42 Declaring ivr1_pr:(fofType->(fofType->fofType))
% 2.88/3.42 FOF formula (((eq (fofType->(fofType->fofType))) ivr1_pr) (fun (X0:fofType)=> rpofpd)) of role definition named def_ivr1_pr
% 2.88/3.42 A new definition: (((eq (fofType->(fofType->fofType))) ivr1_pr) (fun (X0:fofType)=> rpofpd))
% 2.88/3.42 Defined: ivr1_pr:=(fun (X0:fofType)=> rpofpd)
% 2.88/3.42 FOF formula (<kernel.Constant object at 0x2aefbd942b90>, <kernel.DependentProduct object at 0x2aefbd942518>) of role type named typ_rpofp
% 2.88/3.42 Using role type
% 2.88/3.42 Declaring rpofp:(fofType->fofType)
% 2.88/3.42 FOF formula (((eq (fofType->fofType)) rpofp) (fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (pofrp X1)))))) of role definition named def_rpofp
% 2.88/3.42 A new definition: (((eq (fofType->fofType)) rpofp) (fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (pofrp X1))))))
% 2.88/3.42 Defined: rpofp:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (pofrp X1)))))
% 2.88/3.42 FOF formula (<kernel.Constant object at 0x2aefbd942518>, <kernel.DependentProduct object at 0x2aefbd942998>) of role type named typ_ivr1_nr
% 2.88/3.44 Using role type
% 2.88/3.44 Declaring ivr1_nr:(fofType->(fofType->fofType))
% 2.88/3.44 FOF formula (((eq (fofType->(fofType->fofType))) ivr1_nr) (fun (X0:fofType)=> rpofnd)) of role definition named def_ivr1_nr
% 2.88/3.44 A new definition: (((eq (fofType->(fofType->fofType))) ivr1_nr) (fun (X0:fofType)=> rpofnd))
% 2.88/3.44 Defined: ivr1_nr:=(fun (X0:fofType)=> rpofnd)
% 2.88/3.44 FOF formula (<kernel.Constant object at 0x2aefbd942998>, <kernel.DependentProduct object at 0x2aefbd9428c0>) of role type named typ_rpofn
% 2.88/3.44 Using role type
% 2.88/3.44 Declaring rpofn:(fofType->fofType)
% 2.88/3.44 FOF formula (((eq (fofType->fofType)) rpofn) (fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (nofrp X1)))))) of role definition named def_rpofn
% 2.88/3.44 A new definition: (((eq (fofType->fofType)) rpofn) (fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (nofrp X1))))))
% 2.88/3.44 Defined: rpofn:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (nofrp X1)))))
% 2.88/3.44 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) X0))) of role axiom named satz163
% 2.88/3.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) X0)))
% 2.88/3.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is X1) X0)))))) of role axiom named satz164
% 2.88/3.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is X1) X0))))))
% 2.88/3.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->(((r_is X1) X2)->((r_is X0) X2))))))))) of role axiom named satz165
% 2.88/3.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->(((r_is X1) X2)->((r_is X0) X2)))))))))
% 2.88/3.45 FOF formula (<kernel.Constant object at 0x2aefbd942bd8>, <kernel.Single object at 0x2aefbd942998>) of role type named typ_absdr
% 2.88/3.45 Using role type
% 2.88/3.45 Declaring absdr:fofType
% 2.88/3.45 FOF formula (((eq fofType) absdr) ((d_Sigma dif) (fun (X0:fofType)=> (realof (absd X0))))) of role definition named def_absdr
% 2.88/3.45 A new definition: (((eq fofType) absdr) ((d_Sigma dif) (fun (X0:fofType)=> (realof (absd X0)))))
% 2.88/3.45 Defined: absdr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (absd X0))))
% 2.88/3.45 FOF formula (<kernel.Constant object at 0x2aefbd942998>, <kernel.DependentProduct object at 0x2aefbd942b48>) of role type named typ_abs
% 2.88/3.45 Using role type
% 2.88/3.45 Declaring abs:(fofType->fofType)
% 2.88/3.45 FOF formula (((eq (fofType->fofType)) abs) ((indreal real) absdr)) of role definition named def_abs
% 2.88/3.45 A new definition: (((eq (fofType->fofType)) abs) ((indreal real) absdr))
% 2.88/3.45 Defined: abs:=((indreal real) absdr)
% 2.88/3.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(pos (abs X0))))) of role axiom named satz166a
% 2.88/3.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(pos (abs X0)))))
% 2.88/3.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (abs X0))))) of role axiom named satz166b
% 2.88/3.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (abs X0)))))
% 2.88/3.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1)))))))) of role axiom named satz166c
% 2.88/3.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 2.88/3.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1)))))))) of role axiom named satz166d
% 2.88/3.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 2.88/3.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_nis X0) r_0)->(pos (abs X0))))) of role axiom named satz166e
% 2.88/3.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_nis X0) r_0)->(pos (abs X0)))))
% 2.88/3.46 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (abs X0)) r_0)))) of role axiom named satz166f
% 2.88/3.46 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (abs X0)) r_0))))
% 2.88/3.46 FOF formula (<kernel.Constant object at 0x2aefbd9428c0>, <kernel.DependentProduct object at 0x2aefb295b2d8>) of role type named typ_r_more
% 2.88/3.46 Using role type
% 2.88/3.46 Declaring r_more:(fofType->(fofType->Prop))
% 2.88/3.46 FOF formula (((eq (fofType->(fofType->Prop))) r_more) (fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3)))))))) of role definition named def_r_more
% 2.88/3.46 A new definition: (((eq (fofType->(fofType->Prop))) r_more) (fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))))))))
% 2.88/3.46 Defined: r_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3)))))))
% 2.88/3.46 FOF formula (<kernel.Constant object at 0x2aefbd9428c0>, <kernel.DependentProduct object at 0x2aefb295b3f8>) of role type named typ_ivr2_propm
% 2.88/3.46 Using role type
% 2.88/3.46 Declaring ivr2_propm:(fofType->(fofType->(fofType->(fofType->Prop))))
% 2.88/3.46 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) ivr2_propm) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3)))) of role definition named def_ivr2_propm
% 2.88/3.46 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) ivr2_propm) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))))
% 2.88/3.46 Defined: ivr2_propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3)))
% 2.88/3.46 FOF formula (<kernel.Constant object at 0x2aefbd9428c0>, <kernel.DependentProduct object at 0x2aefb295b2d8>) of role type named typ_r_less
% 2.88/3.46 Using role type
% 2.88/3.46 Declaring r_less:(fofType->(fofType->Prop))
% 2.88/3.46 FOF formula (((eq (fofType->(fofType->Prop))) r_less) (fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3)))))))) of role definition named def_r_less
% 2.88/3.46 A new definition: (((eq (fofType->(fofType->Prop))) r_less) (fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))))))))
% 2.88/3.46 Defined: r_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3)))))))
% 2.88/3.46 FOF formula (<kernel.Constant object at 0x2aefb295b2d8>, <kernel.DependentProduct object at 0x2aefb295b290>) of role type named typ_ivr2_propl
% 2.88/3.46 Using role type
% 2.88/3.46 Declaring ivr2_propl:(fofType->(fofType->(fofType->(fofType->Prop))))
% 2.88/3.46 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) ivr2_propl) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3)))) of role definition named def_ivr2_propl
% 2.88/3.46 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) ivr2_propl) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))))
% 2.88/3.48 Defined: ivr2_propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3)))
% 2.88/3.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((orec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1)))))) of role axiom named satz167
% 2.88/3.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((orec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 2.88/3.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((or3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1)))))) of role axiom named satz167a
% 2.88/3.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((or3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 2.88/3.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((ec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1)))))) of role axiom named satz167b
% 2.88/3.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((ec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 2.88/3.48 FOF formula (<kernel.Constant object at 0x2aefb295b7a0>, <kernel.DependentProduct object at 0x2aefb295b878>) of role type named typ_r_moreis
% 2.88/3.48 Using role type
% 2.88/3.48 Declaring r_moreis:(fofType->(fofType->Prop))
% 2.88/3.48 FOF formula (((eq (fofType->(fofType->Prop))) r_moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((r_more X0) X1)) ((r_is X0) X1)))) of role definition named def_r_moreis
% 2.88/3.48 A new definition: (((eq (fofType->(fofType->Prop))) r_moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((r_more X0) X1)) ((r_is X0) X1))))
% 2.88/3.48 Defined: r_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_more X0) X1)) ((r_is X0) X1)))
% 2.88/3.48 FOF formula (<kernel.Constant object at 0x2aefb295b878>, <kernel.DependentProduct object at 0x2aefb295b170>) of role type named typ_r_lessis
% 2.88/3.48 Using role type
% 2.88/3.48 Declaring r_lessis:(fofType->(fofType->Prop))
% 2.88/3.48 FOF formula (((eq (fofType->(fofType->Prop))) r_lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((r_less X0) X1)) ((r_is X0) X1)))) of role definition named def_r_lessis
% 2.88/3.48 A new definition: (((eq (fofType->(fofType->Prop))) r_lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((r_less X0) X1)) ((r_is X0) X1))))
% 2.88/3.48 Defined: r_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_less X0) X1)) ((r_is X0) X1)))
% 2.88/3.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->((r_lessis X1) X0)))))) of role axiom named satz168a
% 2.88/3.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->((r_lessis X1) X0))))))
% 2.88/3.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->((r_moreis X1) X0)))))) of role axiom named satz168b
% 2.88/3.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->((r_moreis X1) X0))))))
% 2.88/3.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->(d_not ((r_less X0) X1))))))) of role axiom named satz167c
% 2.88/3.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->(d_not ((r_less X0) X1)))))))
% 2.88/3.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->(d_not ((r_more X0) X1))))))) of role axiom named satz167d
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->(d_not ((r_more X0) X1)))))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_more X0) X1))->((r_lessis X0) X1)))))) of role axiom named satz167e
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_more X0) X1))->((r_lessis X0) X1))))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_less X0) X1))->((r_moreis X0) X1)))))) of role axiom named satz167f
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_less X0) X1))->((r_moreis X0) X1))))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(d_not ((r_lessis X0) X1))))))) of role axiom named satz167g
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(d_not ((r_lessis X0) X1)))))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(d_not ((r_moreis X0) X1))))))) of role axiom named satz167h
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(d_not ((r_moreis X0) X1)))))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_moreis X0) X1))->((r_less X0) X1)))))) of role axiom named satz167j
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_moreis X0) X1))->((r_less X0) X1))))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_lessis X0) X1))->((r_more X0) X1)))))) of role axiom named satz167k
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_lessis X0) X1))->((r_more X0) X1))))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->((r_more X0) r_0)))) of role axiom named satz169a
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->((r_more X0) r_0))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_more X0) r_0)->(pos X0)))) of role axiom named satz169b
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_more X0) r_0)->(pos X0))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->((r_less X0) r_0)))) of role axiom named satz169c
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->((r_less X0) r_0))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_less X0) r_0)->(neg X0)))) of role axiom named satz169d
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_less X0) r_0)->(neg X0))))
% 2.88/3.50 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_moreis (abs X0)) r_0))) of role axiom named satz170
% 2.88/3.50 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_moreis (abs X0)) r_0)))
% 2.98/3.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (d_not (neg (abs X0))))) of role axiom named satz170a
% 2.98/3.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (d_not (neg (abs X0)))))
% 2.98/3.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_less X1) X2)->((r_less X0) X2))))))))) of role axiom named satz171
% 2.98/3.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_less X1) X2)->((r_less X0) X2)))))))))
% 2.98/3.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_less X1) X2)->((r_less X0) X2))))))))) of role axiom named satz172a
% 2.98/3.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_less X1) X2)->((r_less X0) X2)))))))))
% 2.98/3.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_lessis X1) X2)->((r_less X0) X2))))))))) of role axiom named satz172b
% 2.98/3.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_lessis X1) X2)->((r_less X0) X2)))))))))
% 2.98/3.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_moreis X0) X1)->(((r_more X1) X2)->((r_more X0) X2))))))))) of role axiom named satz172c
% 2.98/3.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_moreis X0) X1)->(((r_more X1) X2)->((r_more X0) X2)))))))))
% 2.98/3.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->(((r_moreis X1) X2)->((r_more X0) X2))))))))) of role axiom named satz172d
% 2.98/3.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->(((r_moreis X1) X2)->((r_more X0) X2)))))))))
% 2.98/3.53 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_lessis X1) X2)->((r_lessis X0) X2))))))))) of role axiom named satz173
% 2.98/3.53 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_lessis X1) X2)->((r_lessis X0) X2)))))))))
% 2.98/3.53 FOF formula (<kernel.Constant object at 0x2aefb295be18>, <kernel.DependentProduct object at 0x2aefb295b7e8>) of role type named typ_ratrl
% 2.98/3.53 Using role type
% 2.98/3.53 Declaring ratrl:(fofType->Prop)
% 2.98/3.53 FOF formula (((eq (fofType->Prop)) ratrl) (fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (ratd X1)))))) of role definition named def_ratrl
% 2.98/3.54 A new definition: (((eq (fofType->Prop)) ratrl) (fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (ratd X1))))))
% 2.98/3.54 Defined: ratrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (ratd X1)))))
% 2.98/3.54 FOF formula (<kernel.Constant object at 0x2aefb295b7e8>, <kernel.DependentProduct object at 0x2aefb295bcf8>) of role type named typ_irratrl
% 2.98/3.54 Using role type
% 2.98/3.54 Declaring irratrl:(fofType->Prop)
% 2.98/3.54 FOF formula (((eq (fofType->Prop)) irratrl) (fun (X0:fofType)=> (d_not (ratrl X0)))) of role definition named def_irratrl
% 2.98/3.54 A new definition: (((eq (fofType->Prop)) irratrl) (fun (X0:fofType)=> (d_not (ratrl X0))))
% 2.98/3.54 Defined: irratrl:=(fun (X0:fofType)=> (d_not (ratrl X0)))
% 2.98/3.54 FOF formula (<kernel.Constant object at 0x2aefb295bcf8>, <kernel.DependentProduct object at 0x2aefb295b878>) of role type named typ_natrl
% 2.98/3.54 Using role type
% 2.98/3.54 Declaring natrl:(fofType->Prop)
% 2.98/3.54 FOF formula (((eq (fofType->Prop)) natrl) (fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (natd X1)))))) of role definition named def_natrl
% 2.98/3.54 A new definition: (((eq (fofType->Prop)) natrl) (fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (natd X1))))))
% 2.98/3.54 Defined: natrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (natd X1)))))
% 2.98/3.54 FOF formula (<kernel.Constant object at 0x2aefb295b878>, <kernel.DependentProduct object at 0x2aefb295bd88>) of role type named typ_rlofnt
% 2.98/3.54 Using role type
% 2.98/3.54 Declaring rlofnt:(fofType->fofType)
% 2.98/3.54 FOF formula (((eq (fofType->fofType)) rlofnt) (fun (X0:fofType)=> (realof (pdofnt X0)))) of role definition named def_rlofnt
% 2.98/3.54 A new definition: (((eq (fofType->fofType)) rlofnt) (fun (X0:fofType)=> (realof (pdofnt X0))))
% 2.98/3.54 Defined: rlofnt:=(fun (X0:fofType)=> (realof (pdofnt X0)))
% 2.98/3.54 FOF formula (<kernel.Constant object at 0x2aefb295bd88>, <kernel.DependentProduct object at 0x2aefb295b5f0>) of role type named typ_ivr2_x0
% 2.98/3.54 Using role type
% 2.98/3.54 Declaring ivr2_x0:(fofType->(fofType->fofType))
% 2.98/3.54 FOF formula (((eq (fofType->(fofType->fofType))) ivr2_x0) (fun (X0:fofType) (X1:fofType)=> (ntofrp ((ivr1_pr X0) X1)))) of role definition named def_ivr2_x0
% 2.98/3.54 A new definition: (((eq (fofType->(fofType->fofType))) ivr2_x0) (fun (X0:fofType) (X1:fofType)=> (ntofrp ((ivr1_pr X0) X1))))
% 2.98/3.54 Defined: ivr2_x0:=(fun (X0:fofType) (X1:fofType)=> (ntofrp ((ivr1_pr X0) X1)))
% 2.98/3.54 FOF formula (<kernel.Constant object at 0x2aefb295b5f0>, <kernel.DependentProduct object at 0x2aefb295b878>) of role type named typ_ntofrl
% 2.98/3.54 Using role type
% 2.98/3.54 Declaring ntofrl:(fofType->fofType)
% 2.98/3.54 FOF formula (((eq (fofType->fofType)) ntofrl) (((soft nat) real) ((d_Sigma nat) rlofnt))) of role definition named def_ntofrl
% 2.98/3.54 A new definition: (((eq (fofType->fofType)) ntofrl) (((soft nat) real) ((d_Sigma nat) rlofnt)))
% 2.98/3.54 Defined: ntofrl:=(((soft nat) real) ((d_Sigma nat) rlofnt))
% 2.98/3.54 FOF formula (<kernel.Constant object at 0x2aefb295bd88>, <kernel.DependentProduct object at 0x2aefb295b878>) of role type named typ_ivr2_xn
% 2.98/3.54 Using role type
% 2.98/3.54 Declaring ivr2_xn:(fofType->fofType)
% 2.98/3.54 FOF formula (((eq (fofType->fofType)) ivr2_xn) (fun (X0:fofType)=> ((((soft nat) real) ((d_Sigma nat) rlofnt)) (rlofnt X0)))) of role definition named def_ivr2_xn
% 2.98/3.54 A new definition: (((eq (fofType->fofType)) ivr2_xn) (fun (X0:fofType)=> ((((soft nat) real) ((d_Sigma nat) rlofnt)) (rlofnt X0))))
% 2.98/3.54 Defined: ivr2_xn:=(fun (X0:fofType)=> ((((soft nat) real) ((d_Sigma nat) rlofnt)) (rlofnt X0)))
% 2.98/3.54 FOF formula (<kernel.Constant object at 0x2aefb295b5f0>, <kernel.DependentProduct object at 0x2aefb295bcf8>) of role type named typ_intrl
% 2.98/3.54 Using role type
% 2.98/3.54 Declaring intrl:(fofType->Prop)
% 2.98/3.54 FOF formula (((eq (fofType->Prop)) intrl) (fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (intd X1)))))) of role definition named def_intrl
% 2.98/3.54 A new definition: (((eq (fofType->Prop)) intrl) (fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (intd X1))))))
% 2.98/3.54 Defined: intrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (intd X1)))))
% 2.98/3.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((intrl X0)->(ratrl X0)))) of role axiom named satz174
% 2.98/3.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((intrl X0)->(ratrl X0))))
% 2.98/3.56 FOF formula (<kernel.Constant object at 0x2aefb295bcf8>, <kernel.Single object at 0x2aefb295bc68>) of role type named typ_plusdr
% 2.98/3.56 Using role type
% 2.98/3.56 Declaring plusdr:fofType
% 2.98/3.56 FOF formula (((eq fofType) plusdr) ((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_pd X0) X1))))))) of role definition named def_plusdr
% 2.98/3.56 A new definition: (((eq fofType) plusdr) ((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_pd X0) X1)))))))
% 2.98/3.56 Defined: plusdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_pd X0) X1))))))
% 2.98/3.56 FOF formula (<kernel.Constant object at 0x2aefb295bd40>, <kernel.DependentProduct object at 0x2aefb294e200>) of role type named typ_r_pl
% 2.98/3.56 Using role type
% 2.98/3.56 Declaring r_pl:(fofType->(fofType->fofType))
% 2.98/3.56 FOF formula (((eq (fofType->(fofType->fofType))) r_pl) ((indreal2 real) plusdr)) of role definition named def_r_pl
% 2.98/3.56 A new definition: (((eq (fofType->(fofType->fofType))) r_pl) ((indreal2 real) plusdr))
% 2.98/3.56 Defined: r_pl:=((indreal2 real) plusdr)
% 2.98/3.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X0) X1)) ((r_pl X1) X0)))))) of role axiom named satz175
% 2.98/3.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X0) X1)) ((r_pl X1) X0))))))
% 2.98/3.56 FOF formula (<kernel.Constant object at 0x2aefb295bcf8>, <kernel.Single object at 0x2aefb294e248>) of role type named typ_m0dr
% 2.98/3.56 Using role type
% 2.98/3.56 Declaring m0dr:fofType
% 2.98/3.56 FOF formula (((eq fofType) m0dr) ((d_Sigma dif) (fun (X0:fofType)=> (realof (m0d X0))))) of role definition named def_m0dr
% 2.98/3.56 A new definition: (((eq fofType) m0dr) ((d_Sigma dif) (fun (X0:fofType)=> (realof (m0d X0)))))
% 2.98/3.56 Defined: m0dr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (m0d X0))))
% 2.98/3.56 FOF formula (<kernel.Constant object at 0x2aefb295bd40>, <kernel.DependentProduct object at 0x2aefb294e560>) of role type named typ_r_m0
% 2.98/3.56 Using role type
% 2.98/3.56 Declaring r_m0:(fofType->fofType)
% 2.98/3.56 FOF formula (((eq (fofType->fofType)) r_m0) ((indreal real) m0dr)) of role definition named def_r_m0
% 2.98/3.56 A new definition: (((eq (fofType->fofType)) r_m0) ((indreal real) m0dr))
% 2.98/3.56 Defined: r_m0:=((indreal real) m0dr)
% 2.98/3.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(neg (r_m0 X0))))) of role axiom named satz176a
% 2.98/3.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(neg (r_m0 X0)))))
% 2.98/3.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (r_m0 X0)) r_0)))) of role axiom named satz176b
% 2.98/3.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (r_m0 X0)) r_0))))
% 2.98/3.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (r_m0 X0))))) of role axiom named satz176c
% 2.98/3.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (r_m0 X0)))))
% 2.98/3.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg (r_m0 X0))->(pos X0)))) of role axiom named satz176d
% 2.98/3.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg (r_m0 X0))->(pos X0))))
% 2.98/3.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is (r_m0 X0)) r_0)->((r_is X0) r_0)))) of role axiom named satz176e
% 2.98/3.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is (r_m0 X0)) r_0)->((r_is X0) r_0))))
% 2.98/3.56 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos (r_m0 X0))->(neg X0)))) of role axiom named satz176f
% 2.98/3.56 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos (r_m0 X0))->(neg X0))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (r_m0 (r_m0 X0))) X0))) of role axiom named satz177
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (r_m0 (r_m0 X0))) X0)))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) (r_m0 (r_m0 X0))))) of role axiom named satz177a
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) (r_m0 (r_m0 X0)))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is (r_m0 X0)) X1)))))) of role axiom named satz177b
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is (r_m0 X0)) X1))))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is X1) (r_m0 X0))))))) of role axiom named satz177c
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is X1) (r_m0 X0)))))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) X1)->((r_is X0) (r_m0 X1))))))) of role axiom named satz177d
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) X1)->((r_is X0) (r_m0 X1)))))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) X1)->((r_is (r_m0 X1)) X0)))))) of role axiom named satz177e
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) X1)->((r_is (r_m0 X1)) X0))))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs (r_m0 X0))) (abs X0)))) of role axiom named satz178
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs (r_m0 X0))) (abs X0))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs X0)) (abs (r_m0 X0))))) of role axiom named satz178a
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs X0)) (abs (r_m0 X0)))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl X0) (r_m0 X0))) r_0))) of role axiom named satz179
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl X0) (r_m0 X0))) r_0)))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl (r_m0 X0)) X0)) r_0))) of role axiom named satz179a
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl (r_m0 X0)) X0)) r_0)))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_pl X0) X1))) ((r_pl (r_m0 X0)) (r_m0 X1))))))) of role axiom named satz180
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_pl X0) X1))) ((r_pl (r_m0 X0)) (r_m0 X1)))))))
% 2.98/3.58 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl (r_m0 X0)) (r_m0 X1))) (r_m0 ((r_pl X0) X1))))))) of role axiom named satz180a
% 2.98/3.58 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl (r_m0 X0)) (r_m0 X1))) (r_m0 ((r_pl X0) X1)))))))
% 3.07/3.61 FOF formula (<kernel.Constant object at 0x2aefb294ebd8>, <kernel.DependentProduct object at 0x2aefb294ecf8>) of role type named typ_r_mn
% 3.07/3.61 Using role type
% 3.07/3.61 Declaring r_mn:(fofType->(fofType->fofType))
% 3.07/3.61 FOF formula (((eq (fofType->(fofType->fofType))) r_mn) (fun (X0:fofType) (X1:fofType)=> ((r_pl X0) (r_m0 X1)))) of role definition named def_r_mn
% 3.07/3.61 A new definition: (((eq (fofType->(fofType->fofType))) r_mn) (fun (X0:fofType) (X1:fofType)=> ((r_pl X0) (r_m0 X1))))
% 3.07/3.61 Defined: r_mn:=(fun (X0:fofType) (X1:fofType)=> ((r_pl X0) (r_m0 X1)))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_mn X0) X1))) ((r_mn X1) X0)))))) of role axiom named satz181
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_mn X0) X1))) ((r_mn X1) X0))))))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_mn X0) X1)) (r_m0 ((r_mn X1) X0))))))) of role axiom named satz181a
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_mn X0) X1)) (r_m0 ((r_mn X1) X0)))))))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_mn X0) X1))->((r_more X0) X1)))))) of role axiom named satz182a
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_mn X0) X1))->((r_more X0) X1))))))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_mn X0) X1)) r_0)->((r_is X0) X1)))))) of role axiom named satz182b
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_mn X0) X1)) r_0)->((r_is X0) X1))))))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_mn X0) X1))->((r_less X0) X1)))))) of role axiom named satz182c
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_mn X0) X1))->((r_less X0) X1))))))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(pos ((r_mn X0) X1))))))) of role axiom named satz182d
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(pos ((r_mn X0) X1)))))))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is ((r_mn X0) X1)) r_0)))))) of role axiom named satz182e
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is ((r_mn X0) X1)) r_0))))))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(neg ((r_mn X0) X1))))))) of role axiom named satz182f
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(neg ((r_mn X0) X1)))))))
% 3.07/3.61 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->((r_less (r_m0 X0)) (r_m0 X1))))))) of role axiom named satz183a
% 3.07/3.61 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->((r_less (r_m0 X0)) (r_m0 X1)))))))
% 3.07/3.63 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is (r_m0 X0)) (r_m0 X1))))))) of role axiom named satz183b
% 3.07/3.63 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is (r_m0 X0)) (r_m0 X1)))))))
% 3.07/3.63 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->((r_more (r_m0 X0)) (r_m0 X1))))))) of role axiom named satz183c
% 3.07/3.63 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->((r_more (r_m0 X0)) (r_m0 X1)))))))
% 3.07/3.63 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less (r_m0 X0)) (r_m0 X1))->((r_more X0) X1)))))) of role axiom named satz183d
% 3.07/3.63 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less (r_m0 X0)) (r_m0 X1))->((r_more X0) X1))))))
% 3.07/3.63 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) (r_m0 X1))->((r_is X0) X1)))))) of role axiom named satz183e
% 3.07/3.63 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) (r_m0 X1))->((r_is X0) X1))))))
% 3.07/3.63 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more (r_m0 X0)) (r_m0 X1))->((r_less X0) X1)))))) of role axiom named satz183f
% 3.07/3.63 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more (r_m0 X0)) (r_m0 X1))->((r_less X0) X1))))))
% 3.07/3.63 FOF formula (<kernel.Constant object at 0x2aefb294ef80>, <kernel.DependentProduct object at 0x2aefb294eab8>) of role type named typ_d_3r184_prop1
% 3.07/3.63 Using role type
% 3.07/3.63 Declaring d_3r184_prop1:(fofType->(fofType->(fofType->Prop)))
% 3.07/3.63 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_3r184_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2))))) of role definition named def_d_3r184_prop1
% 3.07/3.63 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_3r184_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))))
% 3.07/3.63 Defined: d_3r184_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2))))
% 3.07/3.63 FOF formula (<kernel.Constant object at 0x2aefb294eab8>, <kernel.DependentProduct object at 0x2aefb294e170>) of role type named typ_d_3r184_prop2
% 3.07/3.63 Using role type
% 3.07/3.63 Declaring d_3r184_prop2:(fofType->(fofType->Prop))
% 3.07/3.63 FOF formula (((eq (fofType->(fofType->Prop))) d_3r184_prop2) (fun (X0:fofType) (X1:fofType)=> (r_some ((d_3r184_prop1 X0) X1)))) of role definition named def_d_3r184_prop2
% 3.07/3.63 A new definition: (((eq (fofType->(fofType->Prop))) d_3r184_prop2) (fun (X0:fofType) (X1:fofType)=> (r_some ((d_3r184_prop1 X0) X1))))
% 3.07/3.63 Defined: d_3r184_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_some ((d_3r184_prop1 X0) X1)))
% 3.07/3.63 FOF formula (<kernel.Constant object at 0x2aefb294e170>, <kernel.DependentProduct object at 0x2aefb294e830>) of role type named typ_d_3r184_prop3
% 3.07/3.63 Using role type
% 3.07/3.63 Declaring d_3r184_prop3:(fofType->Prop)
% 3.07/3.63 FOF formula (((eq (fofType->Prop)) d_3r184_prop3) (fun (X0:fofType)=> (r_some (d_3r184_prop2 X0)))) of role definition named def_d_3r184_prop3
% 3.07/3.63 A new definition: (((eq (fofType->Prop)) d_3r184_prop3) (fun (X0:fofType)=> (r_some (d_3r184_prop2 X0))))
% 3.07/3.65 Defined: d_3r184_prop3:=(fun (X0:fofType)=> (r_some (d_3r184_prop2 X0)))
% 3.07/3.65 FOF formula (<kernel.Constant object at 0x2aefb294e830>, <kernel.DependentProduct object at 0x2aefb294ee60>) of role type named typ_prop1d
% 3.07/3.65 Using role type
% 3.07/3.65 Declaring prop1d:(fofType->(fofType->(fofType->Prop)))
% 3.07/3.65 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) prop1d) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (posd X1)) (posd X2)) ((rp_eq X0) ((rp_md X1) X2))))) of role definition named def_prop1d
% 3.07/3.65 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) prop1d) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (posd X1)) (posd X2)) ((rp_eq X0) ((rp_md X1) X2)))))
% 3.07/3.65 Defined: prop1d:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (posd X1)) (posd X2)) ((rp_eq X0) ((rp_md X1) X2))))
% 3.07/3.65 FOF formula (<kernel.Constant object at 0x2aefb294ec68>, <kernel.DependentProduct object at 0x2aefb294e290>) of role type named typ_prop2d
% 3.07/3.65 Using role type
% 3.07/3.65 Declaring prop2d:(fofType->(fofType->Prop))
% 3.07/3.65 FOF formula (((eq (fofType->(fofType->Prop))) prop2d) (fun (X0:fofType) (X1:fofType)=> ((l_some dif) ((prop1d X0) X1)))) of role definition named def_prop2d
% 3.07/3.65 A new definition: (((eq (fofType->(fofType->Prop))) prop2d) (fun (X0:fofType) (X1:fofType)=> ((l_some dif) ((prop1d X0) X1))))
% 3.07/3.65 Defined: prop2d:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) ((prop1d X0) X1)))
% 3.07/3.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (r_some (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2))))))))) of role axiom named satz184
% 3.07/3.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (r_some (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))))))))
% 3.07/3.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((r_is ((r_pl ((r_mn X0) X1)) ((r_mn X2) X3))) ((r_mn ((r_pl X0) X2)) ((r_pl X1) X3))))))))))) of role axiom named satz185
% 3.07/3.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((r_is ((r_pl ((r_mn X0) X1)) ((r_mn X2) X3))) ((r_mn ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))
% 3.07/3.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_pl ((r_pl X0) X1)) X2)) ((r_pl X0) ((r_pl X1) X2))))))))) of role axiom named satz186
% 3.07/3.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_pl ((r_pl X0) X1)) X2)) ((r_pl X0) ((r_pl X1) X2)))))))))
% 3.07/3.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X1) ((r_mn X0) X1))) X0))))) of role axiom named satz187a
% 3.07/3.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X1) ((r_mn X0) X1))) X0)))))
% 3.07/3.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0))))))) of role axiom named satz187b
% 3.07/3.65 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0)))))))
% 3.07/3.65 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is ((r_mn X0) X1)) X2)))))))) of role axiom named satz187c
% 3.07/3.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is ((r_mn X0) X1)) X2))))))))
% 3.07/3.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is X2) ((r_mn X0) X1))))))))) of role axiom named satz187d
% 3.07/3.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is X2) ((r_mn X0) X1)))))))))
% 3.07/3.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is ((r_mn X0) X1)) X2)))))))) of role axiom named satz187e
% 3.07/3.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is ((r_mn X0) X1)) X2))))))))
% 3.07/3.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is X2) ((r_mn X0) X1))))))))) of role axiom named satz187f
% 3.07/3.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is X2) ((r_mn X0) X1)))))))))
% 3.07/3.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_one (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0))))))) of role axiom named satz187
% 3.07/3.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_one (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0)))))))
% 3.07/3.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X0) X2)) ((r_pl X1) X2))->((r_more X0) X1)))))))) of role axiom named satz188a
% 3.07/3.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X0) X2)) ((r_pl X1) X2))->((r_more X0) X1))))))))
% 3.07/3.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X0) X2)) ((r_pl X1) X2))->((r_is X0) X1)))))))) of role axiom named satz188b
% 3.07/3.68 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X0) X2)) ((r_pl X1) X2))->((r_is X0) X1))))))))
% 3.07/3.68 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X0) X2)) ((r_pl X1) X2))->((r_less X0) X1)))))))) of role axiom named satz188c
% 3.16/3.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X0) X2)) ((r_pl X1) X2))->((r_less X0) X1))))))))
% 3.16/3.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X0) X2)) ((r_pl X1) X2))))))))) of role axiom named satz188d
% 3.16/3.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 3.16/3.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X0) X2)) ((r_pl X1) X2))))))))) of role axiom named satz188e
% 3.16/3.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 3.16/3.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X0) X2)) ((r_pl X1) X2))))))))) of role axiom named satz188f
% 3.16/3.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 3.16/3.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X2) X0)) ((r_pl X2) X1))->((r_more X0) X1)))))))) of role axiom named satz188g
% 3.16/3.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X2) X0)) ((r_pl X2) X1))->((r_more X0) X1))))))))
% 3.16/3.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X0)) ((r_pl X2) X1))->((r_is X0) X1)))))))) of role axiom named satz188h
% 3.16/3.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X0)) ((r_pl X2) X1))->((r_is X0) X1))))))))
% 3.16/3.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X2) X0)) ((r_pl X2) X1))->((r_less X0) X1)))))))) of role axiom named satz188j
% 3.16/3.70 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X2) X0)) ((r_pl X2) X1))->((r_less X0) X1))))))))
% 3.16/3.70 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X2) X0)) ((r_pl X2) X1))))))))) of role axiom named satz188k
% 3.16/3.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 3.16/3.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X2) X0)) ((r_pl X2) X1))))))))) of role axiom named satz188l
% 3.16/3.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 3.16/3.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X2) X0)) ((r_pl X2) X1))))))))) of role axiom named satz188m
% 3.16/3.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 3.16/3.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz188n
% 3.16/3.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X2) X0)) ((r_pl X3) X1)))))))))))) of role axiom named satz188o
% 3.16/3.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X2) X0)) ((r_pl X3) X1))))))))))))
% 3.16/3.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz188p
% 3.16/3.73 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.73 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X2) X0)) ((r_pl X3) X1)))))))))))) of role axiom named satz188q
% 3.16/3.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X2) X0)) ((r_pl X3) X1))))))))))))
% 3.16/3.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz189
% 3.16/3.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz189a
% 3.16/3.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz190a
% 3.16/3.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_moreis X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz190b
% 3.16/3.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_moreis X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.75 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz190c
% 3.16/3.75 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.77 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_lessis X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz190d
% 3.16/3.77 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_lessis X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.77 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_moreis X2) X3)->((r_moreis ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz191
% 3.16/3.77 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_moreis X2) X3)->((r_moreis ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.77 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_lessis X2) X3)->((r_lessis ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))) of role axiom named satz191a
% 3.16/3.77 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_lessis X2) X3)->((r_lessis ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 3.16/3.77 FOF formula (<kernel.Constant object at 0x2aefb296aef0>, <kernel.Single object at 0x2aefb296a128>) of role type named typ_timesdr
% 3.16/3.77 Using role type
% 3.16/3.77 Declaring timesdr:fofType
% 3.16/3.77 FOF formula (((eq fofType) timesdr) ((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_td X0) X1))))))) of role definition named def_timesdr
% 3.16/3.77 A new definition: (((eq fofType) timesdr) ((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_td X0) X1)))))))
% 3.16/3.77 Defined: timesdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_td X0) X1))))))
% 3.16/3.77 FOF formula (<kernel.Constant object at 0x2aefb296a128>, <kernel.DependentProduct object at 0x2aefb296a050>) of role type named typ_r_ts
% 3.16/3.77 Using role type
% 3.16/3.77 Declaring r_ts:(fofType->(fofType->fofType))
% 3.16/3.77 FOF formula (((eq (fofType->(fofType->fofType))) r_ts) ((indreal2 real) timesdr)) of role definition named def_r_ts
% 3.16/3.77 A new definition: (((eq (fofType->(fofType->fofType))) r_ts) ((indreal2 real) timesdr))
% 3.16/3.77 Defined: r_ts:=((indreal2 real) timesdr)
% 3.16/3.77 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) r_0)->((r_is ((r_ts X0) X1)) r_0)))))) of role axiom named satz192a
% 3.16/3.77 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) r_0)->((r_is ((r_ts X0) X1)) r_0))))))
% 3.16/3.77 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X1) r_0)->((r_is ((r_ts X0) X1)) r_0)))))) of role axiom named satz192b
% 3.16/3.77 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X1) r_0)->((r_is ((r_ts X0) X1)) r_0))))))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_ts X0) X1)) r_0)->((l_or ((r_is X0) r_0)) ((r_is X1) r_0))))))) of role axiom named satz192c
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_ts X0) X1)) r_0)->((l_or ((r_is X0) r_0)) ((r_is X1) r_0)))))))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X0) r_0)->(((r_nis X1) r_0)->((r_nis ((r_ts X0) X1)) r_0))))))) of role axiom named satz192d
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X0) r_0)->(((r_nis X1) r_0)->((r_nis ((r_ts X0) X1)) r_0)))))))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (abs ((r_ts X0) X1))) ((r_ts (abs X0)) (abs X1))))))) of role axiom named satz193
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (abs ((r_ts X0) X1))) ((r_ts (abs X0)) (abs X1)))))))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (abs X0)) (abs X1))) (abs ((r_ts X0) X1))))))) of role axiom named satz193a
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (abs X0)) (abs X1))) (abs ((r_ts X0) X1)))))))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts X1) X0)))))) of role axiom named satz194
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts X1) X0))))))
% 3.26/3.80 FOF formula (<kernel.Constant object at 0x2aefb296acb0>, <kernel.Single object at 0x2aefb296a128>) of role type named typ_d_1rl
% 3.26/3.80 Using role type
% 3.26/3.80 Declaring d_1rl:fofType
% 3.26/3.80 FOF formula (((eq fofType) d_1rl) (realof d_1df)) of role definition named def_d_1rl
% 3.26/3.80 A new definition: (((eq fofType) d_1rl) (realof d_1df))
% 3.26/3.80 Defined: d_1rl:=(realof d_1df)
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts X0) d_1rl)) X0))) of role axiom named satz195
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts X0) d_1rl)) X0)))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts X0) d_1rl)))) of role axiom named satz195a
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts X0) d_1rl))))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts d_1rl) X0)) X0))) of role axiom named satz195b
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts d_1rl) X0)) X0)))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts d_1rl) X0)))) of role axiom named satz195c
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts d_1rl) X0))))
% 3.26/3.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1))))))))) of role axiom named satz196a
% 3.26/3.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))))))))
% 3.28/3.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1))))))))) of role axiom named satz196b
% 3.28/3.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))))))))
% 3.28/3.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((neg X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1)))))))))) of role axiom named satz196c
% 3.28/3.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((neg X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))))))))
% 3.28/3.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((pos X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1)))))))))) of role axiom named satz196d
% 3.28/3.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((pos X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))))))))
% 3.28/3.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1)))))))))) of role axiom named satz196e
% 3.28/3.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1))))))))))
% 3.28/3.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1)))))))))) of role axiom named satz196f
% 3.28/3.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))))
% 3.28/3.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1)))))))) of role axiom named satz196g
% 3.28/3.83 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1))))))))
% 3.28/3.83 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1)))))))) of role axiom named satz196h
% 3.28/3.83 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))
% 3.28/3.83 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) (r_m0 ((r_ts X0) X1))))))) of role axiom named satz197a
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) (r_m0 ((r_ts X0) X1)))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) (r_m0 ((r_ts X0) X1))))))) of role axiom named satz197b
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) (r_m0 ((r_ts X0) X1)))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) ((r_ts X0) (r_m0 X1))))))) of role axiom named satz197c
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) ((r_ts X0) (r_m0 X1)))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) ((r_ts (r_m0 X0)) X1)))))) of role axiom named satz197d
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) ((r_ts (r_m0 X0)) X1))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts (r_m0 X0)) X1)))))) of role axiom named satz197e
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts (r_m0 X0)) X1))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts X0) (r_m0 X1))))))) of role axiom named satz197f
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts X0) (r_m0 X1)))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) (r_m0 X1))) ((r_ts X0) X1)))))) of role axiom named satz198
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) (r_m0 X1))) ((r_ts X0) X1))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts (r_m0 X0)) (r_m0 X1))))))) of role axiom named satz198a
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts (r_m0 X0)) (r_m0 X1)))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts ((r_ts X0) X1)) X2)) ((r_ts X0) ((r_ts X1) X2))))))))) of role axiom named satz199
% 3.28/3.85 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts ((r_ts X0) X1)) X2)) ((r_ts X0) ((r_ts X1) X2)))))))))
% 3.28/3.85 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_pl X1) X2))) ((r_pl ((r_ts X0) X1)) ((r_ts X0) X2))))))))) of role axiom named satz201
% 3.28/3.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_pl X1) X2))) ((r_pl ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 3.28/3.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_mn X1) X2))) ((r_mn ((r_ts X0) X1)) ((r_ts X0) X2))))))))) of role axiom named satz202
% 3.28/3.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_mn X1) X2))) ((r_mn ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 3.28/3.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2)))))))))) of role axiom named satz203a
% 3.28/3.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 3.28/3.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X0) X2)) ((r_ts X1) X2))))))))) of role axiom named satz203b
% 3.28/3.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X0) X2)) ((r_ts X1) X2)))))))))
% 3.28/3.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2)))))))))) of role axiom named satz203c
% 3.28/3.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 3.28/3.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1)))))))))) of role axiom named satz203d
% 3.28/3.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 3.28/3.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X2) X0)) ((r_ts X2) X1))))))))) of role axiom named satz203e
% 3.28/3.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X2) X0)) ((r_ts X2) X1)))))))))
% 3.28/3.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1)))))))))) of role axiom named satz203f
% 3.37/3.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 3.37/3.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2)))))))))) of role axiom named satz203g
% 3.37/3.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 3.37/3.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2)))))))))) of role axiom named satz203j
% 3.37/3.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 3.37/3.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1)))))))))) of role axiom named satz203k
% 3.37/3.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 3.37/3.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1)))))))))) of role axiom named satz203m
% 3.37/3.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 3.37/3.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is ((r_ts X1) X2)) X0)->(((r_is ((r_ts X1) X3)) X0)->((r_is X2) X3)))))))))))) of role axiom named satz204b
% 3.37/3.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is ((r_ts X1) X2)) X0)->(((r_is ((r_ts X1) X3)) X0)->((r_is X2) X3))))))))))))
% 3.37/3.90 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_some (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))))))) of role axiom named satz204a
% 3.37/3.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_some (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 3.37/3.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_one (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))))))) of role axiom named satz204
% 3.37/3.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_one (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 3.37/3.92 FOF formula (<kernel.Constant object at 0x2aefb2985b00>, <kernel.DependentProduct object at 0x2aefb2985a70>) of role type named typ_r_ov
% 3.37/3.92 Using role type
% 3.37/3.92 Declaring r_ov:(fofType->(fofType->fofType))
% 3.37/3.92 FOF formula (((eq (fofType->(fofType->fofType))) r_ov) (fun (X0:fofType) (X1:fofType)=> ((ind real) (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))) of role definition named def_r_ov
% 3.37/3.92 A new definition: (((eq (fofType->(fofType->fofType))) r_ov) (fun (X0:fofType) (X1:fofType)=> ((ind real) (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))))
% 3.37/3.92 Defined: r_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind real) (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))
% 3.37/3.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts X1) ((r_ov X0) X1))) X0)))))) of role axiom named satz204c
% 3.37/3.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts X1) ((r_ov X0) X1))) X0))))))
% 3.37/3.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts X1) ((r_ov X0) X1)))))))) of role axiom named satz204d
% 3.37/3.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts X1) ((r_ov X0) X1))))))))
% 3.37/3.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts ((r_ov X0) X1)) X1)) X0)))))) of role axiom named satz204e
% 3.37/3.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts ((r_ov X0) X1)) X1)) X0))))))
% 3.37/3.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts ((r_ov X0) X1)) X1))))))) of role axiom named satz204f
% 3.37/3.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts ((r_ov X0) X1)) X1)))))))
% 3.37/3.92 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_nis X1) r_0)->(((r_is ((r_ts X1) X2)) X0)->((r_is X2) ((r_ov X0) X1)))))))))) of role axiom named satz204g
% 3.37/3.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_nis X1) r_0)->(((r_is ((r_ts X1) X2)) X0)->((r_is X2) ((r_ov X0) X1))))))))))
% 3.37/3.92 FOF formula (<kernel.Constant object at 0x2aefb2985f38>, <kernel.DependentProduct object at 0x2aefb29850e0>) of role type named typ_s01
% 3.37/3.92 Using role type
% 3.37/3.92 Declaring s01:(fofType->fofType)
% 3.37/3.92 FOF formula (((eq (fofType->fofType)) s01) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_lessis X1) X0))))) of role definition named def_s01
% 3.37/3.92 A new definition: (((eq (fofType->fofType)) s01) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_lessis X1) X0)))))
% 3.37/3.94 Defined: s01:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_lessis X1) X0))))
% 3.37/3.94 FOF formula (<kernel.Constant object at 0x2aefb29850e0>, <kernel.DependentProduct object at 0x2aefb2985050>) of role type named typ_s02
% 3.37/3.94 Using role type
% 3.37/3.94 Declaring s02:(fofType->fofType)
% 3.37/3.94 FOF formula (((eq (fofType->fofType)) s02) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_more X1) X0))))) of role definition named def_s02
% 3.37/3.94 A new definition: (((eq (fofType->fofType)) s02) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_more X1) X0)))))
% 3.37/3.94 Defined: s02:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_more X1) X0))))
% 3.37/3.94 FOF formula (<kernel.Constant object at 0x2aefb2985050>, <kernel.DependentProduct object at 0x2aefb2985440>) of role type named typ_s11
% 3.37/3.94 Using role type
% 3.37/3.94 Declaring s11:(fofType->fofType)
% 3.37/3.94 FOF formula (((eq (fofType->fofType)) s11) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_less X1) X0))))) of role definition named def_s11
% 3.37/3.94 A new definition: (((eq (fofType->fofType)) s11) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_less X1) X0)))))
% 3.37/3.94 Defined: s11:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_less X1) X0))))
% 3.37/3.94 FOF formula (<kernel.Constant object at 0x2aefb2985440>, <kernel.DependentProduct object at 0x2aefb2985fc8>) of role type named typ_s12
% 3.37/3.94 Using role type
% 3.37/3.94 Declaring s12:(fofType->fofType)
% 3.37/3.94 FOF formula (((eq (fofType->fofType)) s12) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_moreis X1) X0))))) of role definition named def_s12
% 3.37/3.94 A new definition: (((eq (fofType->fofType)) s12) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_moreis X1) X0)))))
% 3.37/3.94 Defined: s12:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_moreis X1) X0))))
% 3.37/3.94 FOF formula (<kernel.Constant object at 0x2aefb2985fc8>, <kernel.Single object at 0x2aefb2985440>) of role type named typ_d_2rl
% 3.37/3.94 Using role type
% 3.37/3.94 Declaring d_2rl:fofType
% 3.37/3.94 FOF formula (((eq fofType) d_2rl) ((r_pl d_1rl) d_1rl)) of role definition named def_d_2rl
% 3.37/3.94 A new definition: (((eq fofType) d_2rl) ((r_pl d_1rl) d_1rl))
% 3.37/3.94 Defined: d_2rl:=((r_pl d_1rl) d_1rl)
% 3.37/3.94 FOF formula (<kernel.Constant object at 0x2aefb2985440>, <kernel.Single object at 0x2aefb2985fc8>) of role type named typ_half
% 3.37/3.94 Using role type
% 3.37/3.94 Declaring half:fofType
% 3.37/3.94 FOF formula (((eq fofType) half) ((r_ov d_1rl) d_2rl)) of role definition named def_half
% 3.37/3.94 A new definition: (((eq fofType) half) ((r_ov d_1rl) d_2rl))
% 3.37/3.94 Defined: half:=((r_ov d_1rl) d_2rl)
% 3.37/3.94 FOF formula (<kernel.Constant object at 0x2aefb2985fc8>, <kernel.DependentProduct object at 0x2aefb2985368>) of role type named typ_d_5r205_prop1
% 3.37/3.94 Using role type
% 3.37/3.94 Declaring d_5r205_prop1:(fofType->(fofType->Prop))
% 3.37/3.94 FOF formula (((eq (fofType->(fofType->Prop))) d_5r205_prop1) (fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_less X2) X1)->((r_in X2) X0)))))) of role definition named def_d_5r205_prop1
% 3.37/3.94 A new definition: (((eq (fofType->(fofType->Prop))) d_5r205_prop1) (fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_less X2) X1)->((r_in X2) X0))))))
% 3.37/3.94 Defined: d_5r205_prop1:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_less X2) X1)->((r_in X2) X0)))))
% 3.37/3.94 FOF formula (<kernel.Constant object at 0x2aefb2985368>, <kernel.DependentProduct object at 0x2aefb2985680>) of role type named typ_d_5r205_prop2
% 3.37/3.94 Using role type
% 3.37/3.94 Declaring d_5r205_prop2:(fofType->(fofType->Prop))
% 3.37/3.94 FOF formula (((eq (fofType->(fofType->Prop))) d_5r205_prop2) (fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_more X2) X1)->((r_in X2) X0)))))) of role definition named def_d_5r205_prop2
% 3.37/3.94 A new definition: (((eq (fofType->(fofType->Prop))) d_5r205_prop2) (fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_more X2) X1)->((r_in X2) X0))))))
% 3.37/3.94 Defined: d_5r205_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_more X2) X1)->((r_in X2) X0)))))
% 3.37/3.94 FOF formula (<kernel.Constant object at 0x2aefb2985680>, <kernel.DependentProduct object at 0x2aefb2985050>) of role type named typ_d_5r205_prop3
% 3.37/3.94 Using role type
% 3.37/3.94 Declaring d_5r205_prop3:(fofType->(fofType->(fofType->Prop)))
% 3.37/3.94 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_5r205_prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5r205_prop1 X0) X2)) ((d_5r205_prop2 X1) X2)))) of role definition named def_d_5r205_prop3
% 3.37/3.95 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_5r205_prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5r205_prop1 X0) X2)) ((d_5r205_prop2 X1) X2))))
% 3.37/3.95 Defined: d_5r205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5r205_prop1 X0) X2)) ((d_5r205_prop2 X1) X2)))
% 3.37/3.95 FOF formula (<kernel.Constant object at 0x2aefb2985b90>, <kernel.DependentProduct object at 0x2aefb2985a70>) of role type named typ_mxy
% 3.37/3.95 Using role type
% 3.37/3.95 Declaring mxy:(fofType->(fofType->fofType))
% 3.37/3.95 FOF formula (((eq (fofType->(fofType->fofType))) mxy) (fun (X0:fofType) (X1:fofType)=> ((r_ts half) ((r_pl X0) X1)))) of role definition named def_mxy
% 3.37/3.95 A new definition: (((eq (fofType->(fofType->fofType))) mxy) (fun (X0:fofType) (X1:fofType)=> ((r_ts half) ((r_pl X0) X1))))
% 3.37/3.95 Defined: mxy:=(fun (X0:fofType) (X1:fofType)=> ((r_ts half) ((r_pl X0) X1)))
% 3.37/3.95 FOF formula (<kernel.Constant object at 0x2aefb2985a70>, <kernel.DependentProduct object at 0x2aefb2985b00>) of role type named typ_sc1
% 3.37/3.95 Using role type
% 3.37/3.95 Declaring sc1:(fofType->fofType)
% 3.37/3.95 FOF formula (((eq (fofType->fofType)) sc1) (fun (X0:fofType)=> ((d_Sep cut) (fun (X1:fofType)=> ((r_in (pofrp X1)) X0))))) of role definition named def_sc1
% 3.37/3.95 A new definition: (((eq (fofType->fofType)) sc1) (fun (X0:fofType)=> ((d_Sep cut) (fun (X1:fofType)=> ((r_in (pofrp X1)) X0)))))
% 3.37/3.95 Defined: sc1:=(fun (X0:fofType)=> ((d_Sep cut) (fun (X1:fofType)=> ((r_in (pofrp X1)) X0))))
% 3.37/3.95 FOF formula (<kernel.Constant object at 0x2aefb2985b90>, <kernel.DependentProduct object at 0x2aefb2985050>) of role type named typ_pr1
% 3.37/3.95 Using role type
% 3.37/3.95 Declaring pr1:(fofType->(fofType->fofType))
% 3.37/3.95 FOF formula (((eq (fofType->(fofType->fofType))) pr1) (fun (X0:fofType)=> rpofp)) of role definition named def_pr1
% 3.37/3.95 A new definition: (((eq (fofType->(fofType->fofType))) pr1) (fun (X0:fofType)=> rpofp))
% 3.37/3.95 Defined: pr1:=(fun (X0:fofType)=> rpofp)
% 3.37/3.95 FOF formula (<kernel.Constant object at 0x2aefb2985680>, <kernel.DependentProduct object at 0x2aefbcd5e170>) of role type named typ_ps1
% 3.37/3.95 Using role type
% 3.37/3.95 Declaring ps1:(fofType->(fofType->(fofType->(fofType->fofType))))
% 3.37/3.95 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) ps1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> rpofp)) of role definition named def_ps1
% 3.37/3.95 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) ps1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> rpofp))
% 3.37/3.95 Defined: ps1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> rpofp)
% 3.37/3.95 FOF formula (<kernel.Constant object at 0x2aefb2985a70>, <kernel.DependentProduct object at 0x2aefb2985b00>) of role type named typ_stc
% 3.37/3.95 Using role type
% 3.37/3.95 Declaring stc:(fofType->(fofType->(fofType->fofType)))
% 3.37/3.95 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) stc) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((schnitt (sc1 X0)) (sc1 X1)))) of role definition named def_stc
% 3.37/3.95 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) stc) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((schnitt (sc1 X0)) (sc1 X1))))
% 3.37/3.95 Defined: stc:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((schnitt (sc1 X0)) (sc1 X1)))
% 3.37/3.95 FOF formula (<kernel.Constant object at 0x2aefb2985b90>, <kernel.DependentProduct object at 0x2aefbcd5e3b0>) of role type named typ_stp
% 3.37/3.95 Using role type
% 3.37/3.95 Declaring stp:(fofType->(fofType->(fofType->fofType)))
% 3.37/3.95 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) stp) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (pofrp (((stc X0) X1) X2)))) of role definition named def_stp
% 3.37/3.95 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) stp) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (pofrp (((stc X0) X1) X2))))
% 3.37/3.95 Defined: stp:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (pofrp (((stc X0) X1) X2)))
% 3.37/3.95 FOF formula (<kernel.Constant object at 0x2aefb2985b90>, <kernel.DependentProduct object at 0x2aefbcd5e098>) of role type named typ_d_5r205_sp1
% 3.37/3.95 Using role type
% 3.37/3.95 Declaring d_5r205_sp1:(fofType->fofType)
% 3.37/3.97 FOF formula (((eq (fofType->fofType)) d_5r205_sp1) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_in (r_m0 X1)) X0))))) of role definition named def_d_5r205_sp1
% 3.37/3.97 A new definition: (((eq (fofType->fofType)) d_5r205_sp1) (fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_in (r_m0 X1)) X0)))))
% 3.37/3.97 Defined: d_5r205_sp1:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_in (r_m0 X1)) X0))))
% 3.37/3.97 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->(r_one (fun (X2:fofType)=> ((d_and (r_all (fun (X3:fofType)=> (((r_less X3) X2)->((r_in X3) X0))))) (r_all (fun (X3:fofType)=> (((r_more X3) X2)->((r_in X3) X1))))))))))))))) of role axiom named satz205
% 3.37/3.97 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->(r_one (fun (X2:fofType)=> ((d_and (r_all (fun (X3:fofType)=> (((r_less X3) X2)->((r_in X3) X0))))) (r_all (fun (X3:fofType)=> (((r_more X3) X2)->((r_in X3) X1)))))))))))))))
% 3.37/3.97 FOF formula (<kernel.Constant object at 0x2aefbcd5e1b8>, <kernel.DependentProduct object at 0x2aefbcd5e320>) of role type named typ_r_schnitt
% 3.37/3.97 Using role type
% 3.37/3.97 Declaring r_schnitt:(fofType->(fofType->fofType))
% 3.37/3.97 FOF formula (((eq (fofType->(fofType->fofType))) r_schnitt) (fun (X0:fofType) (X1:fofType)=> ((ind real) ((d_5r205_prop3 X0) X1)))) of role definition named def_r_schnitt
% 3.37/3.97 A new definition: (((eq (fofType->(fofType->fofType))) r_schnitt) (fun (X0:fofType) (X1:fofType)=> ((ind real) ((d_5r205_prop3 X0) X1))))
% 3.37/3.97 Defined: r_schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind real) ((d_5r205_prop3 X0) X1)))
% 3.37/3.97 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X2) ((r_schnitt X0) X1))->((r_in X2) X0)))))))))))) of role axiom named satz205a
% 3.37/3.97 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X2) ((r_schnitt X0) X1))->((r_in X2) X0))))))))))))
% 3.37/3.97 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X2) ((r_schnitt X0) X1))->((r_in X2) X1)))))))))))) of role axiom named satz205b
% 3.37/3.97 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X2) ((r_schnitt X0) X1))->((r_in X2) X1))))))))))))
% 3.37/3.98 FOF formula (<kernel.Constant object at 0x2aefbcd5e5f0>, <kernel.DependentProduct object at 0x2aefbcd5e2d8>) of role type named typ_r_sqrt
% 3.37/3.98 Using role type
% 3.37/3.98 Declaring r_sqrt:(fofType->fofType)
% 3.37/3.98 FOF formula (((eq (fofType->fofType)) r_sqrt) (fun (X0:fofType)=> ((ind real) (fun (X1:fofType)=> ((d_and (d_not (neg X1))) ((r_is ((r_ts X1) X1)) X0)))))) of role definition named def_r_sqrt
% 3.37/3.98 A new definition: (((eq (fofType->fofType)) r_sqrt) (fun (X0:fofType)=> ((ind real) (fun (X1:fofType)=> ((d_and (d_not (neg X1))) ((r_is ((r_ts X1) X1)) X0))))))
% 3.37/3.98 Defined: r_sqrt:=(fun (X0:fofType)=> ((ind real) (fun (X1:fofType)=> ((d_and (d_not (neg X1))) ((r_is ((r_ts X1) X1)) X0)))))
% 3.37/3.98 FOF formula (<kernel.Constant object at 0x2aefbcd5e2d8>, <kernel.DependentProduct object at 0x2aefbcd5e0e0>) of role type named typ_shiftl
% 3.37/3.98 Using role type
% 3.37/3.98 Declaring shiftl:(fofType->(fofType->fofType))
% 3.37/3.98 FOF formula (((eq (fofType->(fofType->fofType))) shiftl) (fun (X0:fofType) (X1:fofType)=> (ntofrl ((r_mn ((r_pl X0) d_1rl)) X1)))) of role definition named def_shiftl
% 3.37/3.98 A new definition: (((eq (fofType->(fofType->fofType))) shiftl) (fun (X0:fofType) (X1:fofType)=> (ntofrl ((r_mn ((r_pl X0) d_1rl)) X1))))
% 3.37/3.98 Defined: shiftl:=(fun (X0:fofType) (X1:fofType)=> (ntofrl ((r_mn ((r_pl X0) d_1rl)) X1)))
% 3.37/3.98 FOF formula (<kernel.Constant object at 0x2aefbcd5e0e0>, <kernel.DependentProduct object at 0x2aefbcd5ed88>) of role type named typ_shift_n1
% 3.37/3.98 Using role type
% 3.37/3.98 Declaring shift_n1:(fofType->(fofType->(fofType->fofType)))
% 3.37/3.98 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) shift_n1) (fun (X0:fofType) (X1:fofType)=> (inn ((shiftl X0) X1)))) of role definition named def_shift_n1
% 3.37/3.98 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) shift_n1) (fun (X0:fofType) (X1:fofType)=> (inn ((shiftl X0) X1))))
% 3.37/3.98 Defined: shift_n1:=(fun (X0:fofType) (X1:fofType)=> (inn ((shiftl X0) X1)))
% 3.37/3.98 FOF formula (<kernel.Constant object at 0x2aefbcd5ed88>, <kernel.DependentProduct object at 0x2aefbcd5e3b0>) of role type named typ_shift_n2
% 3.37/3.98 Using role type
% 3.37/3.98 Declaring shift_n2:(fofType->(fofType->(fofType->fofType)))
% 3.37/3.98 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) shift_n2) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rlofnt (((shift_n1 X0) X1) X2)))) of role definition named def_shift_n2
% 3.37/3.98 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) shift_n2) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rlofnt (((shift_n1 X0) X1) X2))))
% 3.37/3.98 Defined: shift_n2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rlofnt (((shift_n1 X0) X1) X2)))
% 3.37/3.98 FOF formula (<kernel.Constant object at 0x2aefbcd5e3b0>, <kernel.DependentProduct object at 0x2aefbcd5e440>) of role type named typ_shiftr
% 3.37/3.98 Using role type
% 3.37/3.98 Declaring shiftr:(fofType->(fofType->(fofType->fofType)))
% 3.37/3.98 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) shiftr) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((r_mn ((r_pl (((shift_n2 X0) X1) X2)) X1)) d_1rl))) of role definition named def_shiftr
% 3.37/3.98 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) shiftr) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((r_mn ((r_pl (((shift_n2 X0) X1) X2)) X1)) d_1rl)))
% 3.37/3.98 Defined: shiftr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((r_mn ((r_pl (((shift_n2 X0) X1) X2)) X1)) d_1rl))
% 3.37/3.98 FOF formula (<kernel.Constant object at 0x2aefbcd5e440>, <kernel.DependentProduct object at 0x2aefbcd5e1b8>) of role type named typ_shift_ul
% 3.37/3.98 Using role type
% 3.37/3.98 Declaring shift_ul:(fofType->(fofType->(fofType->fofType)))
% 3.37/3.98 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) shift_ul) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((shiftl X2) X1))) of role definition named def_shift_ul
% 3.37/3.98 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) shift_ul) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((shiftl X2) X1)))
% 3.37/3.98 Defined: shift_ul:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((shiftl X2) X1))
% 3.37/3.98 FOF formula (<kernel.Constant object at 0x2aefbcd5e1b8>, <kernel.DependentProduct object at 0x2aefbcd5e5a8>) of role type named typ_shiftl1
% 3.46/4.00 Using role type
% 3.46/4.00 Declaring shiftl1:(fofType->(fofType->(fofType->fofType)))
% 3.46/4.00 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) shiftl1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((shiftl X0) X1)) (((shift_ul X0) X1) X2)))) of role definition named def_shiftl1
% 3.46/4.00 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) shiftl1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((shiftl X0) X1)) (((shift_ul X0) X1) X2))))
% 3.46/4.00 Defined: shiftl1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((shiftl X0) X1)) (((shift_ul X0) X1) X2)))
% 3.46/4.00 FOF formula (<kernel.Constant object at 0x2aefbcd5e5a8>, <kernel.DependentProduct object at 0x2aefbcd5e170>) of role type named typ_seq
% 3.46/4.00 Using role type
% 3.46/4.00 Declaring seq:(fofType->(fofType->(fofType->fofType)))
% 3.46/4.00 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) seq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Pi real) (fun (X3:fofType)=> (((if (intrl X3)) (((if ((r_lessis X1) X3)) (((if ((r_lessis X3) X0)) X2) (ordsucc emptyset))) (ordsucc emptyset))) (ordsucc emptyset)))))) of role definition named def_seq
% 3.46/4.00 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) seq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Pi real) (fun (X3:fofType)=> (((if (intrl X3)) (((if ((r_lessis X1) X3)) (((if ((r_lessis X3) X0)) X2) (ordsucc emptyset))) (ordsucc emptyset))) (ordsucc emptyset))))))
% 3.46/4.00 Defined: seq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Pi real) (fun (X3:fofType)=> (((if (intrl X3)) (((if ((r_lessis X1) X3)) (((if ((r_lessis X3) X0)) X2) (ordsucc emptyset))) (ordsucc emptyset))) (ordsucc emptyset)))))
% 3.46/4.00 FOF formula (<kernel.Constant object at 0x2aefbcd5e170>, <kernel.DependentProduct object at 0x2aefbcd5e7a0>) of role type named typ_proofsirrelevant
% 3.46/4.00 Using role type
% 3.46/4.00 Declaring proofsirrelevant:(fofType->(fofType->(fofType->(fofType->Prop))))
% 3.46/4.00 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) proofsirrelevant) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->((all_of (fun (X5:fofType)=> ((in X5) real))) (fun (X5:fofType)=> ((intrl X5)->(((r_lessis X1) X5)->(((r_lessis X5) X0)->(((r_is X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5))))))))))))))) of role definition named def_proofsirrelevant
% 3.46/4.00 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) proofsirrelevant) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->((all_of (fun (X5:fofType)=> ((in X5) real))) (fun (X5:fofType)=> ((intrl X5)->(((r_lessis X1) X5)->(((r_lessis X5) X0)->(((r_is X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))))))))))
% 3.46/4.00 Defined: proofsirrelevant:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->((all_of (fun (X5:fofType)=> ((in X5) real))) (fun (X5:fofType)=> ((intrl X5)->(((r_lessis X1) X5)->(((r_lessis X5) X0)->(((r_is X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5))))))))))))))
% 3.46/4.00 FOF formula (<kernel.Constant object at 0x2aefbcd5e7a0>, <kernel.DependentProduct object at 0x2aefbcd5eb90>) of role type named typ_shiftf
% 3.46/4.00 Using role type
% 3.46/4.00 Declaring shiftf:(fofType->(fofType->(fofType->(fofType->fofType))))
% 3.46/4.00 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) shiftf) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X4:fofType)=> ((ap X3) (((shiftr X0) X1) X4)))))) of role definition named def_shiftf
% 3.46/4.00 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) shiftf) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X4:fofType)=> ((ap X3) (((shiftr X0) X1) X4))))))
% 3.46/4.00 Defined: shiftf:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X4:fofType)=> ((ap X3) (((shiftr X0) X1) X4)))))
% 3.46/4.02 FOF formula (<kernel.Constant object at 0x2aefbcd5eb90>, <kernel.DependentProduct object at 0x2aefbcd5ec68>) of role type named typ_inseq
% 3.46/4.02 Using role type
% 3.46/4.02 Declaring inseq:(fofType->(fofType->(fofType->Prop)))
% 3.46/4.02 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) inseq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->(((and3 (intrl ((ap X2) X3))) ((r_lessis X1) ((ap X2) X3))) ((r_lessis ((ap X2) X3)) X0))))))))) of role definition named def_inseq
% 3.46/4.02 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) inseq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->(((and3 (intrl ((ap X2) X3))) ((r_lessis X1) ((ap X2) X3))) ((r_lessis ((ap X2) X3)) X0)))))))))
% 3.46/4.02 Defined: inseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->(((and3 (intrl ((ap X2) X3))) ((r_lessis X1) ((ap X2) X3))) ((r_lessis ((ap X2) X3)) X0))))))))
% 3.46/4.02 FOF formula (<kernel.Constant object at 0x2aefbcd5ec68>, <kernel.DependentProduct object at 0x2aefbcd5ebd8>) of role type named typ_injseq
% 3.46/4.02 Using role type
% 3.46/4.02 Declaring injseq:(fofType->(fofType->(fofType->Prop)))
% 3.46/4.02 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) injseq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->(((r_is ((ap X2) X3)) ((ap X2) X4))->((r_is X3) X4)))))))))))))) of role definition named def_injseq
% 3.46/4.02 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) injseq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->(((r_is ((ap X2) X3)) ((ap X2) X4))->((r_is X3) X4))))))))))))))
% 3.46/4.02 Defined: injseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->(((r_is ((ap X2) X3)) ((ap X2) X4))->((r_is X3) X4)))))))))))))
% 3.46/4.02 FOF formula (<kernel.Constant object at 0x2aefbcd5ebd8>, <kernel.DependentProduct object at 0x2aefbcd5e7a0>) of role type named typ_shift_prop1
% 3.46/4.02 Using role type
% 3.46/4.02 Declaring shift_prop1:(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 3.46/4.02 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) shift_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((r_is X3) ((ap X2) X4)))) of role definition named def_shift_prop1
% 3.46/4.02 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) shift_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((r_is X3) ((ap X2) X4))))
% 3.46/4.02 Defined: shift_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((r_is X3) ((ap X2) X4)))
% 3.46/4.02 FOF formula (<kernel.Constant object at 0x2aefbcd5e7a0>, <kernel.DependentProduct object at 0x2aefbcd5e368>) of role type named typ_improp
% 3.46/4.02 Using role type
% 3.46/4.02 Declaring improp:(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 3.46/4.02 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) improp) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and (((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))) ((((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))->(((((shift_prop1 X0) X1) X2) X3) X4))))) of role definition named def_improp
% 3.46/4.03 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))) improp) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and (((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))) ((((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))->(((((shift_prop1 X0) X1) X2) X3) X4)))))
% 3.46/4.03 Defined: improp:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and (((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))) ((((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))->(((((shift_prop1 X0) X1) X2) X3) X4))))
% 3.46/4.03 FOF formula (<kernel.Constant object at 0x2aefbcd5e368>, <kernel.DependentProduct object at 0x2aefbcd5ed40>) of role type named typ_imseq
% 3.46/4.03 Using role type
% 3.46/4.03 Declaring imseq:(fofType->(fofType->(fofType->(fofType->Prop))))
% 3.46/4.03 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) imseq) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (r_some ((((improp X0) X1) X2) X3)))) of role definition named def_imseq
% 3.46/4.03 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) imseq) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (r_some ((((improp X0) X1) X2) X3))))
% 3.46/4.03 Defined: imseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (r_some ((((improp X0) X1) X2) X3)))
% 3.46/4.03 FOF formula (<kernel.Constant object at 0x2aefbcd5ed40>, <kernel.DependentProduct object at 0x2aefbcd5e170>) of role type named typ_surjseq
% 3.46/4.03 Using role type
% 3.46/4.03 Declaring surjseq:(fofType->(fofType->(fofType->Prop)))
% 3.46/4.03 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) surjseq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((((imseq X0) X1) X2) X3)))))))) of role definition named def_surjseq
% 3.46/4.03 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) surjseq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((((imseq X0) X1) X2) X3))))))))
% 3.46/4.03 Defined: surjseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((((imseq X0) X1) X2) X3)))))))
% 3.46/4.03 FOF formula (<kernel.Constant object at 0x2aefbcd5e170>, <kernel.DependentProduct object at 0x2aefbcd5ea28>) of role type named typ_perm
% 3.46/4.03 Using role type
% 3.46/4.03 Declaring perm:(fofType->(fofType->(fofType->Prop)))
% 3.46/4.03 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) perm) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injseq X0) X1) X2)) (((surjseq X0) X1) X2)))) of role definition named def_perm
% 3.46/4.03 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) perm) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injseq X0) X1) X2)) (((surjseq X0) X1) X2))))
% 3.46/4.03 Defined: perm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injseq X0) X1) X2)) (((surjseq X0) X1) X2)))
% 3.46/4.03 FOF formula (<kernel.Constant object at 0x2aefbcd5ea28>, <kernel.DependentProduct object at 0x2aefbcd5e368>) of role type named typ_shift_ns
% 3.46/4.03 Using role type
% 3.46/4.03 Declaring shift_ns:(fofType->(fofType->(fofType->(fofType->fofType))))
% 3.46/4.03 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) shift_ns) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ap X2) (((shiftr X0) X1) X3)))) of role definition named def_shift_ns
% 3.46/4.03 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) shift_ns) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ap X2) (((shiftr X0) X1) X3))))
% 3.46/4.03 Defined: shift_ns:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ap X2) (((shiftr X0) X1) X3)))
% 3.46/4.03 FOF formula (<kernel.Constant object at 0x2aefbcd5e368>, <kernel.DependentProduct object at 0x2aefbcd5edd0>) of role type named typ_shiftseq
% 3.46/4.03 Using role type
% 3.46/4.03 Declaring shiftseq:(fofType->(fofType->(fofType->fofType)))
% 3.46/4.03 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) shiftseq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X3:fofType)=> (((shiftl1 X0) X1) ((((shift_ns X0) X1) X2) X3)))))) of role definition named def_shiftseq
% 3.46/4.04 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) shiftseq) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X3:fofType)=> (((shiftl1 X0) X1) ((((shift_ns X0) X1) X2) X3))))))
% 3.46/4.04 Defined: shiftseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X3:fofType)=> (((shiftl1 X0) X1) ((((shift_ns X0) X1) X2) X3)))))
% 3.46/4.04 FOF formula (<kernel.Constant object at 0x2aefbcd5e9e0>, <kernel.DependentProduct object at 0x2aefbcd5ed40>) of role type named typ_ul1
% 3.46/4.04 Using role type
% 3.46/4.04 Declaring ul1:(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 3.46/4.04 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) ul1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((shiftl1 X0) X1))) of role definition named def_ul1
% 3.46/4.04 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) ul1) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((shiftl1 X0) X1)))
% 3.46/4.04 Defined: ul1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((shiftl1 X0) X1))
% 3.46/4.04 We need to prove []
% 3.46/4.04 Parameter fofType:Type.
% 3.46/4.04 Definition is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)):(fofType->((fofType->Prop)->Prop)).
% 3.46/4.04 Definition all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))):((fofType->Prop)->((fofType->Prop)->Prop)).
% 3.46/4.04 Parameter eps:((fofType->Prop)->fofType).
% 3.46/4.04 Parameter in:(fofType->(fofType->Prop)).
% 3.46/4.04 Definition d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))):(fofType->(fofType->Prop)).
% 3.46/4.04 Axiom set_ext:(forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1)))).
% 3.46/4.04 Axiom k_In_ind:(forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1)))).
% 3.46/4.04 Parameter emptyset:fofType.
% 3.46/4.04 Axiom k_EmptyAx:(((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False).
% 3.46/4.04 Parameter union:(fofType->fofType).
% 3.46/4.04 Axiom k_UnionEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0)))))).
% 3.46/4.04 Parameter power:(fofType->fofType).
% 3.46/4.04 Axiom k_PowerEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0))).
% 3.46/4.04 Parameter repl:(fofType->((fofType->fofType)->fofType)).
% 3.46/4.04 Axiom k_ReplEq:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3))))))).
% 3.46/4.04 Definition d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))):(fofType->Prop).
% 3.46/4.04 Definition d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))):(fofType->Prop).
% 3.46/4.04 Definition d_Repl_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0)))))):(fofType->Prop).
% 3.46/4.04 Definition d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))):(fofType->Prop).
% 3.46/4.04 Parameter univof:(fofType->fofType).
% 3.46/4.04 Axiom k_UnivOf_In:(forall (X0:fofType), ((in X0) (univof X0))).
% 3.46/4.04 Axiom k_UnivOf_ZF_closed:(forall (X0:fofType), (d_ZF_closed (univof X0))).
% 3.46/4.04 Definition if:=(fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2)))))):(Prop->(fofType->(fofType->fofType))).
% 3.46/4.04 Axiom if_i_correct:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2)))).
% 3.46/4.04 Axiom if_i_0:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2))).
% 3.46/4.04 Axiom if_i_1:(forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1))).
% 3.46/4.04 Axiom if_i_or:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2))).
% 3.46/4.04 Definition nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)):(fofType->(fofType->Prop)).
% 3.46/4.04 Axiom k_PowerE:(forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0))).
% 3.46/4.04 Axiom k_PowerI:(forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0)))).
% 3.46/4.04 Axiom k_Self_In_Power:(forall (X0:fofType), ((in X0) (power X0))).
% 3.46/4.04 Definition d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))):(fofType->(fofType->fofType)).
% 3.46/4.04 Definition d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0)):(fofType->fofType).
% 3.46/4.04 Definition binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))):(fofType->(fofType->fofType)).
% 3.46/4.04 Definition famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))):(fofType->((fofType->fofType)->fofType)).
% 3.46/4.04 Definition d_Sep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset)):(fofType->((fofType->Prop)->fofType)).
% 3.46/4.04 Axiom k_SepI:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1))))).
% 3.46/4.04 Axiom k_SepE1:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0))).
% 3.46/4.04 Axiom k_SepE2:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2))).
% 3.46/4.04 Definition d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))):(fofType->((fofType->Prop)->((fofType->fofType)->fofType))).
% 3.46/4.04 Definition setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))):(fofType->(fofType->fofType)).
% 3.46/4.04 Definition d_In_rec_G:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))):((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop))).
% 3.46/4.04 Definition d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1))):((fofType->((fofType->fofType)->fofType))->(fofType->fofType)).
% 3.46/4.04 Definition ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0))):(fofType->fofType).
% 3.46/4.04 Axiom neq_ordsucc_0:(forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset))).
% 3.46/4.04 Axiom ordsucc_inj:(forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1))).
% 3.46/4.04 Axiom k_In_0_1:((in emptyset) (ordsucc emptyset)).
% 3.46/4.04 Definition nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))):(fofType->Prop).
% 3.46/4.04 Axiom nat_ordsucc:(forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0)))).
% 3.46/4.04 Axiom nat_1:(nat_p (ordsucc emptyset)).
% 3.46/4.04 Axiom nat_ind:(forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1)))))).
% 3.46/4.04 Axiom nat_inv:(forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1)))))))).
% 3.46/4.04 Definition omega:=((d_Sep (univof emptyset)) nat_p):fofType.
% 3.46/4.04 Axiom omega_nat_p:(forall (X0:fofType), (((in X0) omega)->(nat_p X0))).
% 3.46/4.04 Axiom nat_p_omega:(forall (X0:fofType), ((nat_p X0)->((in X0) omega))).
% 3.46/4.04 Definition d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))):(fofType->fofType).
% 3.46/4.04 Definition d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1)):(fofType->fofType).
% 3.46/4.04 Definition d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))):(fofType->fofType).
% 3.46/4.04 Definition pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))):(fofType->(fofType->fofType)).
% 3.46/4.04 Definition proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj)):(fofType->fofType).
% 3.46/4.04 Definition _TPTP_proj1:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj)):(fofType->fofType).
% 3.46/4.04 Axiom proj0_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0)).
% 3.46/4.04 Axiom proj1_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1)).
% 3.46/4.04 Definition d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))):(fofType->((fofType->fofType)->fofType)).
% 3.46/4.04 Axiom pair_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1)))))).
% 3.46/4.04 Axiom k_Sigma_eta_proj0_proj1:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))).
% 3.46/4.04 Axiom proj_Sigma_eta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2))).
% 3.46/4.04 Axiom proj0_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0))).
% 3.46/4.04 Axiom proj1_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))).
% 3.46/4.04 Definition setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))):(fofType->(fofType->fofType)).
% 3.46/4.04 Definition ap:=(fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1)):(fofType->(fofType->fofType)).
% 3.46/4.04 Axiom beta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2)))).
% 3.46/4.04 Definition pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)):(fofType->Prop).
% 3.46/4.04 Definition d_Pi:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))))):(fofType->((fofType->fofType)->fofType)).
% 3.46/4.04 Axiom lam_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1)))).
% 3.46/4.04 Axiom ap_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))).
% 3.46/4.04 Axiom k_Pi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3)))))).
% 3.46/4.04 Axiom xi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2)))).
% 3.46/4.04 Axiom k_If_In_01:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset))))).
% 3.46/4.04 Axiom k_If_In_then_E:(forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2)))).
% 3.46/4.04 Definition imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1)):(Prop->(Prop->Prop)).
% 3.46/4.04 Definition d_not:=(fun (X0:Prop)=> ((imp X0) False)):(Prop->Prop).
% 3.46/4.04 Definition wel:=(fun (X0:Prop)=> (d_not (d_not X0))):(Prop->Prop).
% 3.46/4.04 Axiom l_et:(forall (X0:Prop), ((wel X0)->X0)).
% 3.46/4.04 Definition obvious:=((imp False) False):Prop.
% 3.46/4.04 Definition l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))):(Prop->(Prop->Prop)).
% 3.46/4.04 Definition d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))):(Prop->(Prop->Prop)).
% 3.46/4.05 Definition l_or:=(fun (X0:Prop)=> (imp (d_not X0))):(Prop->(Prop->Prop)).
% 3.46/4.05 Definition orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))):(Prop->(Prop->Prop)).
% 3.46/4.05 Definition l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))):(Prop->(Prop->Prop)).
% 3.46/4.05 Definition all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))):(fofType->((fofType->Prop)->Prop)).
% 3.46/4.05 Definition non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))):(fofType->((fofType->Prop)->(fofType->Prop))).
% 3.46/4.05 Definition l_some:=(fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1)))):(fofType->((fofType->Prop)->Prop)).
% 3.46/4.05 Definition or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 3.46/4.05 Definition and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 3.46/4.05 Definition ec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0))):(Prop->(Prop->(Prop->Prop))).
% 3.46/4.05 Definition orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 3.46/4.05 Definition e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.05 Axiom refis:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1)))).
% 3.46/4.05 Axiom e_isp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3)))))))).
% 3.46/4.05 Definition amone:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3)))))))):(fofType->((fofType->Prop)->Prop)).
% 3.46/4.05 Definition one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))):(fofType->((fofType->Prop)->Prop)).
% 3.46/4.05 Definition ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))):(fofType->((fofType->Prop)->fofType)).
% 3.46/4.05 Axiom ind_p:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0))))).
% 3.46/4.05 Axiom oneax:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1)))).
% 3.46/4.05 Definition injective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4))))))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.05 Definition image:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.46/4.05 Definition tofs:=(fun (X0:fofType) (X1:fofType)=> ap):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.05 Definition soft:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.05 Definition inverse:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset)))):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.05 Definition surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.05 Definition bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.05 Definition invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.05 Definition inj_h:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType))))).
% 3.46/4.05 Axiom e_fisi:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3))))))).
% 3.46/4.05 Definition e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2):(fofType->((fofType->Prop)->(fofType->fofType))).
% 3.46/4.05 Axiom e_in_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0)))))).
% 3.46/4.05 Axiom e_inp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2))))).
% 3.46/4.05 Axiom otax1:(forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))).
% 3.46/4.05 Axiom otax2:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2))))).
% 3.46/4.05 Definition out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))):(fofType->((fofType->Prop)->(fofType->fofType))).
% 3.46/4.05 Definition d_pair:=(fun (X0:fofType) (X1:fofType)=> pair):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.05 Axiom e_pair_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1))))))))).
% 3.46/4.05 Definition first:=(fun (X0:fofType) (X1:fofType)=> proj0):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.05 Axiom first_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0)))))).
% 3.46/4.05 Definition second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.05 Axiom second_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1)))))).
% 3.46/4.05 Axiom pairis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2)))).
% 3.46/4.05 Axiom firstis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2)))))).
% 3.46/4.05 Axiom secondis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3)))))).
% 3.46/4.05 Definition prop1:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3)))):(Prop->(fofType->(fofType->(fofType->(fofType->Prop))))).
% 3.46/4.05 Definition ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))):(Prop->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.05 Definition wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3)):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.05 Definition wissel_wb:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.05 Definition wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.05 Definition changef:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType))))).
% 3.46/4.05 Definition r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))):(Prop->(Prop->Prop)).
% 3.46/4.05 Definition esti:=(fun (X0:fofType)=> in):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.05 Axiom setof_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0))))).
% 3.46/4.05 Axiom estii:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1)))))).
% 3.46/4.05 Axiom estie:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2))))).
% 3.46/4.05 Definition empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))):(fofType->(fofType->Prop)).
% 3.46/4.05 Definition nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))):(fofType->(fofType->Prop)).
% 3.46/4.05 Definition incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.05 Definition st_disj:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.05 Axiom isseti:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2)))))))).
% 3.46/4.05 Definition nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2)))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.46/4.05 Definition unmore:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4))))))):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.05 Definition ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 3.46/4.05 Definition ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 3.46/4.05 Definition anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->Prop))).
% 3.46/4.05 Definition ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->fofType)).
% 3.46/4.05 Definition ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 3.46/4.05 Definition ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 3.46/4.05 Definition ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 3.46/4.05 Definition fixfu:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 3.46/4.05 Definition d_10_prop1:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))))).
% 3.46/4.05 Definition prop2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop)))))).
% 3.46/4.05 Definition indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType))))).
% 3.46/4.05 Definition fixfu2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7))))))))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 3.46/4.05 Definition d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2)))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType))))).
% 3.46/4.05 Definition indeq2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType)))))).
% 3.46/4.05 Definition nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))):fofType.
% 3.46/4.05 Definition n_is:=(e_is nat):(fofType->(fofType->Prop)).
% 3.46/4.05 Definition nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.05 Definition n_in:=(esti nat):(fofType->(fofType->Prop)).
% 3.46/4.05 Definition n_some:=(l_some nat):((fofType->Prop)->Prop).
% 3.46/4.05 Definition n_all:=(all nat):((fofType->Prop)->Prop).
% 3.46/4.05 Definition n_one:=(one nat):((fofType->Prop)->Prop).
% 3.46/4.05 Definition n_1:=(ordsucc emptyset):fofType.
% 3.46/4.05 Axiom n_1_p:((is_of n_1) (fun (X0:fofType)=> ((in X0) nat))).
% 3.46/4.05 Axiom suc_p:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat))))).
% 3.46/4.05 Axiom n_ax3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1))).
% 3.46/4.05 Axiom n_ax4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1)))))).
% 3.46/4.05 Definition cond1:=(n_in n_1):(fofType->Prop).
% 3.46/4.05 Definition cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))):(fofType->Prop).
% 3.46/4.05 Axiom n_ax5:((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0))))))).
% 3.46/4.05 Definition i1_s:=(d_Sep nat):((fofType->Prop)->fofType).
% 3.46/4.05 Axiom satz1:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1))))))).
% 3.46/4.05 Definition d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0)):(fofType->Prop).
% 3.46/4.05 Axiom satz2:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))).
% 3.46/4.05 Definition d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))):(fofType->Prop).
% 3.46/4.05 Axiom satz3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))).
% 3.46/4.05 Axiom satz3a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))).
% 3.46/4.05 Definition d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))):(fofType->Prop).
% 3.46/4.05 Definition d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1))):(fofType->(fofType->Prop)).
% 3.46/4.05 Definition prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.06 Definition prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->Prop).
% 3.46/4.06 Definition d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))):(fofType->fofType).
% 3.46/4.06 Axiom satz4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2)))))))))).
% 3.46/4.06 Definition plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->fofType).
% 3.46/4.06 Definition n_pl:=(fun (X0:fofType)=> (ap (plus X0))):(fofType->(fofType->fofType)).
% 3.46/4.06 Axiom satz4a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0)))).
% 3.46/4.06 Axiom satz4b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1))))))).
% 3.46/4.06 Axiom satz4c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0)))).
% 3.46/4.06 Axiom satz4d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1))))))).
% 3.46/4.06 Axiom satz4e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1)))).
% 3.46/4.06 Axiom satz4f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1))))))).
% 3.46/4.06 Axiom satz4g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0)))).
% 3.46/4.06 Axiom satz4h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1)))))).
% 3.46/4.06 Definition d_25_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.06 Axiom satz5:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2))))))))).
% 3.46/4.06 Definition d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))):(fofType->(fofType->Prop)).
% 3.46/4.06 Axiom satz6:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))))).
% 3.46/4.06 Definition d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.06 Axiom satz7:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))))).
% 3.46/4.06 Definition d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.06 Axiom satz8:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2))))))))).
% 3.46/4.06 Axiom satz8a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2)))))))).
% 3.46/4.06 Definition diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.06 Axiom satz8b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))))))).
% 3.46/4.06 Definition d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.06 Definition iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))):(fofType->(fofType->Prop)).
% 3.46/4.06 Definition d_29_prop1:=(fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.06 Axiom satz9:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2))))))))).
% 3.46/4.06 Axiom satz9a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0))))))).
% 3.46/4.06 Axiom satz9b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0))))))).
% 3.46/4.06 Axiom satz10:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))).
% 3.46/4.06 Axiom satz10a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))).
% 3.46/4.06 Axiom satz10b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))).
% 3.46/4.06 Axiom satz11:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0)))))).
% 3.46/4.06 Axiom satz12:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0)))))).
% 3.46/4.06 Definition moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.06 Definition lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.06 Axiom satz13:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0)))))).
% 3.46/4.06 Axiom satz14:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0)))))).
% 3.46/4.06 Axiom satz10c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1))))))).
% 3.46/4.06 Axiom satz10d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1))))))).
% 3.46/4.06 Axiom satz10e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1)))))).
% 3.46/4.06 Axiom satz10f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1)))))).
% 3.46/4.06 Axiom satz10g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1))))))).
% 3.46/4.06 Axiom satz10h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1))))))).
% 3.46/4.06 Axiom satz10j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1)))))).
% 3.46/4.06 Axiom satz10k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1)))))).
% 3.46/4.06 Axiom satz15:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2))))))))).
% 3.46/4.06 Axiom satz16a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2))))))))).
% 3.46/4.06 Axiom satz16b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2))))))))).
% 3.46/4.06 Axiom satz16c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2))))))))).
% 3.46/4.06 Axiom satz16d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2))))))))).
% 3.46/4.06 Axiom satz17:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((lessis X1) X2)->((lessis X0) X2))))))))).
% 3.46/4.06 Axiom satz18:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0))))).
% 3.46/4.06 Axiom satz18a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1)))))).
% 3.46/4.06 Axiom satz18b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0))).
% 3.46/4.06 Axiom satz18c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0)))).
% 3.46/4.06 Axiom satz19a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 3.46/4.06 Axiom satz19b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 3.46/4.06 Axiom satz19c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 3.46/4.06 Axiom satz19d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 3.46/4.06 Axiom satz19e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 3.46/4.06 Axiom satz19f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 3.46/4.06 Axiom satz19g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.06 Axiom satz19h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1)))))))))))).
% 3.46/4.06 Axiom satz19j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.06 Axiom satz19k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1)))))))))))).
% 3.46/4.06 Axiom satz19l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 3.46/4.06 Axiom satz19m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 3.46/4.06 Axiom satz19n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 3.46/4.06 Axiom satz19o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 3.46/4.06 Axiom satz20a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1)))))))).
% 3.46/4.06 Axiom satz20b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1)))))))).
% 3.46/4.06 Axiom satz20c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1)))))))).
% 3.46/4.06 Axiom satz20d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1)))))))).
% 3.46/4.06 Axiom satz20e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1)))))))).
% 3.46/4.06 Axiom satz20f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1)))))))).
% 3.46/4.07 Axiom satz21:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.07 Axiom satz21a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.07 Axiom satz22a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.07 Axiom satz22b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.07 Axiom satz22c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.07 Axiom satz22d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.07 Axiom satz23:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.07 Axiom satz23a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 3.46/4.07 Axiom satz24:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1))).
% 3.46/4.07 Axiom satz24a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1)).
% 3.46/4.07 Axiom satz24b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1))).
% 3.46/4.07 Axiom satz24c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0)))).
% 3.46/4.07 Axiom satz25:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1))))))).
% 3.46/4.07 Axiom satz25a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0))))))).
% 3.46/4.07 Axiom satz25b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0)))))).
% 3.46/4.07 Axiom satz25c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0)))))).
% 3.46/4.07 Axiom satz26:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0)))))).
% 3.46/4.07 Axiom satz26a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0)))))).
% 3.46/4.07 Axiom satz26b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0)))))).
% 3.46/4.07 Axiom satz26c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0)))))).
% 3.46/4.07 Definition lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))):((fofType->Prop)->(fofType->(fofType->Prop))).
% 3.46/4.07 Definition n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))):((fofType->Prop)->(fofType->Prop)).
% 3.46/4.07 Definition min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop)).
% 3.46/4.07 Axiom satz27:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0)))).
% 3.46/4.07 Axiom satz27a:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0)))).
% 3.46/4.07 Definition d_428_prop1:=(fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))):(fofType->(fofType->Prop)).
% 3.46/4.07 Definition d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.07 Definition d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->Prop).
% 3.46/4.07 Definition d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0)):fofType.
% 3.46/4.07 Definition d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))):(fofType->fofType).
% 3.46/4.07 Axiom satz28:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))))))).
% 3.46/4.07 Definition times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->fofType).
% 3.46/4.07 Definition n_ts:=(fun (X0:fofType)=> (ap (times X0))):(fofType->(fofType->fofType)).
% 3.46/4.07 Axiom satz28a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0))).
% 3.46/4.07 Axiom satz28b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0)))))).
% 3.46/4.07 Axiom satz28c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0))).
% 3.46/4.07 Axiom satz28d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1)))))).
% 3.46/4.07 Axiom satz28e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1)))).
% 3.46/4.07 Axiom satz28f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1))))))).
% 3.46/4.07 Axiom satz28g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0)))).
% 3.46/4.07 Axiom satz28h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1)))))).
% 3.46/4.07 Definition d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))):(fofType->(fofType->Prop)).
% 3.46/4.07 Axiom satz29:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))))).
% 3.46/4.07 Definition d_430_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.07 Axiom satz30:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2))))))))).
% 3.46/4.07 Definition d_431_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))):(fofType->(fofType->(fofType->Prop))).
% 3.46/4.07 Axiom satz31:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2))))))))).
% 3.46/4.07 Axiom satz32a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 3.46/4.07 Axiom satz32b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 3.46/4.07 Axiom satz32c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 3.46/4.07 Axiom satz32d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 3.46/4.07 Axiom satz32e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 3.46/4.07 Axiom satz32f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 3.46/4.07 Axiom satz32g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz32h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1)))))))))))).
% 3.46/4.07 Axiom satz32j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz32k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1)))))))))))).
% 3.46/4.07 Axiom satz32l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 3.46/4.07 Axiom satz32m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 3.46/4.07 Axiom satz32n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 3.46/4.07 Axiom satz32o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 3.46/4.07 Axiom satz33a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1)))))))).
% 3.46/4.07 Axiom satz33b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1)))))))).
% 3.46/4.07 Axiom satz33c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1)))))))).
% 3.46/4.07 Axiom satz34:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz34a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz35a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz35b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz35c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz35d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz36:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Axiom satz36a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 3.46/4.07 Definition n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))):(fofType->(fofType->fofType)).
% 3.46/4.07 Definition d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->fofType).
% 3.46/4.07 Definition outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType)).
% 3.46/4.07 Definition inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType)).
% 3.46/4.07 Definition n_1o:=((outn n_1) n_1):fofType.
% 3.46/4.07 Definition singlet_u0:=(inn n_1):(fofType->fofType).
% 3.46/4.07 Definition n_2:=((n_pl n_1) n_1):fofType.
% 3.46/4.07 Definition n_1t:=((outn n_2) n_1):fofType.
% 3.46/4.07 Definition n_2t:=((outn n_2) n_2):fofType.
% 3.46/4.07 Definition pair_u0:=(inn n_2):(fofType->fofType).
% 3.46/4.07 Definition pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))):(fofType->fofType).
% 3.46/4.07 Definition pair1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2)))):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.07 Definition first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)):(fofType->(fofType->fofType)).
% 3.46/4.07 Definition second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)):(fofType->(fofType->fofType)).
% 3.46/4.07 Definition pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))):(fofType->(fofType->fofType)).
% 3.46/4.07 Definition d_1out:=(fun (X0:fofType)=> ((outn X0) n_1)):(fofType->fofType).
% 3.46/4.07 Definition xout:=(fun (X0:fofType)=> ((outn X0) X0)):(fofType->fofType).
% 3.46/4.07 Definition left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.07 Definition right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))):(fofType->(fofType->(fofType->fofType))).
% 3.46/4.07 Definition left:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.07 Definition right:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.07 Definition left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.07 Definition left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.46/4.07 Definition frac:=(pair1type nat):fofType.
% 3.46/4.07 Definition n_fr:=(pair1 nat):(fofType->(fofType->fofType)).
% 3.46/4.07 Definition num:=(first1 nat):(fofType->fofType).
% 3.46/4.07 Definition den:=(second1 nat):(fofType->fofType).
% 3.46/4.07 Definition n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop)).
% 3.46/4.07 Axiom satz37:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0))).
% 3.46/4.07 Axiom satz38:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0)))))).
% 3.46/4.07 Axiom satz39:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2))))))))).
% 3.46/4.08 Axiom satz40:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))))))).
% 3.46/4.08 Axiom satz40a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0))))).
% 3.46/4.08 Axiom satz40b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 3.46/4.08 Axiom satz40c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1)))))))).
% 3.46/4.08 Definition moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop)).
% 3.46/4.08 Definition lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop)).
% 3.46/4.08 Axiom satz41:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))).
% 3.46/4.08 Axiom satz41a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))).
% 3.46/4.08 Axiom satz41b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))).
% 3.46/4.08 Axiom satz42:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0)))))).
% 3.46/4.08 Axiom satz43:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0)))))).
% 3.46/4.08 Axiom satz44:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3)))))))))))).
% 3.46/4.08 Axiom satz45:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3)))))))))))).
% 3.46/4.08 Definition moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.08 Definition lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop)).
% 3.46/4.08 Axiom satz41c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1))))))).
% 3.46/4.08 Axiom satz41d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1))))))).
% 3.46/4.08 Axiom satz41e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1)))))).
% 3.46/4.08 Axiom satz41f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1)))))).
% 3.46/4.08 Axiom satz41g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1))))))).
% 3.46/4.08 Axiom satz41h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1))))))).
% 3.46/4.08 Axiom satz41j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1)))))).
% 3.46/4.08 Axiom satz41k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1)))))).
% 3.46/4.08 Axiom satz46:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3)))))))))))).
% 3.46/4.08 Axiom satz47:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3)))))))))))).
% 3.46/4.08 Axiom satz48:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0)))))).
% 3.46/4.08 Axiom satz49:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0)))))).
% 3.46/4.08 Axiom satz50:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2))))))))).
% 3.46/4.08 Axiom satz51a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2))))))))).
% 3.46/4.08 Axiom satz51b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2))))))))).
% 3.46/4.08 Axiom satz51c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2))))))))).
% 3.46/4.08 Axiom satz51d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2))))))))).
% 3.46/4.08 Axiom satz52:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lesseq X1) X2)->((lesseq X0) X2))))))))).
% 3.46/4.08 Axiom satz53:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0))))).
% 3.46/4.08 Axiom satz54:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0))))).
% 3.46/4.08 Axiom satz55:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1))))))))).
% 3.46/4.08 Definition n_pf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType)).
% 3.46/4.08 Axiom satz56:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.08 Axiom satz57:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2)))))))).
% 3.46/4.08 Axiom satz57a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))))))))).
% 3.46/4.08 Axiom satz58:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_pf X0) X1)) ((n_pf X1) X0)))))).
% 3.46/4.08 Axiom satz59:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2))))))))).
% 3.46/4.08 Axiom satz60:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((moref ((n_pf X0) X1)) X0))))).
% 3.46/4.08 Axiom satz60a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((lessf X0) ((n_pf X0) X1)))))).
% 3.46/4.08 Axiom satz61:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2))))))))).
% 3.46/4.08 Axiom satz62b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))))))))).
% 3.46/4.08 Axiom satz62c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X0) X2)) ((n_pf X1) X2))))))))).
% 3.46/4.08 Axiom satz62d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1))))))))).
% 3.46/4.08 Axiom satz62e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))))))))).
% 3.46/4.08 Axiom satz62f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X2) X0)) ((n_pf X2) X1))))))))).
% 3.46/4.08 Axiom satz62g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.08 Axiom satz62h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1)))))))))))).
% 3.46/4.08 Axiom satz62j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.08 Axiom satz62k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1)))))))))))).
% 3.46/4.08 Axiom satz63a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1)))))))).
% 3.46/4.08 Axiom satz63b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1)))))))).
% 3.46/4.08 Axiom satz63c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1)))))))).
% 3.46/4.08 Axiom satz63d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1)))))))).
% 3.46/4.08 Axiom satz63e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1)))))))).
% 3.46/4.08 Axiom satz63f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1)))))))).
% 3.46/4.08 Axiom satz64:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.08 Axiom satz64a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.08 Axiom satz65a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.08 Axiom satz65b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.08 Axiom satz65c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.09 Axiom satz65d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.09 Axiom satz66:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.09 Axiom satz66a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 3.46/4.09 Axiom satz67b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3))))))))))).
% 3.46/4.09 Definition d_367_vo:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))):(fofType->(fofType->fofType)).
% 3.46/4.09 Definition d_367_w:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType)).
% 3.46/4.09 Axiom satz67a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0)))))))).
% 3.46/4.09 Axiom k_satz67c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0)))))).
% 3.46/4.09 Axiom satz67d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1)))))))).
% 3.46/4.09 Axiom satz67e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1)))))))))).
% 3.46/4.09 Definition n_tf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType)).
% 3.46/4.09 Axiom satz68:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.46/4.09 Axiom satz69:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_tf X0) X1)) ((n_tf X1) X0)))))).
% 3.46/4.09 Axiom satz70:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2))))))))).
% 3.46/4.09 Axiom satz71:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2))))))))).
% 3.56/4.09 Axiom satz72a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2))))))))).
% 3.56/4.09 Axiom satz72b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))))))))).
% 3.56/4.09 Axiom satz72c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X0) X2)) ((n_tf X1) X2))))))))).
% 3.56/4.09 Axiom satz72d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1))))))))).
% 3.56/4.09 Axiom satz72e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))))))))).
% 3.56/4.09 Axiom satz72f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X2) X0)) ((n_tf X2) X1))))))))).
% 3.56/4.09 Axiom satz72g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz72h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1)))))))))))).
% 3.56/4.09 Axiom satz72j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz72k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1)))))))))))).
% 3.56/4.09 Axiom satz73a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1)))))))).
% 3.56/4.09 Axiom satz73b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1)))))))).
% 3.56/4.09 Axiom satz73c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1)))))))).
% 3.56/4.09 Axiom satz73d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1)))))))).
% 3.56/4.09 Axiom satz73e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1)))))))).
% 3.56/4.09 Axiom satz73f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1)))))))).
% 3.56/4.09 Axiom satz74:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz74a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz75a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz75b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz75c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz75d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz76:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz76a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 3.56/4.09 Axiom satz77b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3))))))))))).
% 3.56/4.09 Definition d_477_v:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1)))):(fofType->(fofType->fofType)).
% 3.56/4.09 Axiom satz77a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0))))))).
% 3.56/4.09 Definition inf:=(esti frac):(fofType->(fofType->Prop)).
% 3.56/4.09 Definition rat:=((ect frac) n_eq):fofType.
% 3.56/4.09 Definition rt_is:=(e_is rat):(fofType->(fofType->Prop)).
% 3.56/4.09 Definition rt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1))):(fofType->(fofType->Prop)).
% 3.56/4.09 Definition rt_some:=(l_some rat):((fofType->Prop)->Prop).
% 3.56/4.09 Definition rt_all:=(all rat):((fofType->Prop)->Prop).
% 3.56/4.09 Definition rt_one:=(one rat):((fofType->Prop)->Prop).
% 3.56/4.09 Definition rt_in:=(esti rat):(fofType->(fofType->Prop)).
% 3.56/4.09 Definition ratof:=((ectelt frac) n_eq):(fofType->fofType).
% 3.56/4.09 Definition class:=((ecect frac) n_eq):(fofType->fofType).
% 3.56/4.09 Definition fixf:=((fixfu2 frac) n_eq):(fofType->(fofType->Prop)).
% 3.56/4.09 Definition indrat:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1)):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.56/4.09 Axiom satz78:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0))).
% 3.56/4.09 Axiom satz79:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0)))))).
% 3.56/4.09 Axiom satz80:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2))))))))).
% 3.56/4.09 Definition rt_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))))):(fofType->(fofType->Prop)).
% 3.56/4.09 Definition propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.56/4.09 Definition rt_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))))):(fofType->(fofType->Prop)).
% 3.56/4.09 Definition propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.56/4.09 Axiom satz81:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))).
% 3.56/4.09 Axiom satz81a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))).
% 3.56/4.09 Axiom satz81b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))).
% 3.56/4.09 Axiom satz82:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0)))))).
% 3.56/4.09 Axiom satz83:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0)))))).
% 3.56/4.09 Definition rt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop)).
% 3.56/4.09 Definition rt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop)).
% 3.56/4.09 Axiom satz81c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1))))))).
% 3.56/4.09 Axiom satz81d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1))))))).
% 3.56/4.09 Axiom satz81e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1)))))).
% 3.56/4.09 Axiom satz81f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1)))))).
% 3.56/4.09 Axiom satz81g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1))))))).
% 3.56/4.09 Axiom satz81h:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(d_not ((rt_moreis X0) X1))))))).
% 3.56/4.09 Axiom satz81j:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_moreis X0) X1))->((rt_less X0) X1)))))).
% 3.56/4.09 Axiom satz81k:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_lessis X0) X1))->((rt_more X0) X1)))))).
% 3.56/4.09 Axiom satz84:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->((rt_lessis X1) X0)))))).
% 3.56/4.09 Axiom satz85:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->((rt_moreis X1) X0)))))).
% 3.56/4.09 Axiom satz86:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2))))))))).
% 3.56/4.09 Axiom satz87a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2))))))))).
% 3.56/4.09 Axiom satz87b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_lessis X1) X2)->((rt_less X0) X2))))))))).
% 3.56/4.09 Axiom satz87c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_moreis X0) X1)->(((rt_more X1) X2)->((rt_more X0) X2))))))))).
% 3.56/4.09 Axiom satz87d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_moreis X1) X2)->((rt_more X0) X2))))))))).
% 3.56/4.09 Axiom satz88:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X1) X2)->((rt_lessis X0) X2))))))))).
% 3.56/4.09 Axiom satz89:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_more X1) X0))))).
% 3.56/4.09 Axiom satz90:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_less X1) X0))))).
% 3.56/4.09 Axiom satz91:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rt_less X0) X2)) ((rt_less X2) X1))))))))).
% 3.56/4.09 Definition plusfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_pf X0) X1)))))):fofType.
% 3.56/4.09 Definition rt_pl:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) plusfrt)):(fofType->(fofType->fofType)).
% 3.56/4.10 Axiom satz92:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_pl X0) X1)) ((rt_pl X1) X0)))))).
% 3.56/4.10 Axiom satz93:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_pl ((rt_pl X0) X1)) X2)) ((rt_pl X0) ((rt_pl X1) X2))))))))).
% 3.56/4.10 Axiom satz94:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_more ((rt_pl X0) X1)) X0))))).
% 3.56/4.10 Axiom satz94a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_less X0) ((rt_pl X0) X1)))))).
% 3.56/4.10 Axiom satz95:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))))))))).
% 3.56/4.10 Axiom satz96b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))))))))).
% 3.56/4.10 Axiom satz96c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))))))))).
% 3.56/4.10 Axiom satz96d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X2) X0)) ((rt_pl X2) X1))))))))).
% 3.56/4.10 Axiom satz96e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X2) X0)) ((rt_pl X2) X1))))))))).
% 3.56/4.10 Axiom satz96f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X2) X0)) ((rt_pl X2) X1))))))))).
% 3.56/4.10 Axiom satz97a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_more X0) X1)))))))).
% 3.56/4.10 Axiom satz97b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_is X0) X1)))))))).
% 3.56/4.10 Axiom satz97c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_less X0) X1)))))))).
% 3.56/4.10 Axiom satz98:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))).
% 3.56/4.10 Axiom satz98a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))).
% 3.56/4.10 Axiom satz99a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))).
% 3.56/4.10 Axiom satz99b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))).
% 3.56/4.10 Axiom satz99c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))).
% 3.56/4.10 Axiom satz99d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))).
% 3.56/4.10 Axiom satz100:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))).
% 3.56/4.10 Axiom satz100a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_pl X0) X2)) ((rt_pl X1) X3)))))))))))).
% 3.56/4.10 Axiom satz101a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_some (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))))))).
% 3.56/4.10 Axiom satz101b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_pl X1) X2)) X0)->(((rt_is ((rt_pl X1) X3)) X0)->((rt_is X2) X3))))))))))).
% 3.56/4.10 Axiom satz101:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_one (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))))))).
% 3.56/4.10 Definition rt_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))):(fofType->(fofType->fofType)).
% 3.56/4.10 Axiom satz101c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl X1) ((rt_mn X0) X1))) X0)))))).
% 3.56/4.10 Axiom satz101d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl X1) ((rt_mn X0) X1)))))))).
% 3.56/4.10 Axiom satz101e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl ((rt_mn X0) X1)) X1)) X0)))))).
% 3.56/4.10 Axiom satz101f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl ((rt_mn X0) X1)) X1))))))).
% 3.56/4.10 Axiom satz101g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_is ((rt_pl X1) X2)) X0)->((rt_is X2) ((rt_mn X0) X1)))))))))).
% 3.56/4.10 Definition timesfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_tf X0) X1)))))):fofType.
% 3.56/4.10 Definition rt_ts:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) timesfrt)):(fofType->(fofType->fofType)).
% 3.56/4.10 Axiom satz102:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X0) X1)) ((rt_ts X1) X0)))))).
% 3.56/4.10 Axiom satz103:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts ((rt_ts X0) X1)) X2)) ((rt_ts X0) ((rt_ts X1) X2))))))))).
% 3.56/4.10 Axiom satz104:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts X0) ((rt_pl X1) X2))) ((rt_pl ((rt_ts X0) X1)) ((rt_ts X0) X2))))))))).
% 3.56/4.10 Axiom satz105a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))))))))).
% 3.56/4.10 Axiom satz105b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))))))))).
% 3.56/4.10 Axiom satz105c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))))))))).
% 3.56/4.10 Axiom satz105d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X2) X0)) ((rt_ts X2) X1))))))))).
% 3.56/4.10 Axiom satz105e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X2) X0)) ((rt_ts X2) X1))))))))).
% 3.56/4.10 Axiom satz105f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X2) X0)) ((rt_ts X2) X1))))))))).
% 3.56/4.10 Axiom satz106a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_more X0) X1)))))))).
% 3.56/4.10 Axiom satz106b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_is X0) X1)))))))).
% 3.56/4.10 Axiom satz106c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_less X0) X1)))))))).
% 3.56/4.10 Axiom satz107:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))).
% 3.56/4.10 Axiom satz107a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))).
% 3.56/4.10 Axiom satz108a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))).
% 3.56/4.10 Axiom satz108b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))).
% 3.56/4.10 Axiom satz108c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))).
% 3.56/4.10 Axiom satz108d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))).
% 3.56/4.10 Axiom satz109:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))).
% 3.56/4.10 Axiom satz109a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_ts X0) X2)) ((rt_ts X1) X3)))))))))))).
% 3.56/4.10 Axiom satz110a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0))))))).
% 3.56/4.10 Axiom satz110b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->(((rt_is ((rt_ts X1) X3)) X0)->((rt_is X2) X3))))))))))).
% 3.56/4.10 Axiom satz110:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_one (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0))))))).
% 3.56/4.10 Axiom satz111a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))->((d_29_ii X0) X1)))))).
% 3.56/4.10 Axiom satz111b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))->((n_is X0) X1)))))).
% 3.56/4.10 Axiom satz111c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))->((iii X0) X1)))))).
% 3.56/4.11 Axiom satz111d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))))))).
% 3.56/4.11 Axiom satz111e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is X0) X1)->((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))))))).
% 3.56/4.11 Axiom satz111f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))))))).
% 3.56/4.11 Definition natprop:=(fun (X0:fofType) (X1:fofType)=> ((inf ((n_fr X1) n_1)) (class X0))):(fofType->(fofType->Prop)).
% 3.56/4.11 Definition natrt:=(fun (X0:fofType)=> (n_some (natprop X0))):(fofType->Prop).
% 3.56/4.11 Axiom satz111g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->(n_one (natprop X0))))).
% 3.56/4.11 Definition nofrt:=(fun (X0:fofType)=> ((ind nat) (natprop X0))):(fofType->fofType).
% 3.56/4.11 Definition rtofn:=(fun (X0:fofType)=> (ratof ((n_fr X0) n_1))):(fofType->fofType).
% 3.56/4.11 Axiom satz112a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_pf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_pl X0) X1)) n_1)))))).
% 3.56/4.11 Axiom satz112b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_tf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_ts X0) X1)) n_1)))))).
% 3.56/4.11 Axiom satz112c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_pl (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_pl X0) X1))))))))).
% 3.56/4.11 Axiom satz112d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_pl X0) X1)))))))).
% 3.56/4.11 Axiom satz112e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_ts (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_ts X0) X1))))))))).
% 3.56/4.11 Axiom satz112f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_ts X0) X1)))))))).
% 3.56/4.11 Axiom satz112g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(((rt_more X0) X1)->(natrt ((rt_mn X0) X1))))))))).
% 3.56/4.11 Axiom satz112h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_pl (rtofn X0)) (rtofn X1))) (rtofn ((n_pl X0) X1))))))).
% 3.56/4.11 Axiom satz112j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X0)) (rtofn X1))) (rtofn ((n_ts X0) X1))))))).
% 3.56/4.11 Definition natt:=((d_Sep rat) natrt):fofType.
% 3.56/4.11 Definition ntofrt:=((out rat) natrt):(fofType->fofType).
% 3.56/4.11 Definition nt_is:=(e_is natt):(fofType->(fofType->Prop)).
% 3.56/4.11 Definition nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((nt_is X0) X1))):(fofType->(fofType->Prop)).
% 3.56/4.11 Definition nt_all:=(all natt):((fofType->Prop)->Prop).
% 3.56/4.11 Definition nt_some:=(l_some natt):((fofType->Prop)->Prop).
% 3.56/4.11 Definition nt_one:=(one natt):((fofType->Prop)->Prop).
% 3.56/4.11 Definition nt_in:=(esti natt):(fofType->(fofType->Prop)).
% 3.56/4.11 Definition rtofnt:=((e_in rat) natrt):(fofType->fofType).
% 3.56/4.11 Definition ntofn:=(fun (X0:fofType)=> (ntofrt (rtofn X0))):(fofType->fofType).
% 3.56/4.11 Definition nofnt:=(fun (X0:fofType)=> (nofrt (rtofnt X0))):(fofType->fofType).
% 3.56/4.11 Definition nt_1t:=(ntofn n_1):fofType.
% 3.56/4.11 Definition suct:=((d_Sigma natt) (fun (X0:fofType)=> (ntofn (ordsucc (nofnt X0))))):fofType.
% 3.56/4.11 Axiom satz113a:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((nt_nis ((ap suct) X0)) nt_1t))).
% 3.58/4.11 Axiom satz113b:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_is ((ap suct) X0)) ((ap suct) X1))->((nt_is X0) X1)))))).
% 3.58/4.11 Definition nt_cond1:=(nt_in nt_1t):(fofType->Prop).
% 3.58/4.11 Definition nt_cond2:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((imp ((nt_in X1) X0)) ((nt_in ((ap suct) X1)) X0))))):(fofType->Prop).
% 3.58/4.11 Definition d_5113_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nt_in (ntofn X1)) X0)):(fofType->(fofType->Prop)).
% 3.58/4.11 Axiom satz113c:((all_of (fun (X0:fofType)=> ((in X0) (power natt)))) (fun (X0:fofType)=> ((nt_cond1 X0)->((nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((nt_in X1) X0))))))).
% 3.58/4.11 Axiom nt_satz1:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_nis X0) X1)->((nt_nis ((ap suct) X0)) ((ap suct) X1))))))).
% 3.58/4.11 Definition prop1t:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((nt_is ((ap X0) ((ap suct) X1))) ((ap suct) ((ap X0) X1)))))):(fofType->Prop).
% 3.58/4.11 Definition prop2t:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (prop1t X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition d_54_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc (nofnt X0)))) (d_24_prop1 X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition d_54_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (nofnt ((ap X0) (ntofn X1)))))):(fofType->fofType).
% 3.58/4.11 Definition d_54_gt:=(fun (X0:fofType)=> ((d_Sigma natt) (fun (X1:fofType)=> (ntofn ((ap X0) (nofnt X1)))))):(fofType->fofType).
% 3.58/4.11 Axiom nt_satz4:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((one ((d_Pi natt) (fun (X1:fofType)=> natt))) (fun (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (nt_all (fun (X2:fofType)=> ((nt_is ((ap X1) ((ap suct) X2))) ((ap suct) ((ap X1) X2)))))))))).
% 3.58/4.11 Definition nt_pl:=(fun (X0:fofType) (X1:fofType)=> (ntofrt ((rt_pl (rtofnt X0)) (rtofnt X1)))):(fofType->(fofType->fofType)).
% 3.58/4.11 Axiom nt_satz5:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((nt_is ((nt_pl ((nt_pl X0) X1)) X2)) ((nt_pl X0) ((nt_pl X1) X2))))))))).
% 3.58/4.11 Definition nt_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.11 Definition iit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition iiit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X1) X0))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition d_59_i:=(fun (X0:fofType) (X1:fofType)=> ((n_is (nofnt X0)) (nofnt X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition d_59_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X0)) (nofnt X1)))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition d_59_iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X1)) (nofnt X0)))):(fofType->(fofType->Prop)).
% 3.58/4.11 Axiom nt_satz9:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((orec3 ((nt_is X0) X1)) (nt_some (fun (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))))) (nt_some (fun (X2:fofType)=> ((nt_is X1) ((nt_pl X0) X2))))))))).
% 3.58/4.11 Definition nt_more:=(fun (X0:fofType) (X1:fofType)=> ((rt_more (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition nt_less:=(fun (X0:fofType) (X1:fofType)=> ((rt_less (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition nt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((rt_moreis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition nt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((rt_lessis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Axiom nt_satz15:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> (((nt_less X0) X1)->(((nt_less X1) X2)->((nt_less X0) X2))))))))).
% 3.58/4.11 Axiom nt_satz21:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) natt))) (fun (X3:fofType)=> (((nt_more X0) X1)->(((nt_more X2) X3)->((nt_more ((nt_pl X0) X2)) ((nt_pl X1) X3)))))))))))).
% 3.58/4.11 Definition nt_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (nt_all (fun (X2:fofType)=> ((imp (X0 X2)) ((nt_lessis X1) X2))))):((fofType->Prop)->(fofType->Prop)).
% 3.58/4.11 Definition nt_min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((nt_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop)).
% 3.58/4.11 Definition d_527_q:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (X0 (ntofn X1))):((fofType->Prop)->(fofType->Prop)).
% 3.58/4.11 Axiom nt_satz27:(forall (X0:(fofType->Prop)), ((nt_some X0)->(nt_some (nt_min X0)))).
% 3.58/4.11 Definition d_1rt:=(rtofn n_1):fofType.
% 3.58/4.11 Axiom satz114:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((rt_is ((rt_ts (rtofn (den X0))) (ratof X0))) (rtofn (num X0))))).
% 3.58/4.11 Axiom satz114a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X1)) (ratof ((n_fr X0) X1)))) (rtofn X0)))))).
% 3.58/4.11 Definition rt_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))):(fofType->(fofType->fofType)).
% 3.58/4.11 Axiom satz110c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X1) ((rt_ov X0) X1))) X0))))).
% 3.58/4.11 Axiom satz110d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts X1) ((rt_ov X0) X1))))))).
% 3.58/4.11 Axiom satz110e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov X0) X1)) X1)) X0))))).
% 3.58/4.11 Axiom satz110f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts ((rt_ov X0) X1)) X1)))))).
% 3.58/4.11 Axiom satz110g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->((rt_is X2) ((rt_ov X0) X1))))))))).
% 3.58/4.11 Axiom satz114b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is (ratof ((n_fr X0) X1))) ((rt_ov (rtofn X0)) (rtofn X1))))))).
% 3.58/4.11 Axiom satz114c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ov (rtofn X0)) (rtofn X1))) (ratof ((n_fr X0) X1))))))).
% 3.58/4.11 Axiom satz115:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (n_some (fun (X2:fofType)=> ((rt_more ((rt_ts (rtofn X2)) X0)) X1))))))).
% 3.58/4.11 Axiom satz115a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and (natrt X2)) ((rt_more ((rt_ts X2) X0)) X1)))))))).
% 3.58/4.11 Definition cutprop1a:=(nonempty rat):(fofType->Prop).
% 3.58/4.11 Definition cutprop1b:=(fun (X0:fofType)=> (d_not (rt_all (fun (X1:fofType)=> ((rt_in X1) X0))))):(fofType->Prop).
% 3.58/4.11 Definition cutprop1:=(fun (X0:fofType)=> ((d_and (cutprop1a X0)) (cutprop1b X0))):(fofType->Prop).
% 3.58/4.11 Definition cutprop2a:=(fun (X0:fofType) (X1:fofType)=> (rt_all (fun (X2:fofType)=> ((imp (d_not ((rt_in X2) X0))) ((rt_less X1) X2))))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition cutprop2:=(fun (X0:fofType)=> (rt_all (fun (X1:fofType)=> ((imp ((rt_in X1) X0)) ((cutprop2a X0) X1))))):(fofType->Prop).
% 3.58/4.11 Definition ubprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_moreis X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.11 Definition rt_ub:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((ubprop X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition max:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_ub X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition cutprop3:=(fun (X0:fofType)=> (d_not (rt_some (max X0)))):(fofType->Prop).
% 3.58/4.11 Definition cutprop:=(fun (X0:fofType)=> (((and3 (cutprop1 X0)) (cutprop2 X0)) (cutprop3 X0))):(fofType->Prop).
% 3.58/4.11 Definition iii1_lbprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_lessis X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.11 Definition rt_lb:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((iii1_lbprop X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition rt_min:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_lb X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition cut:=((d_Sep (power rat)) cutprop):fofType.
% 3.58/4.11 Definition lcl:=((e_in (power rat)) cutprop):(fofType->fofType).
% 3.58/4.11 Definition lrt:=(fun (X0:fofType) (X1:fofType)=> ((rt_in X1) (lcl X0))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition urt:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_in X1) (lcl X0)))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition rp_is:=(e_is cut):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition rp_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_is X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition cutof:=((out (power rat)) cutprop):(fofType->fofType).
% 3.58/4.11 Definition rp_all:=(all cut):((fofType->Prop)->Prop).
% 3.58/4.11 Definition rp_some:=(l_some cut):((fofType->Prop)->Prop).
% 3.58/4.11 Definition rp_one:=(one cut):((fofType->Prop)->Prop).
% 3.58/4.11 Axiom satz116:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) X0))).
% 3.58/4.11 Axiom satz117:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_is X0) X1)->((rp_is X1) X0)))))).
% 3.58/4.11 Axiom satz118:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->(((rp_is X1) X2)->((rp_is X0) X2))))))))).
% 3.58/4.11 Axiom satz119:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X2) X1)->((urt X0) X2))))))))).
% 3.58/4.11 Axiom satz119a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X1) X2)->((urt X0) X2))))))))).
% 3.58/4.11 Axiom satz120:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X2) X1)->((lrt X0) X2))))))))).
% 3.58/4.11 Axiom satz120a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X1) X2)->((lrt X0) X2))))))))).
% 3.58/4.11 Definition rp_more:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((lrt X0) X2)) ((urt X1) X2))))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition rp_less:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((urt X0) X2)) ((lrt X1) X2))))):(fofType->(fofType->Prop)).
% 3.58/4.11 Axiom satz121:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_less X1) X0)))))).
% 3.58/4.11 Axiom satz122:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->((rp_more X1) X0)))))).
% 3.58/4.11 Axiom satz123:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((orec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1)))))).
% 3.58/4.11 Axiom k_satz123a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((or3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1)))))).
% 3.58/4.11 Axiom k_satz123b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((ec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1)))))).
% 3.58/4.11 Definition rp_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_more X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Definition rp_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_less X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.11 Axiom satz124:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->((rp_lessis X1) X0)))))).
% 3.58/4.11 Axiom satz125:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->((rp_moreis X1) X0)))))).
% 3.58/4.11 Axiom satz123c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->(d_not ((rp_less X0) X1))))))).
% 3.58/4.11 Axiom satz123d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->(d_not ((rp_more X0) X1))))))).
% 3.58/4.11 Axiom satz123e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_more X0) X1))->((rp_lessis X0) X1)))))).
% 3.58/4.11 Axiom satz123f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_less X0) X1))->((rp_moreis X0) X1)))))).
% 3.58/4.11 Axiom satz123g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(d_not ((rp_lessis X0) X1))))))).
% 3.58/4.11 Axiom satz123h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(d_not ((rp_moreis X0) X1))))))).
% 3.58/4.11 Axiom satz123j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_moreis X0) X1))->((rp_less X0) X1)))))).
% 3.58/4.11 Axiom satz123k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_lessis X0) X1))->((rp_more X0) X1)))))).
% 3.58/4.11 Axiom satz126:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2))))))))).
% 3.58/4.11 Axiom satz127a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2))))))))).
% 3.58/4.11 Axiom satz127b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_lessis X1) X2)->((rp_less X0) X2))))))))).
% 3.58/4.11 Axiom satz127c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_moreis X0) X1)->(((rp_more X1) X2)->((rp_more X0) X2))))))))).
% 3.58/4.11 Axiom satz127d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_moreis X1) X2)->((rp_more X0) X2))))))))).
% 3.58/4.11 Axiom satz128:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X1) X2)->((rp_lessis X0) X2))))))))).
% 3.58/4.12 Definition sumprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_pl X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))).
% 3.58/4.12 Definition sumprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((sumprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.12 Definition sum:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((sumprop X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.12 Axiom satz129a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_pl X2) X3)) ((sum X0) X1))))))))))))).
% 3.58/4.12 Definition d_3129_z1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X0) ((rt_pl X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.12 Axiom satz129:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((sum X0) X1)))))).
% 3.58/4.12 Definition rp_pl:=(fun (X0:fofType) (X1:fofType)=> (cutof ((sum X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.12 Axiom satz130:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_pl X0) X1)) ((rp_pl X1) X0)))))).
% 3.58/4.12 Axiom satz131:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_pl ((rp_pl X0) X1)) X2)) ((rp_pl X0) ((rp_pl X1) X2))))))))).
% 3.58/4.12 Definition d_3132_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((lrt X0) X1)) ((urt X0) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.12 Definition d_3132_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((rt_is ((rt_mn X3) X2)) X1)):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.58/4.12 Definition d_3132_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((d_3132_prop1 X0) X2) X3)) ((((d_3132_prop1 X0) X2) X3)->((((d_3132_prop2 X0) X1) X2) X3)))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.58/4.12 Definition d_3132_prop4:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (((d_3132_prop3 X0) X1) X2))))):(fofType->(fofType->Prop)).
% 3.58/4.12 Definition d_3132_u0:=(fun (X0:fofType) (X1:fofType)=> ((rt_pl X1) X0)):(fofType->(fofType->fofType)).
% 3.58/4.12 Definition um10:=(fun (X0:fofType)=> ((rt_mn (rtofn X0)) d_1rt)):(fofType->fofType).
% 3.58/4.12 Definition um1:=(fun (X0:fofType)=> (nofrt (um10 X0))):(fofType->fofType).
% 3.58/4.12 Definition d_3132_v0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (um10 X2)) X0))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.12 Definition d_3132_w0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (rtofn X2)) X0))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.12 Axiom satz132:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (fun (X3:fofType)=> ((d_and ((d_and ((lrt X0) X2)) ((urt X0) X3))) (((d_and ((lrt X0) X2)) ((urt X0) X3))->((rt_is ((rt_mn X3) X2)) X1))))))))))).
% 3.58/4.12 Axiom satz132app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (forall (X1:Prop), ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((lrt X0) X3)->((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((urt X0) X4)->(((rt_is ((rt_mn X4) X3)) X2)->X1)))))))->X1)))))).
% 3.58/4.12 Axiom satz133:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_more ((rp_pl X0) X1)) X0))))).
% 3.58/4.12 Axiom satz133a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_less X0) ((rp_pl X0) X1)))))).
% 3.58/4.12 Axiom satz134:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))))))))).
% 3.58/4.12 Axiom satz135b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))))))))).
% 3.58/4.12 Axiom satz135c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))))))))).
% 3.58/4.12 Axiom satz135d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))))))))).
% 3.58/4.12 Axiom satz135e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))))))))).
% 3.58/4.12 Axiom satz135f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))))))))).
% 3.58/4.12 Axiom satz135g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz135h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X2) X0)) ((rp_pl X3) X1)))))))))))).
% 3.58/4.12 Axiom satz135j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz135k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X2) X0)) ((rp_pl X3) X1)))))))))))).
% 3.58/4.12 Axiom satz136a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_more X0) X1)))))))).
% 3.58/4.12 Axiom satz136b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_is X0) X1)))))))).
% 3.58/4.12 Axiom satz136c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_less X0) X1)))))))).
% 3.58/4.12 Axiom satz136d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_more X0) X1)))))))).
% 3.58/4.12 Axiom satz136e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_is X0) X1)))))))).
% 3.58/4.12 Axiom satz136f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_less X0) X1)))))))).
% 3.58/4.12 Axiom satz137:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz137a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz138a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz138b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz138c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz138d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz139:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz139a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_pl X0) X2)) ((rp_pl X1) X3)))))))))))).
% 3.58/4.12 Axiom satz140b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_pl X1) X2)) X0)->(((rp_is ((rp_pl X1) X3)) X0)->((rp_is X2) X3))))))))))).
% 3.58/4.12 Definition diffprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((rt_more X1) X2)) (((rt_more X1) X2)->((rt_is X0) ((rt_mn X1) X2))))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.12 Definition diffprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((urt X1) X4)) (((diffprop1 X2) X3) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))).
% 3.58/4.12 Definition rp_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((diffprop2 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.12 Definition diff:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((rp_diffprop X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.12 Axiom satz140h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(cutprop ((diff X0) X1))))))).
% 3.58/4.12 Definition chi:=(fun (X0:fofType) (X1:fofType)=> (cutof ((diff X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.12 Axiom satz140a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_some (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))))))).
% 3.58/4.12 Axiom satz140:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_one (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))))))).
% 3.58/4.12 Definition rp_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))):(fofType->(fofType->fofType)).
% 3.58/4.12 Axiom satz140c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl X1) ((rp_mn X0) X1))) X0)))))).
% 3.58/4.12 Axiom satz140d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl X1) ((rp_mn X0) X1)))))))).
% 3.58/4.12 Axiom satz140e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl ((rp_mn X0) X1)) X1)) X0)))))).
% 3.58/4.12 Axiom satz140f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl ((rp_mn X0) X1)) X1))))))).
% 3.58/4.12 Axiom satz140g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_is ((rp_pl X1) X2)) X0)->((rp_is X2) ((rp_mn X0) X1)))))))))).
% 3.58/4.12 Definition prodprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_ts X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))).
% 3.58/4.12 Definition prodprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((prodprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.12 Definition prod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((prodprop X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.12 Axiom satz141a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_ts X2) X3)) ((prod X0) X1))))))))))))).
% 3.58/4.12 Definition d_4141_v0:=(fun (X0:fofType) (X1:fofType)=> ((rt_ts ((rt_ov d_1rt) X1)) X0)):(fofType->(fofType->fofType)).
% 3.58/4.12 Axiom satz141b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov d_1rt) X1)) X0)) ((rt_ov X0) X1)))))).
% 3.58/4.13 Axiom satz141c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ov X0) X1)) ((rt_ts ((rt_ov d_1rt) X1)) X0)))))).
% 3.58/4.13 Axiom satz141:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((prod X0) X1)))))).
% 3.58/4.13 Definition rp_ts:=(fun (X0:fofType) (X1:fofType)=> (cutof ((prod X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.13 Axiom satz142:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) ((rp_ts X1) X0)))))).
% 3.58/4.13 Axiom satz143:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts ((rp_ts X0) X1)) X2)) ((rp_ts X0) ((rp_ts X1) X2))))))))).
% 3.58/4.13 Definition d_4144_x2:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_moreis X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType)).
% 3.58/4.13 Axiom satz144:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts X0) ((rp_pl X1) X2))) ((rp_pl ((rp_ts X0) X1)) ((rp_ts X0) X2))))))))).
% 3.58/4.13 Axiom satz145a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))))))))).
% 3.58/4.13 Axiom satz145b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))))))))).
% 3.58/4.13 Axiom satz145c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))))))))).
% 3.58/4.13 Axiom satz145d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))))))))).
% 3.58/4.13 Axiom satz145e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))))))))).
% 3.58/4.13 Axiom satz145f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))))))))).
% 3.58/4.13 Axiom satz145g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz145h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X2) X0)) ((rp_ts X3) X1)))))))))))).
% 3.58/4.13 Axiom satz145j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz145k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X2) X0)) ((rp_ts X3) X1)))))))))))).
% 3.58/4.13 Axiom satz146a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_more X0) X1)))))))).
% 3.58/4.13 Axiom satz146b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_is X0) X1)))))))).
% 3.58/4.13 Axiom satz146c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_less X0) X1)))))))).
% 3.58/4.13 Axiom satz146d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_more X0) X1)))))))).
% 3.58/4.13 Axiom satz146e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_is X0) X1)))))))).
% 3.58/4.13 Axiom satz146f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_less X0) X1)))))))).
% 3.58/4.13 Axiom satz147:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz147a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz148a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz148b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz148c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz148d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz149:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Axiom satz149a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_ts X0) X2)) ((rp_ts X1) X3)))))))))))).
% 3.58/4.13 Definition ratset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rt_less X1) X0)))):(fofType->fofType).
% 3.58/4.13 Axiom satz150:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (cutprop (ratset X0)))).
% 3.58/4.13 Definition rpofrt:=(fun (X0:fofType)=> (cutof (ratset X0))):(fofType->fofType).
% 3.58/4.13 Definition d_1rp:=(rpofrt d_1rt):fofType.
% 3.58/4.13 Axiom satz151:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) d_1rp)) X0))).
% 3.58/4.13 Axiom satz151a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts X0) d_1rp)))).
% 3.58/4.13 Axiom satz151b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts d_1rp) X0)) X0))).
% 3.58/4.13 Axiom satz151c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts d_1rp) X0)))).
% 3.58/4.13 Definition invprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((urt X0) X2)) ((rt_less X2) X1))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.13 Definition invprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 ((urt X0) X2)) (rt_some ((invprop1 X0) X2))) ((rt_is X1) ((rt_ov d_1rt) X2)))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.13 Definition invprop:=(fun (X0:fofType) (X1:fofType)=> (rt_some ((invprop2 X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.13 Definition inv:=(fun (X0:fofType)=> ((d_Sep rat) (invprop X0))):(fofType->fofType).
% 3.58/4.13 Definition d_2x0:=(fun (X0:fofType)=> ((rt_pl X0) X0)):(fofType->fofType).
% 3.58/4.13 Definition d_4152_chi:=(fun (X0:fofType)=> (cutof (inv X0))):(fofType->fofType).
% 3.58/4.13 Axiom satz152:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_some (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) d_1rp))))).
% 3.58/4.13 Axiom satz153b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->(((rp_is ((rp_ts X1) X3)) X0)->((rp_is X2) X3))))))))))).
% 3.58/4.13 Definition d_4153_chi:=(fun (X0:fofType) (X1:fofType)=> ((rp_ts X1) X0)):(fofType->(fofType->fofType)).
% 3.58/4.13 Axiom satz153a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0))))))).
% 3.58/4.13 Axiom satz153:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_one (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0))))))).
% 3.58/4.13 Definition rp_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))):(fofType->(fofType->fofType)).
% 3.58/4.13 Axiom satz153c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) ((rp_ov X0) X1))) X0))))).
% 3.58/4.13 Axiom satz153d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts X1) ((rp_ov X0) X1))))))).
% 3.58/4.13 Axiom satz153e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts ((rp_ov X0) X1)) X1)) X0))))).
% 3.58/4.13 Axiom satz153f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts ((rp_ov X0) X1)) X1)))))).
% 3.58/4.13 Axiom satz153g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->((rp_is X2) ((rp_ov X0) X1))))))))).
% 3.58/4.13 Definition ratrp:=(((image rat) cut) ((d_Sigma rat) rpofrt)):(fofType->Prop).
% 3.58/4.13 Definition rpofnt:=(fun (X0:fofType)=> (rpofrt (rtofn X0))):(fofType->fofType).
% 3.58/4.13 Definition natrp:=(((image nat) cut) ((d_Sigma nat) rpofnt)):(fofType->Prop).
% 3.58/4.13 Axiom satz154a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_more (rpofrt X0)) (rpofrt X1))))))).
% 3.58/4.13 Axiom satz154b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rp_is (rpofrt X0)) (rpofrt X1))))))).
% 3.58/4.13 Axiom satz154c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rp_less (rpofrt X0)) (rpofrt X1))))))).
% 3.58/4.13 Axiom satz154d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_more (rpofrt X0)) (rpofrt X1))->((rt_more X0) X1)))))).
% 3.58/4.13 Axiom satz154e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_is (rpofrt X0)) (rpofrt X1))->((rt_is X0) X1)))))).
% 3.58/4.13 Axiom satz154f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X0)) (rpofrt X1))->((rt_less X0) X1)))))).
% 3.58/4.13 Definition rtofrp:=(((soft rat) cut) ((d_Sigma rat) rpofrt)):(fofType->fofType).
% 3.58/4.13 Definition ntofrp:=(((soft nat) cut) ((d_Sigma nat) rpofnt)):(fofType->fofType).
% 3.58/4.13 Definition u01:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X2) ((rt_pl X0) X1))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.13 Axiom satz155a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_pl X0) X1))) ((rp_pl (rpofrt X0)) (rpofrt X1))))))).
% 3.58/4.13 Axiom satz155b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_is (rpofrt ((rt_mn X0) X1))) ((rp_mn (rpofrt X0)) (rpofrt X1)))))))).
% 3.58/4.13 Axiom satz155c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ts X0) X1))) ((rp_ts (rpofrt X0)) (rpofrt X1))))))).
% 3.58/4.13 Axiom satz155d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ov X0) X1))) ((rp_ov (rpofrt X0)) (rpofrt X1))))))).
% 3.58/4.13 Axiom satz155e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_pl X0) X1))) ((rp_pl (rpofnt X0)) (rpofnt X1))))))).
% 3.58/4.13 Axiom satz155f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_ts X0) X1))) ((rp_ts (rpofnt X0)) (rpofnt X1))))))).
% 3.58/4.13 Definition nt_natt:=((d_Sep cut) natrp):fofType.
% 3.58/4.13 Definition nttofrp:=((out cut) natrp):(fofType->fofType).
% 3.58/4.13 Definition rp_nt_is:=(e_is nt_natt):(fofType->(fofType->Prop)).
% 3.58/4.13 Definition rp_nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_nt_is X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.13 Definition rp_nt_all:=(all nt_natt):((fofType->Prop)->Prop).
% 3.58/4.13 Definition rp_nt_some:=(l_some nt_natt):((fofType->Prop)->Prop).
% 3.58/4.13 Definition rp_nt_one:=(one nt_natt):((fofType->Prop)->Prop).
% 3.58/4.13 Definition rp_nt_in:=(esti nt_natt):(fofType->(fofType->Prop)).
% 3.58/4.13 Definition rpofntt:=((e_in cut) natrp):(fofType->fofType).
% 3.58/4.13 Definition nttofnt:=(fun (X0:fofType)=> (nttofrp (rpofnt X0))):(fofType->fofType).
% 3.58/4.13 Definition ntofntt:=(fun (X0:fofType)=> (ntofrp (rpofntt X0))):(fofType->fofType).
% 3.58/4.13 Definition rp_nt_1t:=(nttofnt n_1):fofType.
% 3.58/4.13 Definition nt_suct:=((d_Sigma nt_natt) (fun (X0:fofType)=> (nttofnt (ordsucc (ntofntt X0))))):fofType.
% 3.58/4.13 Axiom satz156a:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((rp_nt_nis ((ap nt_suct) X0)) rp_nt_1t))).
% 3.58/4.13 Axiom satz156b:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> (((rp_nt_is ((ap nt_suct) X0)) ((ap nt_suct) X1))->((rp_nt_is X0) X1)))))).
% 3.58/4.13 Definition rp_nt_cond1:=(rp_nt_in rp_nt_1t):(fofType->Prop).
% 3.58/4.13 Definition rp_nt_cond2:=(fun (X0:fofType)=> (rp_nt_all (fun (X1:fofType)=> ((imp ((rp_nt_in X1) X0)) ((rp_nt_in ((ap nt_suct) X1)) X0))))):(fofType->Prop).
% 3.58/4.13 Definition d_5156_prop1:=(fun (X0:fofType) (X1:fofType)=> ((rp_nt_in (nttofnt X1)) X0)):(fofType->(fofType->Prop)).
% 3.58/4.13 Axiom satz156c:((all_of (fun (X0:fofType)=> ((in X0) (power nt_natt)))) (fun (X0:fofType)=> ((rp_nt_cond1 X0)->((rp_nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> ((rp_nt_in X1) X0))))))).
% 3.58/4.13 Definition ratt:=((d_Sep cut) ratrp):fofType.
% 3.58/4.13 Definition rttofrp:=((out cut) ratrp):(fofType->fofType).
% 3.58/4.13 Definition rtt_is:=(e_is ratt):(fofType->(fofType->Prop)).
% 3.58/4.13 Definition rtt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rtt_is X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.13 Definition rtt_all:=(all ratt):((fofType->Prop)->Prop).
% 3.58/4.13 Definition rtt_some:=(l_some ratt):((fofType->Prop)->Prop).
% 3.58/4.13 Definition rtt_one:=(one ratt):((fofType->Prop)->Prop).
% 3.58/4.13 Definition rpofrtt:=((e_in cut) ratrp):(fofType->fofType).
% 3.58/4.13 Definition rttofrt:=(fun (X0:fofType)=> (rttofrp (rpofrt X0))):(fofType->fofType).
% 3.58/4.13 Definition rtofrtt:=(fun (X0:fofType)=> (rtofrp (rpofrtt X0))):(fofType->fofType).
% 3.58/4.13 Definition d_5157_s1:=(fun (X0:fofType)=> ((d_Sep rat) (urt X0))):(fofType->fofType).
% 3.58/4.13 Axiom satz157a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->((rt_min ((d_Sep rat) (urt X0))) (rtofrp X0))))).
% 3.58/4.13 Axiom satz157b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->(rt_some (rt_min ((d_Sep rat) (urt X0))))))).
% 3.58/4.13 Axiom satz157c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_min ((d_Sep rat) (urt X0))) X1)->((rp_is X0) (rpofrt X1))))))).
% 3.58/4.13 Axiom satz157d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rt_some (rt_min ((d_Sep rat) (urt X0))))->(ratrp X0)))).
% 3.58/4.13 Axiom satz158a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((rp_less (rpofrt X1)) X0)))))).
% 3.58/4.13 Axiom satz158b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((rp_moreis (rpofrt X1)) X0)))))).
% 3.58/4.13 Axiom satz158c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X1)) X0)->((lrt X0) X1)))))).
% 3.58/4.13 Axiom satz158d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_moreis (rpofrt X1)) X0)->((urt X0) X1)))))).
% 3.58/4.13 Axiom satz159:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rp_less X0) (rpofrt X2))) ((rp_less (rpofrt X2)) X1))))))))).
% 3.58/4.13 Axiom satz159a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rp_some (fun (X2:fofType)=> (((and3 (ratrp X2)) ((rp_less X0) X2)) ((rp_less X2) X1))))))))).
% 3.58/4.14 Axiom satz159app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(forall (X2:Prop), (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rp_less X0) (rpofrt X3))->(((rp_less (rpofrt X3)) X1)->X2))))->X2))))))).
% 3.58/4.14 Definition d_5160_nm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_mn (rpofrt X2)) ((rp_ts X0) X1))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.14 Definition d_5160_dn:=(fun (X0:fofType) (X1:fofType)=> ((rp_pl ((rp_pl X0) X1)) d_1rp)):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition d_5160_fr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_ov (((d_5160_nm X0) X1) X2)) ((d_5160_dn X0) X1))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.14 Definition zeta:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((((ite ((rp_less (((d_5160_fr X0) X1) X2)) d_1rp)) cut) (((d_5160_fr X0) X1) X2)) d_1rp)):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.14 Definition d_5160_xr:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((rt_ov X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition d_5160_y0:=(fun (X0:fofType)=> X0):(fofType->fofType).
% 3.58/4.14 Definition d_5160_yr:=(fun (X0:fofType)=> (rpofrt (d_5160_y0 X0))):(fofType->fofType).
% 3.58/4.14 Definition d_5160_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))).
% 3.58/4.14 Definition d_5160_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((d_5160_prop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.14 Axiom satz160:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(rt_some (fun (X3:fofType)=> (rt_some (fun (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2))))))))))))).
% 3.58/4.14 Axiom satz160app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(forall (X3:Prop), (((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((rp_more (rpofrt X4)) X0)->((all_of (fun (X5:fofType)=> ((in X5) rat))) (fun (X5:fofType)=> (((rp_more (rpofrt X5)) X1)->(((rt_is ((rt_ts X4) X5)) X2)->X3)))))))->X3))))))))).
% 3.58/4.14 Definition d_5161_min:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_less X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition d_5161_max:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_more X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition sq1:=(fun (X0:fofType)=> ((rp_ts X0) X0)):(fofType->fofType).
% 3.58/4.14 Definition sqrtset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rp_less ((rp_ts (rpofrt X1)) (rpofrt X1))) X0)))):(fofType->fofType).
% 3.58/4.14 Definition d_5161_nm:=(fun (X0:fofType) (X1:fofType)=> ((rp_mn X0) ((rp_ts (rpofrt X1)) (rpofrt X1)))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition d_5161_dn:=(fun (X0:fofType)=> ((rp_pl (rpofrt X0)) ((rp_pl (rpofrt X0)) d_1rp))):(fofType->fofType).
% 3.58/4.14 Definition d_5161_fr:=(fun (X0:fofType) (X1:fofType)=> ((rp_ov ((d_5161_nm X0) X1)) (d_5161_dn X1))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition rtc:=(fun (X0:fofType)=> (cutof (sqrtset X0))):(fofType->fofType).
% 3.58/4.14 Definition d_5161_xm:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_more X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition xrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_xm X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition d_5161_ym:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_less X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition yrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_ym X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.14 Axiom satz161:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_one (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0))))).
% 3.58/4.14 Definition irratrp:=(fun (X0:fofType)=> (d_not (ratrp X0))):(fofType->Prop).
% 3.58/4.14 Definition d_5162_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_eq ((n_tf ((n_fr X1) X0)) ((n_fr X1) X0))) ((n_fr (ordsucc n_1)) n_1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition d_5162_prop2:=(fun (X0:fofType)=> (n_some (d_5162_prop1 X0))):(fofType->Prop).
% 3.58/4.14 Definition d_5162_prop3:=(n_some d_5162_prop2):Prop.
% 3.58/4.14 Definition d_5162_y:=((ind nat) (min d_5162_prop2)):fofType.
% 3.58/4.14 Definition ksi:=((ind cut) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) X0)) (rpofnt (ordsucc n_1))))):fofType.
% 3.58/4.14 Definition d_5162_x0:=(rtofrp ksi):fofType.
% 3.58/4.14 Axiom satz162:(rp_some irratrp).
% 3.58/4.14 Definition sqrt:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))):(fofType->fofType).
% 3.58/4.14 Definition iiia_x0:=(fun (X0:fofType)=> (rtofn (ntofrp X0))):(fofType->fofType).
% 3.58/4.14 Definition xpy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_pl (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition xty:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_ts (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition xmy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_mn (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition dif:=(pair1type cut):fofType.
% 3.58/4.14 Definition rp_df:=(pair1 cut):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition stm:=(first1 cut):(fofType->fofType).
% 3.58/4.14 Definition std:=(second1 cut):(fofType->fofType).
% 3.58/4.14 Definition rp_eq:=(fun (X0:fofType) (X1:fofType)=> ((rp_is ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition posd:=(fun (X0:fofType)=> ((rp_more (stm X0)) (std X0))):(fofType->Prop).
% 3.58/4.14 Definition zero:=(fun (X0:fofType)=> ((rp_is (stm X0)) (std X0))):(fofType->Prop).
% 3.58/4.14 Definition negd:=(fun (X0:fofType)=> ((rp_less (stm X0)) (std X0))):(fofType->Prop).
% 3.58/4.14 Definition pdofrp:=(fun (X0:fofType)=> ((rp_df ((rp_pl X0) d_1rp)) d_1rp)):(fofType->fofType).
% 3.58/4.14 Definition ndofrp:=(fun (X0:fofType)=> ((rp_df d_1rp) ((rp_pl X0) d_1rp))):(fofType->fofType).
% 3.58/4.14 Definition rpofpd:=(fun (X0:fofType)=> ((rp_mn (stm X0)) (std X0))):(fofType->fofType).
% 3.58/4.14 Definition rpofnd:=(fun (X0:fofType)=> ((rp_mn (std X0)) (stm X0))):(fofType->fofType).
% 3.58/4.14 Definition absd:=(fun (X0:fofType)=> ((((ite (negd X0)) dif) ((rp_df (std X0)) (stm X0))) X0)):(fofType->fofType).
% 3.58/4.14 Definition mored:=(fun (X0:fofType) (X1:fofType)=> ((rp_more ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition lessd:=(fun (X0:fofType) (X1:fofType)=> ((rp_less ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition rp_moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((mored X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition rp_lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessd X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition ratd:=(fun (X0:fofType)=> ((d_not (zero X0))->(ratrp (rpofpd (absd X0))))):(fofType->Prop).
% 3.58/4.14 Definition irratd:=(fun (X0:fofType)=> (d_not (ratd X0))):(fofType->Prop).
% 3.58/4.14 Definition natd:=(fun (X0:fofType)=> ((d_and (posd X0)) ((posd X0)->(natrp (rpofpd X0))))):(fofType->Prop).
% 3.58/4.14 Definition pdofnt:=(fun (X0:fofType)=> (pdofrp (rpofnt X0))):(fofType->fofType).
% 3.58/4.14 Definition intd:=(fun (X0:fofType)=> ((l_or (zero X0)) (natd (absd X0)))):(fofType->Prop).
% 3.58/4.14 Definition rp_pd:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl (stm X0)) (stm X1))) ((rp_pl (std X0)) (std X1)))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition m0d:=(fun (X0:fofType)=> ((rp_df (std X0)) (stm X0))):(fofType->fofType).
% 3.58/4.14 Definition rp_md:=(fun (X0:fofType) (X1:fofType)=> ((rp_pd X0) (m0d X1))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition rp_td:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl ((rp_ts (stm X0)) (stm X1))) ((rp_ts (std X0)) (std X1)))) ((rp_pl ((rp_ts (stm X0)) (std X1))) ((rp_ts (std X0)) (stm X1))))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition d_1df:=(pdofrp d_1rp):fofType.
% 3.58/4.14 Definition p1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (posd X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition p1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (negd X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition n1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (posd X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition n1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (negd X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition arpi:=(fun (X0:fofType)=> ((rp_ov d_1rp) (rpofpd X0))):(fofType->fofType).
% 3.58/4.14 Definition iv4d_ai:=(fun (X0:fofType)=> (pdofrp (arpi X0))):(fofType->fofType).
% 3.58/4.14 Definition iv5d_2:=((rp_pl d_1rp) d_1rp):fofType.
% 3.58/4.14 Definition rp1:=(fun (X0:fofType)=> ((rp_pl X0) d_1rp)):(fofType->fofType).
% 3.58/4.14 Definition rp_in:=(esti cut):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition d_5p205_prop1:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_less X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition d_5p205_prop2:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_more X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition d_5p205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5p205_prop1 X0) X2)) ((d_5p205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.14 Definition schnittprop:=(fun (X0:fofType) (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((d_and ((rp_in X2) X0)) ((lrt X2) X1))))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition schnittset:=(fun (X0:fofType)=> ((d_Sep rat) (schnittprop X0))):(fofType->fofType).
% 3.58/4.14 Definition snt:=(fun (X0:fofType) (X1:fofType)=> (cutof (schnittset X0))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) ((d_5p205_prop3 X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition srp:=(fun (X0:fofType)=> (sqrt (rpofpd X0))):(fofType->fofType).
% 3.58/4.14 Definition d161_s:=(fun (X0:fofType)=> (pdofrp (srp X0))):(fofType->fofType).
% 3.58/4.14 Definition apb1:=(fun (X0:fofType) (X1:fofType)=> (rpofpd ((rp_pd X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition intd_b2:=(fun (X0:fofType)=> (rpofpd (m0d X0))):(fofType->fofType).
% 3.58/4.14 Definition intd_a3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X0))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition intd_b3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X1))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition atb3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd ((rp_td X0) X1)))):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition r_inn:=(esti dif):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition real:=((ect dif) rp_eq):fofType.
% 3.58/4.14 Definition r_is:=(e_is real):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition r_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((r_is X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition r_some:=(l_some real):((fofType->Prop)->Prop).
% 3.58/4.14 Definition r_all:=(all real):((fofType->Prop)->Prop).
% 3.58/4.14 Definition r_one:=(one real):((fofType->Prop)->Prop).
% 3.58/4.14 Definition r_in:=(esti real):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition realof:=((ectelt dif) rp_eq):(fofType->fofType).
% 3.58/4.14 Definition r_class:=((ecect dif) rp_eq):(fofType->fofType).
% 3.58/4.14 Definition r_fixf:=((fixfu dif) rp_eq):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition indreal:=((indeq dif) rp_eq):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.14 Definition fixf2:=((fixfu2 dif) rp_eq):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition indreal2:=((indeq2 dif) rp_eq):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.58/4.14 Definition r_0:=(realof ((rp_df d_1rp) d_1rp)):fofType.
% 3.58/4.14 Definition propp:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (posd X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition pos:=(fun (X0:fofType)=> ((l_some dif) (propp X0))):(fofType->Prop).
% 3.58/4.14 Definition propn:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (negd X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition neg:=(fun (X0:fofType)=> ((l_some dif) (propn X0))):(fofType->Prop).
% 3.58/4.14 Definition pofrp:=(fun (X0:fofType)=> (realof (pdofrp X0))):(fofType->fofType).
% 3.58/4.14 Definition nofrp:=(fun (X0:fofType)=> (realof (ndofrp X0))):(fofType->fofType).
% 3.58/4.14 Definition ivr1_pr:=(fun (X0:fofType)=> rpofpd):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition rpofp:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (pofrp X1))))):(fofType->fofType).
% 3.58/4.14 Definition ivr1_nr:=(fun (X0:fofType)=> rpofnd):(fofType->(fofType->fofType)).
% 3.58/4.14 Definition rpofn:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (nofrp X1))))):(fofType->fofType).
% 3.58/4.14 Axiom satz163:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) X0))).
% 3.58/4.14 Axiom satz164:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is X1) X0)))))).
% 3.58/4.14 Axiom satz165:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->(((r_is X1) X2)->((r_is X0) X2))))))))).
% 3.58/4.14 Definition absdr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (absd X0)))):fofType.
% 3.58/4.14 Definition abs:=((indreal real) absdr):(fofType->fofType).
% 3.58/4.14 Axiom satz166a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(pos (abs X0))))).
% 3.58/4.14 Axiom satz166b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (abs X0))))).
% 3.58/4.14 Axiom satz166c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1)))))))).
% 3.58/4.14 Axiom satz166d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1)))))))).
% 3.58/4.14 Axiom satz166e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_nis X0) r_0)->(pos (abs X0))))).
% 3.58/4.14 Axiom satz166f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (abs X0)) r_0)))).
% 3.58/4.14 Definition r_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))))))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition ivr2_propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.58/4.14 Definition r_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))))))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition ivr2_propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.58/4.14 Axiom satz167:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((orec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1)))))).
% 3.58/4.14 Axiom satz167a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((or3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1)))))).
% 3.58/4.14 Axiom satz167b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((ec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1)))))).
% 3.58/4.14 Definition r_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_more X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Definition r_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_less X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.14 Axiom satz168a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->((r_lessis X1) X0)))))).
% 3.58/4.14 Axiom satz168b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->((r_moreis X1) X0)))))).
% 3.58/4.14 Axiom satz167c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->(d_not ((r_less X0) X1))))))).
% 3.58/4.14 Axiom satz167d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->(d_not ((r_more X0) X1))))))).
% 3.58/4.14 Axiom satz167e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_more X0) X1))->((r_lessis X0) X1)))))).
% 3.58/4.14 Axiom satz167f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_less X0) X1))->((r_moreis X0) X1)))))).
% 3.58/4.14 Axiom satz167g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(d_not ((r_lessis X0) X1))))))).
% 3.58/4.14 Axiom satz167h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(d_not ((r_moreis X0) X1))))))).
% 3.58/4.14 Axiom satz167j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_moreis X0) X1))->((r_less X0) X1)))))).
% 3.58/4.14 Axiom satz167k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_lessis X0) X1))->((r_more X0) X1)))))).
% 3.58/4.14 Axiom satz169a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->((r_more X0) r_0)))).
% 3.58/4.14 Axiom satz169b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_more X0) r_0)->(pos X0)))).
% 3.58/4.14 Axiom satz169c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->((r_less X0) r_0)))).
% 3.58/4.14 Axiom satz169d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_less X0) r_0)->(neg X0)))).
% 3.58/4.14 Axiom satz170:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_moreis (abs X0)) r_0))).
% 3.58/4.14 Axiom satz170a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (d_not (neg (abs X0))))).
% 3.58/4.14 Axiom satz171:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_less X1) X2)->((r_less X0) X2))))))))).
% 3.58/4.14 Axiom satz172a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_less X1) X2)->((r_less X0) X2))))))))).
% 3.58/4.14 Axiom satz172b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_lessis X1) X2)->((r_less X0) X2))))))))).
% 3.58/4.14 Axiom satz172c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_moreis X0) X1)->(((r_more X1) X2)->((r_more X0) X2))))))))).
% 3.58/4.14 Axiom satz172d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->(((r_moreis X1) X2)->((r_more X0) X2))))))))).
% 3.58/4.14 Axiom satz173:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_lessis X1) X2)->((r_lessis X0) X2))))))))).
% 3.58/4.14 Definition ratrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (ratd X1))))):(fofType->Prop).
% 3.58/4.14 Definition irratrl:=(fun (X0:fofType)=> (d_not (ratrl X0))):(fofType->Prop).
% 3.58/4.14 Definition natrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (natd X1))))):(fofType->Prop).
% 3.58/4.15 Definition rlofnt:=(fun (X0:fofType)=> (realof (pdofnt X0))):(fofType->fofType).
% 3.58/4.15 Definition ivr2_x0:=(fun (X0:fofType) (X1:fofType)=> (ntofrp ((ivr1_pr X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.15 Definition ntofrl:=(((soft nat) real) ((d_Sigma nat) rlofnt)):(fofType->fofType).
% 3.58/4.15 Definition ivr2_xn:=(fun (X0:fofType)=> ((((soft nat) real) ((d_Sigma nat) rlofnt)) (rlofnt X0))):(fofType->fofType).
% 3.58/4.15 Definition intrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (intd X1))))):(fofType->Prop).
% 3.58/4.15 Axiom satz174:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((intrl X0)->(ratrl X0)))).
% 3.58/4.15 Definition plusdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_pd X0) X1)))))):fofType.
% 3.58/4.15 Definition r_pl:=((indreal2 real) plusdr):(fofType->(fofType->fofType)).
% 3.58/4.15 Axiom satz175:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X0) X1)) ((r_pl X1) X0)))))).
% 3.58/4.15 Definition m0dr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (m0d X0)))):fofType.
% 3.58/4.15 Definition r_m0:=((indreal real) m0dr):(fofType->fofType).
% 3.58/4.15 Axiom satz176a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(neg (r_m0 X0))))).
% 3.58/4.15 Axiom satz176b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (r_m0 X0)) r_0)))).
% 3.58/4.15 Axiom satz176c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (r_m0 X0))))).
% 3.58/4.15 Axiom satz176d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg (r_m0 X0))->(pos X0)))).
% 3.58/4.15 Axiom satz176e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is (r_m0 X0)) r_0)->((r_is X0) r_0)))).
% 3.58/4.15 Axiom satz176f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos (r_m0 X0))->(neg X0)))).
% 3.58/4.15 Axiom satz177:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (r_m0 (r_m0 X0))) X0))).
% 3.58/4.15 Axiom satz177a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) (r_m0 (r_m0 X0))))).
% 3.58/4.15 Axiom satz177b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is (r_m0 X0)) X1)))))).
% 3.58/4.15 Axiom satz177c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is X1) (r_m0 X0))))))).
% 3.58/4.15 Axiom satz177d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) X1)->((r_is X0) (r_m0 X1))))))).
% 3.58/4.15 Axiom satz177e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) X1)->((r_is (r_m0 X1)) X0)))))).
% 3.58/4.15 Axiom satz178:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs (r_m0 X0))) (abs X0)))).
% 3.58/4.15 Axiom satz178a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs X0)) (abs (r_m0 X0))))).
% 3.58/4.15 Axiom satz179:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl X0) (r_m0 X0))) r_0))).
% 3.58/4.15 Axiom satz179a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl (r_m0 X0)) X0)) r_0))).
% 3.58/4.15 Axiom satz180:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_pl X0) X1))) ((r_pl (r_m0 X0)) (r_m0 X1))))))).
% 3.58/4.15 Axiom satz180a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl (r_m0 X0)) (r_m0 X1))) (r_m0 ((r_pl X0) X1))))))).
% 3.58/4.15 Definition r_mn:=(fun (X0:fofType) (X1:fofType)=> ((r_pl X0) (r_m0 X1))):(fofType->(fofType->fofType)).
% 3.58/4.15 Axiom satz181:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_mn X0) X1))) ((r_mn X1) X0)))))).
% 3.58/4.15 Axiom satz181a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_mn X0) X1)) (r_m0 ((r_mn X1) X0))))))).
% 3.58/4.15 Axiom satz182a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_mn X0) X1))->((r_more X0) X1)))))).
% 3.58/4.15 Axiom satz182b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_mn X0) X1)) r_0)->((r_is X0) X1)))))).
% 3.58/4.15 Axiom satz182c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_mn X0) X1))->((r_less X0) X1)))))).
% 3.58/4.15 Axiom satz182d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(pos ((r_mn X0) X1))))))).
% 3.58/4.15 Axiom satz182e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is ((r_mn X0) X1)) r_0)))))).
% 3.58/4.15 Axiom satz182f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(neg ((r_mn X0) X1))))))).
% 3.58/4.15 Axiom satz183a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->((r_less (r_m0 X0)) (r_m0 X1))))))).
% 3.58/4.15 Axiom satz183b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is (r_m0 X0)) (r_m0 X1))))))).
% 3.58/4.15 Axiom satz183c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->((r_more (r_m0 X0)) (r_m0 X1))))))).
% 3.58/4.15 Axiom satz183d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less (r_m0 X0)) (r_m0 X1))->((r_more X0) X1)))))).
% 3.58/4.15 Axiom satz183e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) (r_m0 X1))->((r_is X0) X1)))))).
% 3.58/4.15 Axiom satz183f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more (r_m0 X0)) (r_m0 X1))->((r_less X0) X1)))))).
% 3.58/4.15 Definition d_3r184_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.15 Definition d_3r184_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_some ((d_3r184_prop1 X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.15 Definition d_3r184_prop3:=(fun (X0:fofType)=> (r_some (d_3r184_prop2 X0))):(fofType->Prop).
% 3.58/4.15 Definition prop1d:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (posd X1)) (posd X2)) ((rp_eq X0) ((rp_md X1) X2)))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.15 Definition prop2d:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) ((prop1d X0) X1))):(fofType->(fofType->Prop)).
% 3.58/4.15 Axiom satz184:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (r_some (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2))))))))).
% 3.58/4.15 Axiom satz185:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((r_is ((r_pl ((r_mn X0) X1)) ((r_mn X2) X3))) ((r_mn ((r_pl X0) X2)) ((r_pl X1) X3))))))))))).
% 3.58/4.15 Axiom satz186:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_pl ((r_pl X0) X1)) X2)) ((r_pl X0) ((r_pl X1) X2))))))))).
% 3.58/4.15 Axiom satz187a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X1) ((r_mn X0) X1))) X0))))).
% 3.58/4.15 Axiom satz187b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0))))))).
% 3.58/4.15 Axiom satz187c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is ((r_mn X0) X1)) X2)))))))).
% 3.58/4.15 Axiom satz187d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is X2) ((r_mn X0) X1))))))))).
% 3.58/4.15 Axiom satz187e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is ((r_mn X0) X1)) X2)))))))).
% 3.58/4.15 Axiom satz187f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is X2) ((r_mn X0) X1))))))))).
% 3.58/4.15 Axiom satz187:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_one (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0))))))).
% 3.58/4.15 Axiom satz188a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X0) X2)) ((r_pl X1) X2))->((r_more X0) X1)))))))).
% 3.58/4.15 Axiom satz188b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X0) X2)) ((r_pl X1) X2))->((r_is X0) X1)))))))).
% 3.58/4.15 Axiom satz188c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X0) X2)) ((r_pl X1) X2))->((r_less X0) X1)))))))).
% 3.58/4.15 Axiom satz188d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X0) X2)) ((r_pl X1) X2))))))))).
% 3.58/4.15 Axiom satz188e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X0) X2)) ((r_pl X1) X2))))))))).
% 3.58/4.15 Axiom satz188f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X0) X2)) ((r_pl X1) X2))))))))).
% 3.58/4.15 Axiom satz188g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X2) X0)) ((r_pl X2) X1))->((r_more X0) X1)))))))).
% 3.58/4.15 Axiom satz188h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X0)) ((r_pl X2) X1))->((r_is X0) X1)))))))).
% 3.58/4.15 Axiom satz188j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X2) X0)) ((r_pl X2) X1))->((r_less X0) X1)))))))).
% 3.58/4.15 Axiom satz188k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X2) X0)) ((r_pl X2) X1))))))))).
% 3.58/4.15 Axiom satz188l:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X2) X0)) ((r_pl X2) X1))))))))).
% 3.58/4.15 Axiom satz188m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X2) X0)) ((r_pl X2) X1))))))))).
% 3.58/4.15 Axiom satz188n:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.15 Axiom satz188o:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X2) X0)) ((r_pl X3) X1)))))))))))).
% 3.58/4.15 Axiom satz188p:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.15 Axiom satz188q:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X2) X0)) ((r_pl X3) X1)))))))))))).
% 3.58/4.15 Axiom satz189:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.15 Axiom satz189a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.15 Axiom satz190a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.15 Axiom satz190b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_moreis X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.15 Axiom satz190c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.16 Axiom satz190d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_lessis X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.16 Axiom satz191:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_moreis X2) X3)->((r_moreis ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.16 Axiom satz191a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_lessis X2) X3)->((r_lessis ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))).
% 3.58/4.16 Definition timesdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_td X0) X1)))))):fofType.
% 3.58/4.16 Definition r_ts:=((indreal2 real) timesdr):(fofType->(fofType->fofType)).
% 3.58/4.16 Axiom satz192a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) r_0)->((r_is ((r_ts X0) X1)) r_0)))))).
% 3.58/4.16 Axiom satz192b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X1) r_0)->((r_is ((r_ts X0) X1)) r_0)))))).
% 3.58/4.16 Axiom satz192c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_ts X0) X1)) r_0)->((l_or ((r_is X0) r_0)) ((r_is X1) r_0))))))).
% 3.58/4.16 Axiom satz192d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X0) r_0)->(((r_nis X1) r_0)->((r_nis ((r_ts X0) X1)) r_0))))))).
% 3.58/4.16 Axiom satz193:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (abs ((r_ts X0) X1))) ((r_ts (abs X0)) (abs X1))))))).
% 3.58/4.16 Axiom satz193a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (abs X0)) (abs X1))) (abs ((r_ts X0) X1))))))).
% 3.58/4.16 Axiom satz194:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts X1) X0)))))).
% 3.58/4.16 Definition d_1rl:=(realof d_1df):fofType.
% 3.58/4.16 Axiom satz195:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts X0) d_1rl)) X0))).
% 3.58/4.16 Axiom satz195a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts X0) d_1rl)))).
% 3.58/4.16 Axiom satz195b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts d_1rl) X0)) X0))).
% 3.58/4.16 Axiom satz195c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts d_1rl) X0)))).
% 3.58/4.16 Axiom satz196a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1))))))))).
% 3.58/4.16 Axiom satz196b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1))))))))).
% 3.58/4.16 Axiom satz196c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((neg X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1)))))))))).
% 3.58/4.16 Axiom satz196d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((pos X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1)))))))))).
% 3.58/4.16 Axiom satz196e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1)))))))))).
% 3.58/4.16 Axiom satz196f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1)))))))))).
% 3.58/4.16 Axiom satz196g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1)))))))).
% 3.58/4.16 Axiom satz196h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1)))))))).
% 3.58/4.16 Axiom satz197a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) (r_m0 ((r_ts X0) X1))))))).
% 3.58/4.16 Axiom satz197b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) (r_m0 ((r_ts X0) X1))))))).
% 3.58/4.16 Axiom satz197c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) ((r_ts X0) (r_m0 X1))))))).
% 3.58/4.16 Axiom satz197d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) ((r_ts (r_m0 X0)) X1)))))).
% 3.58/4.16 Axiom satz197e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts (r_m0 X0)) X1)))))).
% 3.58/4.16 Axiom satz197f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts X0) (r_m0 X1))))))).
% 3.58/4.16 Axiom satz198:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) (r_m0 X1))) ((r_ts X0) X1)))))).
% 3.58/4.16 Axiom satz198a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts (r_m0 X0)) (r_m0 X1))))))).
% 3.58/4.16 Axiom satz199:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts ((r_ts X0) X1)) X2)) ((r_ts X0) ((r_ts X1) X2))))))))).
% 3.58/4.16 Axiom satz201:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_pl X1) X2))) ((r_pl ((r_ts X0) X1)) ((r_ts X0) X2))))))))).
% 3.58/4.16 Axiom satz202:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_mn X1) X2))) ((r_mn ((r_ts X0) X1)) ((r_ts X0) X2))))))))).
% 3.58/4.16 Axiom satz203a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2)))))))))).
% 3.58/4.16 Axiom satz203b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X0) X2)) ((r_ts X1) X2))))))))).
% 3.58/4.16 Axiom satz203c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2)))))))))).
% 3.58/4.16 Axiom satz203d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1)))))))))).
% 3.58/4.16 Axiom satz203e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X2) X0)) ((r_ts X2) X1))))))))).
% 3.58/4.16 Axiom satz203f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1)))))))))).
% 3.58/4.16 Axiom satz203g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2)))))))))).
% 3.58/4.16 Axiom satz203j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2)))))))))).
% 3.58/4.16 Axiom satz203k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1)))))))))).
% 3.58/4.16 Axiom satz203m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1)))))))))).
% 3.58/4.16 Axiom satz204b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is ((r_ts X1) X2)) X0)->(((r_is ((r_ts X1) X3)) X0)->((r_is X2) X3)))))))))))).
% 3.58/4.16 Axiom satz204a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_some (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))))))).
% 3.58/4.16 Axiom satz204:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_one (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))))))).
% 3.58/4.16 Definition r_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind real) (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))):(fofType->(fofType->fofType)).
% 3.58/4.16 Axiom satz204c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts X1) ((r_ov X0) X1))) X0)))))).
% 3.58/4.16 Axiom satz204d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts X1) ((r_ov X0) X1)))))))).
% 3.58/4.16 Axiom satz204e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts ((r_ov X0) X1)) X1)) X0)))))).
% 3.58/4.16 Axiom satz204f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts ((r_ov X0) X1)) X1))))))).
% 3.58/4.16 Axiom satz204g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_nis X1) r_0)->(((r_is ((r_ts X1) X2)) X0)->((r_is X2) ((r_ov X0) X1)))))))))).
% 3.58/4.16 Definition s01:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_lessis X1) X0)))):(fofType->fofType).
% 3.58/4.16 Definition s02:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_more X1) X0)))):(fofType->fofType).
% 3.58/4.16 Definition s11:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_less X1) X0)))):(fofType->fofType).
% 3.58/4.16 Definition s12:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_moreis X1) X0)))):(fofType->fofType).
% 3.58/4.16 Definition d_2rl:=((r_pl d_1rl) d_1rl):fofType.
% 3.58/4.16 Definition half:=((r_ov d_1rl) d_2rl):fofType.
% 3.58/4.16 Definition d_5r205_prop1:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_less X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop)).
% 3.58/4.16 Definition d_5r205_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_more X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop)).
% 3.58/4.16 Definition d_5r205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5r205_prop1 X0) X2)) ((d_5r205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.16 Definition mxy:=(fun (X0:fofType) (X1:fofType)=> ((r_ts half) ((r_pl X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.16 Definition sc1:=(fun (X0:fofType)=> ((d_Sep cut) (fun (X1:fofType)=> ((r_in (pofrp X1)) X0)))):(fofType->fofType).
% 3.58/4.16 Definition pr1:=(fun (X0:fofType)=> rpofp):(fofType->(fofType->fofType)).
% 3.58/4.16 Definition ps1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> rpofp):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.58/4.16 Definition stc:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((schnitt (sc1 X0)) (sc1 X1))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.16 Definition stp:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (pofrp (((stc X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.16 Definition d_5r205_sp1:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_in (r_m0 X1)) X0)))):(fofType->fofType).
% 3.58/4.16 Axiom satz205:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->(r_one (fun (X2:fofType)=> ((d_and (r_all (fun (X3:fofType)=> (((r_less X3) X2)->((r_in X3) X0))))) (r_all (fun (X3:fofType)=> (((r_more X3) X2)->((r_in X3) X1))))))))))))))).
% 3.58/4.16 Definition r_schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind real) ((d_5r205_prop3 X0) X1))):(fofType->(fofType->fofType)).
% 3.58/4.16 Axiom satz205a:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X2) ((r_schnitt X0) X1))->((r_in X2) X0)))))))))))).
% 3.58/4.16 Axiom satz205b:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X2) ((r_schnitt X0) X1))->((r_in X2) X1)))))))))))).
% 3.58/4.16 Definition r_sqrt:=(fun (X0:fofType)=> ((ind real) (fun (X1:fofType)=> ((d_and (d_not (neg X1))) ((r_is ((r_ts X1) X1)) X0))))):(fofType->fofType).
% 3.58/4.16 Definition shiftl:=(fun (X0:fofType) (X1:fofType)=> (ntofrl ((r_mn ((r_pl X0) d_1rl)) X1))):(fofType->(fofType->fofType)).
% 3.58/4.16 Definition shift_n1:=(fun (X0:fofType) (X1:fofType)=> (inn ((shiftl X0) X1))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.16 Definition shift_n2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rlofnt (((shift_n1 X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.16 Definition shiftr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((r_mn ((r_pl (((shift_n2 X0) X1) X2)) X1)) d_1rl)):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.16 Definition shift_ul:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((shiftl X2) X1)):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.16 Definition shiftl1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((shiftl X0) X1)) (((shift_ul X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.16 Definition seq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Pi real) (fun (X3:fofType)=> (((if (intrl X3)) (((if ((r_lessis X1) X3)) (((if ((r_lessis X3) X0)) X2) (ordsucc emptyset))) (ordsucc emptyset))) (ordsucc emptyset))))):(fofType->(fofType->(fofType->fofType))).
% 3.58/4.16 Definition proofsirrelevant:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->((all_of (fun (X5:fofType)=> ((in X5) real))) (fun (X5:fofType)=> ((intrl X5)->(((r_lessis X1) X5)->(((r_lessis X5) X0)->(((r_is X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))))))))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.58/4.16 Definition shiftf:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X4:fofType)=> ((ap X3) (((shiftr X0) X1) X4))))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 3.58/4.16 Definition inseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->(((and3 (intrl ((ap X2) X3))) ((r_lessis X1) ((ap X2) X3))) ((r_lessis ((ap X2) X3)) X0)))))))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.16 Definition injseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->(((r_is ((ap X2) X3)) ((ap X2) X4))->((r_is X3) X4))))))))))))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.16 Definition shift_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((r_is X3) ((ap X2) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))).
% 3.58/4.17 Definition improp:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and (((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))) ((((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))->(((((shift_prop1 X0) X1) X2) X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))).
% 3.58/4.17 Definition imseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (r_some ((((improp X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 3.58/4.17 Definition surjseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((((imseq X0) X1) X2) X3))))))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.17 Definition perm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injseq X0) X1) X2)) (((surjseq X0) X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 3.58/4.17 Definition shift_ns:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ap X2) (((shiftr X0) X1) X3))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 4.58/5.16 Definition shiftseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X3:fofType)=> (((shiftl1 X0) X1) ((((shift_ns X0) X1) X2) X3))))):(fofType->(fofType->(fofType->fofType))).
% 4.58/5.16 Definition ul1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((shiftl1 X0) X1)):(fofType->(fofType->(fofType->(fofType->(fofType->fofType))))).
% 4.58/5.16 There are no conjectures!
% 4.58/5.16 Adding conjecture False, to look for Unsatisfiability
% 4.58/5.16 Trying to prove False
% 4.58/5.16 --- does not match type in application fofType vs Prop in (((e_in X0) X1) ((ex fofType) (fun X0:fofType=> ((in X0) emptyset))))
% 4.58/5.16 ---context
% 4.58/5.16 False:Prop
% 4.58/5.16 False_rect:(forall (P:Type), (False->P))
% 4.58/5.16 I:True
% 4.58/5.16 NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% 4.58/5.16 True:Prop
% 4.58/5.16 _TPTP_proj1:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj)):(fofType->fofType)
% 4.58/5.16 abs:=((indreal real) absdr):(fofType->fofType)
% 4.58/5.16 absd:=(fun (X0:fofType)=> ((((ite (negd X0)) dif) ((rp_df (std X0)) (stm X0))) X0)):(fofType->fofType)
% 4.58/5.16 absdr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (absd X0)))):fofType
% 4.58/5.16 all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))):(fofType->((fofType->Prop)->Prop))
% 4.58/5.16 all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))):((fofType->Prop)->((fofType->Prop)->Prop))
% 4.58/5.16 amone:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3)))))))):(fofType->((fofType->Prop)->Prop))
% 4.58/5.16 and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.58/5.16 and:(Prop->(Prop->Prop))
% 4.58/5.16 and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 4.58/5.16 and_rect:=(fun (A:Prop) (B:Prop) (P:Type) (X:(A->(B->P))) (H:((and A) B))=> ((X (((proj1 A) B) H)) (((proj2 A) B) H))):(forall (A:Prop) (B:Prop) (P:Type), ((A->(B->P))->(((and A) B)->P)))
% 4.58/5.16 anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->Prop)))
% 4.58/5.16 ap:=(fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1)):(fofType->(fofType->fofType))
% 4.58/5.16 ap_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))
% 4.58/5.16 apb1:=(fun (X0:fofType) (X1:fofType)=> (rpofpd ((rp_pd X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 arpi:=(fun (X0:fofType)=> ((rp_ov d_1rp) (rpofpd X0))):(fofType->fofType)
% 4.58/5.16 atb3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd ((rp_td X0) X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 beta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2))))
% 4.58/5.16 bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 changef:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.58/5.16 chi:=(fun (X0:fofType) (X1:fofType)=> (cutof ((diff X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% 4.58/5.16 choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% 4.58/5.16 class:=((ecect frac) n_eq):(fofType->fofType)
% 4.58/5.16 classic:(forall (P:Prop), ((or P) (not P)))
% 4.58/5.16 classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 4.58/5.16 cond1:=(n_in n_1):(fofType->Prop)
% 4.58/5.16 cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))):(fofType->Prop)
% 4.58/5.16 conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 4.58/5.16 cut:=((d_Sep (power rat)) cutprop):fofType
% 4.58/5.16 cutof:=((out (power rat)) cutprop):(fofType->fofType)
% 4.58/5.16 cutprop1:=(fun (X0:fofType)=> ((d_and (cutprop1a X0)) (cutprop1b X0))):(fofType->Prop)
% 4.58/5.16 cutprop1a:=(nonempty rat):(fofType->Prop)
% 4.58/5.16 cutprop1b:=(fun (X0:fofType)=> (d_not (rt_all (fun (X1:fofType)=> ((rt_in X1) X0))))):(fofType->Prop)
% 4.58/5.16 cutprop2:=(fun (X0:fofType)=> (rt_all (fun (X1:fofType)=> ((imp ((rt_in X1) X0)) ((cutprop2a X0) X1))))):(fofType->Prop)
% 4.58/5.16 cutprop2a:=(fun (X0:fofType) (X1:fofType)=> (rt_all (fun (X2:fofType)=> ((imp (d_not ((rt_in X2) X0))) ((rt_less X1) X2))))):(fofType->(fofType->Prop))
% 4.58/5.16 cutprop3:=(fun (X0:fofType)=> (d_not (rt_some (max X0)))):(fofType->Prop)
% 4.58/5.16 cutprop:=(fun (X0:fofType)=> (((and3 (cutprop1 X0)) (cutprop2 X0)) (cutprop3 X0))):(fofType->Prop)
% 4.58/5.16 d161_s:=(fun (X0:fofType)=> (pdofrp (srp X0))):(fofType->fofType)
% 4.58/5.16 d_10_prop1:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))
% 4.58/5.16 d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2)))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 4.58/5.16 d_1df:=(pdofrp d_1rp):fofType
% 4.58/5.16 d_1out:=(fun (X0:fofType)=> ((outn X0) n_1)):(fofType->fofType)
% 4.58/5.16 d_1rl:=(realof d_1df):fofType
% 4.58/5.16 d_1rp:=(rpofrt d_1rt):fofType
% 4.58/5.16 d_1rt:=(rtofn n_1):fofType
% 4.58/5.16 d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->fofType)
% 4.58/5.16 d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0)):(fofType->Prop)
% 4.58/5.16 d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))):(fofType->Prop)
% 4.58/5.16 d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))):(fofType->fofType)
% 4.58/5.16 d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))):(fofType->Prop)
% 4.58/5.16 d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_25_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))):(fofType->(fofType->Prop))
% 4.58/5.16 d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_29_prop1:=(fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_2rl:=((r_pl d_1rl) d_1rl):fofType
% 4.58/5.16 d_2x0:=(fun (X0:fofType)=> ((rt_pl X0) X0)):(fofType->fofType)
% 4.58/5.16 d_3129_z1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X0) ((rt_pl X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 d_3132_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((lrt X0) X1)) ((urt X0) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_3132_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((rt_is ((rt_mn X3) X2)) X1)):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 d_3132_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((d_3132_prop1 X0) X2) X3)) ((((d_3132_prop1 X0) X2) X3)->((((d_3132_prop2 X0) X1) X2) X3)))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 d_3132_prop4:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (((d_3132_prop3 X0) X1) X2))))):(fofType->(fofType->Prop))
% 4.58/5.16 d_3132_u0:=(fun (X0:fofType) (X1:fofType)=> ((rt_pl X1) X0)):(fofType->(fofType->fofType))
% 4.58/5.16 d_3132_v0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (um10 X2)) X0))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 d_3132_w0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (rtofn X2)) X0))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 d_367_vo:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))):(fofType->(fofType->fofType))
% 4.58/5.16 d_367_w:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 d_3r184_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_3r184_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_some ((d_3r184_prop1 X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_3r184_prop3:=(fun (X0:fofType)=> (r_some (d_3r184_prop2 X0))):(fofType->Prop)
% 4.58/5.16 d_4141_v0:=(fun (X0:fofType) (X1:fofType)=> ((rt_ts ((rt_ov d_1rt) X1)) X0)):(fofType->(fofType->fofType))
% 4.58/5.16 d_4144_x2:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_moreis X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.58/5.16 d_4152_chi:=(fun (X0:fofType)=> (cutof (inv X0))):(fofType->fofType)
% 4.58/5.16 d_4153_chi:=(fun (X0:fofType) (X1:fofType)=> ((rp_ts X1) X0)):(fofType->(fofType->fofType))
% 4.58/5.16 d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))):(fofType->fofType)
% 4.58/5.16 d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0)):fofType
% 4.58/5.16 d_428_prop1:=(fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))):(fofType->(fofType->Prop))
% 4.58/5.16 d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->Prop)
% 4.58/5.16 d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))):(fofType->(fofType->Prop))
% 4.58/5.16 d_430_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_431_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_477_v:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 d_5113_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nt_in (ntofn X1)) X0)):(fofType->(fofType->Prop))
% 4.58/5.16 d_5156_prop1:=(fun (X0:fofType) (X1:fofType)=> ((rp_nt_in (nttofnt X1)) X0)):(fofType->(fofType->Prop))
% 4.58/5.16 d_5157_s1:=(fun (X0:fofType)=> ((d_Sep rat) (urt X0))):(fofType->fofType)
% 4.58/5.16 d_5160_dn:=(fun (X0:fofType) (X1:fofType)=> ((rp_pl ((rp_pl X0) X1)) d_1rp)):(fofType->(fofType->fofType))
% 4.58/5.16 d_5160_fr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_ov (((d_5160_nm X0) X1) X2)) ((d_5160_dn X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 d_5160_nm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_mn (rpofrt X2)) ((rp_ts X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 d_5160_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.58/5.16 d_5160_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((d_5160_prop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_5160_xr:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((rt_ov X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 d_5160_y0:=(fun (X0:fofType)=> X0):(fofType->fofType)
% 4.58/5.16 d_5160_yr:=(fun (X0:fofType)=> (rpofrt (d_5160_y0 X0))):(fofType->fofType)
% 4.58/5.16 d_5161_dn:=(fun (X0:fofType)=> ((rp_pl (rpofrt X0)) ((rp_pl (rpofrt X0)) d_1rp))):(fofType->fofType)
% 4.58/5.16 d_5161_fr:=(fun (X0:fofType) (X1:fofType)=> ((rp_ov ((d_5161_nm X0) X1)) (d_5161_dn X1))):(fofType->(fofType->fofType))
% 4.58/5.16 d_5161_max:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_more X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType))
% 4.58/5.16 d_5161_min:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_less X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType))
% 4.58/5.16 d_5161_nm:=(fun (X0:fofType) (X1:fofType)=> ((rp_mn X0) ((rp_ts (rpofrt X1)) (rpofrt X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 d_5161_xm:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_more X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.58/5.16 d_5161_ym:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_less X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.58/5.16 d_5162_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_eq ((n_tf ((n_fr X1) X0)) ((n_fr X1) X0))) ((n_fr (ordsucc n_1)) n_1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_5162_prop2:=(fun (X0:fofType)=> (n_some (d_5162_prop1 X0))):(fofType->Prop)
% 4.58/5.16 d_5162_prop3:=(n_some d_5162_prop2):Prop
% 4.58/5.16 d_5162_x0:=(rtofrp ksi):fofType
% 4.58/5.16 d_5162_y:=((ind nat) (min d_5162_prop2)):fofType
% 4.58/5.16 d_527_q:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (X0 (ntofn X1))):((fofType->Prop)->(fofType->Prop))
% 4.58/5.16 d_54_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (nofnt ((ap X0) (ntofn X1)))))):(fofType->fofType)
% 4.58/5.16 d_54_gt:=(fun (X0:fofType)=> ((d_Sigma natt) (fun (X1:fofType)=> (ntofn ((ap X0) (nofnt X1)))))):(fofType->fofType)
% 4.58/5.16 d_54_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc (nofnt X0)))) (d_24_prop1 X1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_59_i:=(fun (X0:fofType) (X1:fofType)=> ((n_is (nofnt X0)) (nofnt X1))):(fofType->(fofType->Prop))
% 4.58/5.16 d_59_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X0)) (nofnt X1)))):(fofType->(fofType->Prop))
% 4.58/5.16 d_59_iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X1)) (nofnt X0)))):(fofType->(fofType->Prop))
% 4.58/5.16 d_5p205_prop1:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_less X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop))
% 4.58/5.16 d_5p205_prop2:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_more X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop))
% 4.58/5.16 d_5p205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5p205_prop1 X0) X2)) ((d_5p205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_5r205_prop1:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_less X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop))
% 4.58/5.16 d_5r205_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_more X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop))
% 4.58/5.16 d_5r205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5r205_prop1 X0) X2)) ((d_5r205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 d_5r205_sp1:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_in (r_m0 X1)) X0)))):(fofType->fofType)
% 4.58/5.16 d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1))):((fofType->((fofType->fofType)->fofType))->(fofType->fofType))
% 4.58/5.16 d_In_rec_G:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))):((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))
% 4.58/5.16 d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1)):(fofType->fofType)
% 4.58/5.16 d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))):(fofType->fofType)
% 4.58/5.16 d_Pi:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))))):(fofType->((fofType->fofType)->fofType))
% 4.58/5.16 d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))):(fofType->Prop)
% 4.58/5.16 d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))):(fofType->((fofType->Prop)->((fofType->fofType)->fofType)))
% 4.58/5.16 d_Repl_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0)))))):(fofType->Prop)
% 4.58/5.16 d_Sep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset)):(fofType->((fofType->Prop)->fofType))
% 4.58/5.16 d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))):(fofType->((fofType->fofType)->fofType))
% 4.58/5.16 d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0)):(fofType->fofType)
% 4.58/5.16 d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))):(fofType->(fofType->Prop))
% 4.58/5.16 d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))):(fofType->Prop)
% 4.58/5.16 d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))):(fofType->fofType)
% 4.58/5.16 d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))):(fofType->Prop)
% 4.58/5.16 d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))):(Prop->(Prop->Prop))
% 4.58/5.16 d_not:=(fun (X0:Prop)=> ((imp X0) False)):(Prop->Prop)
% 4.58/5.16 d_pair:=(fun (X0:fofType) (X1:fofType)=> pair):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 den:=(second1 nat):(fofType->fofType)
% 4.58/5.16 dependent_unique_choice:(forall (A:Type) (B:(A->Type)) (R:(forall (x:A), ((B x)->Prop))), ((forall (x:A), ((ex (B x)) ((unique (B x)) (fun (y:(B x))=> ((R x) y)))))->((ex (forall (x:A), (B x))) (fun (f:(forall (x:A), (B x)))=> (forall (x:A), ((R x) (f x)))))))
% 4.58/5.16 dif:=(pair1type cut):fofType
% 4.58/5.16 diff:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((rp_diffprop X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 diffprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((rt_more X1) X2)) (((rt_more X1) X2)->((rt_is X0) ((rt_mn X1) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 diffprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((urt X1) X4)) (((diffprop1 X2) X3) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.58/5.16 diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 e_fisi:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3)))))))
% 4.58/5.16 e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2):(fofType->((fofType->Prop)->(fofType->fofType)))
% 4.58/5.16 e_in_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 4.58/5.16 e_inp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2)))))
% 4.58/5.16 e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 e_isp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3))))))))
% 4.58/5.16 e_pair_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1)))))))))
% 4.58/5.16 ec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0))):(Prop->(Prop->(Prop->Prop)))
% 4.58/5.16 ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.58/5.16 ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.58/5.16 ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.58/5.16 ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->fofType))
% 4.58/5.16 ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.58/5.16 ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.58/5.16 empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))):(fofType->(fofType->Prop))
% 4.58/5.16 emptyset:fofType
% 4.58/5.16 eps:((fofType->Prop)->fofType)
% 4.58/5.16 eq:=(fun (T:Type) (a:T) (b:T)=> (forall (P:(T->Prop)), ((P a)->(P b)))):(forall (T:Type), (T->(T->Prop)))
% 4.58/5.16 eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% 4.58/5.16 eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% 4.58/5.16 eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% 4.58/5.16 eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 4.58/5.16 eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 4.58/5.16 esti:=(fun (X0:fofType)=> in):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 estie:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2)))))
% 4.58/5.16 estii:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1))))))
% 4.58/5.16 eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% 4.58/5.16 eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% 4.58/5.16 ex:(forall (A:Type), ((A->Prop)->Prop))
% 4.58/5.16 ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% 4.58/5.16 ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% 4.58/5.16 famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))):(fofType->((fofType->fofType)->fofType))
% 4.58/5.16 first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)):(fofType->(fofType->fofType))
% 4.58/5.16 first:=(fun (X0:fofType) (X1:fofType)=> proj0):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 first_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 4.58/5.16 firstis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2))))))
% 4.58/5.16 fixf2:=((fixfu2 dif) rp_eq):(fofType->(fofType->Prop))
% 4.58/5.16 fixf:=((fixfu2 frac) n_eq):(fofType->(fofType->Prop))
% 4.58/5.16 fixfu2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7))))))))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.58/5.16 fixfu:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.58/5.16 fofType:Type
% 4.58/5.16 frac:=(pair1type nat):fofType
% 4.58/5.16 functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% 4.58/5.16 functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 4.58/5.16 functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% 4.58/5.16 half:=((r_ov d_1rl) d_2rl):fofType
% 4.58/5.16 i1_s:=(d_Sep nat):((fofType->Prop)->fofType)
% 4.58/5.16 if:=(fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2)))))):(Prop->(fofType->(fofType->fofType)))
% 4.58/5.16 if_i_0:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2)))
% 4.58/5.16 if_i_1:(forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1)))
% 4.58/5.16 if_i_correct:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2))))
% 4.58/5.16 if_i_or:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2)))
% 4.58/5.16 iff:=(fun (A:Prop) (B:Prop)=> ((and (A->B)) (B->A))):(Prop->(Prop->Prop))
% 4.58/5.16 iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 4.58/5.16 iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 4.58/5.16 iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 4.58/5.16 iii1_lbprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_lessis X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))):(fofType->(fofType->Prop))
% 4.58/5.16 iiia_x0:=(fun (X0:fofType)=> (rtofn (ntofrp X0))):(fofType->fofType)
% 4.58/5.16 iiit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X1) X0))):(fofType->(fofType->Prop))
% 4.58/5.16 iit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 image:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1)):(Prop->(Prop->Prop))
% 4.58/5.16 improp:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and (((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))) ((((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))->(((((shift_prop1 X0) X1) X2) X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.58/5.16 imseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (r_some ((((improp X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 in:(fofType->(fofType->Prop))
% 4.58/5.16 incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))):(fofType->((fofType->Prop)->fofType))
% 4.58/5.16 ind_p:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0)))))
% 4.58/5.16 indeq2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))
% 4.58/5.16 indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 4.58/5.16 indrat:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 indreal2:=((indeq2 dif) rp_eq):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 indreal:=((indeq dif) rp_eq):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 inf:=(esti frac):(fofType->(fofType->Prop))
% 4.58/5.16 inj_h:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.58/5.16 injective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4))))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 injseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->(((r_is ((ap X2) X3)) ((ap X2) X4))->((r_is X3) X4))))))))))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType))
% 4.58/5.16 inseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->(((and3 (intrl ((ap X2) X3))) ((r_lessis X1) ((ap X2) X3))) ((r_lessis ((ap X2) X3)) X0)))))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 intd:=(fun (X0:fofType)=> ((l_or (zero X0)) (natd (absd X0)))):(fofType->Prop)
% 4.58/5.16 intd_a3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X0))):(fofType->(fofType->fofType))
% 4.58/5.16 intd_b2:=(fun (X0:fofType)=> (rpofpd (m0d X0))):(fofType->fofType)
% 4.58/5.16 intd_b3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X1))):(fofType->(fofType->fofType))
% 4.58/5.16 intrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (intd X1))))):(fofType->Prop)
% 4.58/5.16 inv:=(fun (X0:fofType)=> ((d_Sep rat) (invprop X0))):(fofType->fofType)
% 4.58/5.16 inverse:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset)))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 invprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((urt X0) X2)) ((rt_less X2) X1))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 invprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 ((urt X0) X2)) (rt_some ((invprop1 X0) X2))) ((rt_is X1) ((rt_ov d_1rt) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 invprop:=(fun (X0:fofType) (X1:fofType)=> (rt_some ((invprop2 X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 irratd:=(fun (X0:fofType)=> (d_not (ratd X0))):(fofType->Prop)
% 4.58/5.16 irratrl:=(fun (X0:fofType)=> (d_not (ratrl X0))):(fofType->Prop)
% 4.58/5.16 irratrp:=(fun (X0:fofType)=> (d_not (ratrp X0))):(fofType->Prop)
% 4.58/5.16 is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)):(fofType->((fofType->Prop)->Prop))
% 4.58/5.16 isseti:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2))))))))
% 4.58/5.16 ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))):(Prop->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 iv4d_ai:=(fun (X0:fofType)=> (pdofrp (arpi X0))):(fofType->fofType)
% 4.58/5.16 iv5d_2:=((rp_pl d_1rp) d_1rp):fofType
% 4.58/5.16 ivr1_nr:=(fun (X0:fofType)=> rpofnd):(fofType->(fofType->fofType))
% 4.58/5.16 ivr1_pr:=(fun (X0:fofType)=> rpofpd):(fofType->(fofType->fofType))
% 4.58/5.16 ivr2_propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 ivr2_propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 ivr2_x0:=(fun (X0:fofType) (X1:fofType)=> (ntofrp ((ivr1_pr X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 ivr2_xn:=(fun (X0:fofType)=> ((((soft nat) real) ((d_Sigma nat) rlofnt)) (rlofnt X0))):(fofType->fofType)
% 4.58/5.16 k_EmptyAx:(((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False)
% 4.58/5.16 k_If_In_01:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset)))))
% 4.58/5.16 k_If_In_then_E:(forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2))))
% 4.58/5.16 k_In_0_1:((in emptyset) (ordsucc emptyset))
% 4.58/5.16 k_In_ind:(forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1))))
% 4.58/5.16 k_Pi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3))))))
% 4.58/5.16 k_PowerE:(forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0)))
% 4.58/5.16 k_PowerEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0)))
% 4.58/5.16 k_PowerI:(forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0))))
% 4.58/5.16 k_ReplEq:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3)))))))
% 4.58/5.16 k_Self_In_Power:(forall (X0:fofType), ((in X0) (power X0)))
% 4.58/5.16 k_SepE1:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0)))
% 4.58/5.16 k_SepE2:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2)))
% 4.58/5.16 k_SepI:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1)))))
% 4.58/5.16 k_Sigma_eta_proj0_proj1:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))))
% 4.58/5.16 k_UnionEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0))))))
% 4.58/5.16 k_UnivOf_In:(forall (X0:fofType), ((in X0) (univof X0)))
% 4.58/5.16 k_UnivOf_ZF_closed:(forall (X0:fofType), (d_ZF_closed (univof X0)))
% 4.58/5.16 k_satz123a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((or3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.58/5.16 k_satz123b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((ec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.58/5.16 k_satz67c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0))))))
% 4.58/5.16 ksi:=((ind cut) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) X0)) (rpofnt (ordsucc n_1))))):fofType
% 4.58/5.16 l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))):(Prop->(Prop->Prop))
% 4.58/5.16 l_et:(forall (X0:Prop), ((wel X0)->X0))
% 4.58/5.16 l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))):(Prop->(Prop->Prop))
% 4.58/5.16 l_or:=(fun (X0:Prop)=> (imp (d_not X0))):(Prop->(Prop->Prop))
% 4.58/5.16 l_some:=(fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1)))):(fofType->((fofType->Prop)->Prop))
% 4.58/5.16 lam_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1))))
% 4.58/5.16 lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))):((fofType->Prop)->(fofType->(fofType->Prop)))
% 4.58/5.16 lcl:=((e_in (power rat)) cutprop):(fofType->fofType)
% 4.58/5.16 left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 left:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 lessd:=(fun (X0:fofType) (X1:fofType)=> ((rp_less ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.58/5.16 lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.58/5.16 lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 lrt:=(fun (X0:fofType) (X1:fofType)=> ((rt_in X1) (lcl X0))):(fofType->(fofType->Prop))
% 4.58/5.16 m0d:=(fun (X0:fofType)=> ((rp_df (std X0)) (stm X0))):(fofType->fofType)
% 4.58/5.16 m0dr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (m0d X0)))):fofType
% 4.58/5.16 max:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_ub X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop))
% 4.58/5.16 min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop))
% 4.58/5.16 mored:=(fun (X0:fofType) (X1:fofType)=> ((rp_more ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.58/5.16 moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.58/5.16 moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 mxy:=(fun (X0:fofType) (X1:fofType)=> ((r_ts half) ((r_pl X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 n1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (negd X1))):(fofType->(fofType->Prop))
% 4.58/5.16 n1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (posd X1))):(fofType->(fofType->Prop))
% 4.58/5.16 nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)):(fofType->(fofType->Prop))
% 4.58/5.16 n_1:=(ordsucc emptyset):fofType
% 4.58/5.16 n_1_p:((is_of n_1) (fun (X0:fofType)=> ((in X0) nat)))
% 4.58/5.16 n_1o:=((outn n_1) n_1):fofType
% 4.58/5.16 n_1t:=((outn n_2) n_1):fofType
% 4.58/5.16 n_2:=((n_pl n_1) n_1):fofType
% 4.58/5.16 n_2t:=((outn n_2) n_2):fofType
% 4.58/5.16 n_all:=(all nat):((fofType->Prop)->Prop)
% 4.58/5.16 n_ax3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1)))
% 4.58/5.16 n_ax4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1))))))
% 4.58/5.16 n_ax5:((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0)))))))
% 4.58/5.16 n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.58/5.16 n_fr:=(pair1 nat):(fofType->(fofType->fofType))
% 4.58/5.16 n_in:=(esti nat):(fofType->(fofType->Prop))
% 4.58/5.16 n_is:=(e_is nat):(fofType->(fofType->Prop))
% 4.58/5.16 n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))):((fofType->Prop)->(fofType->Prop))
% 4.58/5.16 n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 n_one:=(one nat):((fofType->Prop)->Prop)
% 4.58/5.16 n_pf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 n_pl:=(fun (X0:fofType)=> (ap (plus X0))):(fofType->(fofType->fofType))
% 4.58/5.16 n_some:=(l_some nat):((fofType->Prop)->Prop)
% 4.58/5.16 n_tf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 n_ts:=(fun (X0:fofType)=> (ap (times X0))):(fofType->(fofType->fofType))
% 4.58/5.16 nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))):fofType
% 4.58/5.16 nat_1:(nat_p (ordsucc emptyset))
% 4.58/5.16 nat_ind:(forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1))))))
% 4.58/5.16 nat_inv:(forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1))))))))
% 4.58/5.16 nat_ordsucc:(forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0))))
% 4.58/5.16 nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))):(fofType->Prop)
% 4.58/5.16 nat_p_omega:(forall (X0:fofType), ((nat_p X0)->((in X0) omega)))
% 4.58/5.16 natd:=(fun (X0:fofType)=> ((d_and (posd X0)) ((posd X0)->(natrp (rpofpd X0))))):(fofType->Prop)
% 4.58/5.16 natprop:=(fun (X0:fofType) (X1:fofType)=> ((inf ((n_fr X1) n_1)) (class X0))):(fofType->(fofType->Prop))
% 4.58/5.16 natrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (natd X1))))):(fofType->Prop)
% 4.58/5.16 natrp:=(((image nat) cut) ((d_Sigma nat) rpofnt)):(fofType->Prop)
% 4.58/5.16 natrt:=(fun (X0:fofType)=> (n_some (natprop X0))):(fofType->Prop)
% 4.58/5.16 natt:=((d_Sep rat) natrt):fofType
% 4.58/5.16 ndofrp:=(fun (X0:fofType)=> ((rp_df d_1rp) ((rp_pl X0) d_1rp))):(fofType->fofType)
% 4.58/5.16 neg:=(fun (X0:fofType)=> ((l_some dif) (propn X0))):(fofType->Prop)
% 4.58/5.16 negd:=(fun (X0:fofType)=> ((rp_less (stm X0)) (std X0))):(fofType->Prop)
% 4.58/5.16 neq_ordsucc_0:(forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset)))
% 4.58/5.16 nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2)))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 nofnt:=(fun (X0:fofType)=> (nofrt (rtofnt X0))):(fofType->fofType)
% 4.58/5.16 nofrp:=(fun (X0:fofType)=> (realof (ndofrp X0))):(fofType->fofType)
% 4.58/5.16 nofrt:=(fun (X0:fofType)=> ((ind nat) (natprop X0))):(fofType->fofType)
% 4.58/5.16 non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))):(fofType->((fofType->Prop)->(fofType->Prop)))
% 4.58/5.16 nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))):(fofType->(fofType->Prop))
% 4.58/5.16 not:=(fun (P:Prop)=> (P->False)):(Prop->Prop)
% 4.58/5.16 nt_1t:=(ntofn n_1):fofType
% 4.58/5.16 nt_all:=(all natt):((fofType->Prop)->Prop)
% 4.58/5.16 nt_cond1:=(nt_in nt_1t):(fofType->Prop)
% 4.58/5.16 nt_cond2:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((imp ((nt_in X1) X0)) ((nt_in ((ap suct) X1)) X0))))):(fofType->Prop)
% 4.58/5.16 nt_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 nt_in:=(esti natt):(fofType->(fofType->Prop))
% 4.58/5.16 nt_is:=(e_is natt):(fofType->(fofType->Prop))
% 4.58/5.16 nt_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (nt_all (fun (X2:fofType)=> ((imp (X0 X2)) ((nt_lessis X1) X2))))):((fofType->Prop)->(fofType->Prop))
% 4.58/5.16 nt_less:=(fun (X0:fofType) (X1:fofType)=> ((rt_less (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.58/5.16 nt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((rt_lessis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.58/5.16 nt_min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((nt_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop))
% 4.58/5.16 nt_more:=(fun (X0:fofType) (X1:fofType)=> ((rt_more (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.58/5.16 nt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((rt_moreis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.58/5.16 nt_natt:=((d_Sep cut) natrp):fofType
% 4.58/5.16 nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((nt_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 nt_one:=(one natt):((fofType->Prop)->Prop)
% 4.58/5.16 nt_pl:=(fun (X0:fofType) (X1:fofType)=> (ntofrt ((rt_pl (rtofnt X0)) (rtofnt X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 nt_satz15:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> (((nt_less X0) X1)->(((nt_less X1) X2)->((nt_less X0) X2)))))))))
% 4.58/5.16 nt_satz1:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_nis X0) X1)->((nt_nis ((ap suct) X0)) ((ap suct) X1)))))))
% 4.58/5.16 nt_satz21:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) natt))) (fun (X3:fofType)=> (((nt_more X0) X1)->(((nt_more X2) X3)->((nt_more ((nt_pl X0) X2)) ((nt_pl X1) X3))))))))))))
% 4.58/5.16 nt_satz27:(forall (X0:(fofType->Prop)), ((nt_some X0)->(nt_some (nt_min X0))))
% 4.58/5.16 nt_satz4:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((one ((d_Pi natt) (fun (X1:fofType)=> natt))) (fun (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (nt_all (fun (X2:fofType)=> ((nt_is ((ap X1) ((ap suct) X2))) ((ap suct) ((ap X1) X2))))))))))
% 4.58/5.16 nt_satz5:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((nt_is ((nt_pl ((nt_pl X0) X1)) X2)) ((nt_pl X0) ((nt_pl X1) X2)))))))))
% 4.58/5.16 nt_satz9:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((orec3 ((nt_is X0) X1)) (nt_some (fun (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))))) (nt_some (fun (X2:fofType)=> ((nt_is X1) ((nt_pl X0) X2)))))))))
% 4.58/5.16 nt_some:=(l_some natt):((fofType->Prop)->Prop)
% 4.58/5.16 nt_suct:=((d_Sigma nt_natt) (fun (X0:fofType)=> (nttofnt (ordsucc (ntofntt X0))))):fofType
% 4.58/5.16 ntofn:=(fun (X0:fofType)=> (ntofrt (rtofn X0))):(fofType->fofType)
% 4.58/5.16 ntofntt:=(fun (X0:fofType)=> (ntofrp (rpofntt X0))):(fofType->fofType)
% 4.58/5.16 ntofrl:=(((soft nat) real) ((d_Sigma nat) rlofnt)):(fofType->fofType)
% 4.58/5.16 ntofrp:=(((soft nat) cut) ((d_Sigma nat) rpofnt)):(fofType->fofType)
% 4.58/5.16 ntofrt:=((out rat) natrt):(fofType->fofType)
% 4.58/5.16 nttofnt:=(fun (X0:fofType)=> (nttofrp (rpofnt X0))):(fofType->fofType)
% 4.58/5.16 nttofrp:=((out cut) natrp):(fofType->fofType)
% 4.58/5.16 num:=(first1 nat):(fofType->fofType)
% 4.58/5.16 obvious:=((imp False) False):Prop
% 4.58/5.16 omega:=((d_Sep (univof emptyset)) nat_p):fofType
% 4.58/5.16 omega_nat_p:(forall (X0:fofType), (((in X0) omega)->(nat_p X0)))
% 4.58/5.16 one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))):(fofType->((fofType->Prop)->Prop))
% 4.58/5.16 oneax:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1))))
% 4.58/5.16 or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.58/5.16 or:(Prop->(Prop->Prop))
% 4.58/5.16 or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 4.58/5.16 or_first:=(fun (A:Prop) (B:Prop)=> (((((or_ind A) B) ((B->A)->A)) (fun (x:A) (x0:(B->A))=> x)) (fun (x:B) (x0:(B->A))=> (x0 x)))):(forall (A:Prop) (B:Prop), (((or A) B)->((B->A)->A)))
% 4.58/5.16 or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 4.58/5.16 or_introl:(forall (A:Prop) (B:Prop), (A->((or A) B)))
% 4.58/5.16 or_intror:(forall (A:Prop) (B:Prop), (B->((or A) B)))
% 4.58/5.16 or_second:=(fun (A:Prop) (B:Prop) (x:((or A) B))=> (((or_first B) A) (((or_comm_i A) B) x))):(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B)))
% 4.58/5.16 ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0))):(fofType->fofType)
% 4.58/5.16 ordsucc_inj:(forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1)))
% 4.58/5.16 orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.58/5.16 orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))):(Prop->(Prop->Prop))
% 4.58/5.16 otax1:(forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 4.58/5.16 otax2:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2)))))
% 4.58/5.16 out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))):(fofType->((fofType->Prop)->(fofType->fofType)))
% 4.58/5.16 outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType))
% 4.58/5.16 p1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (negd X1))):(fofType->(fofType->Prop))
% 4.58/5.16 p1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (posd X1))):(fofType->(fofType->Prop))
% 4.58/5.16 pair1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2)))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))):(fofType->fofType)
% 4.58/5.16 pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))):(fofType->(fofType->fofType))
% 4.58/5.16 pair_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1))))))
% 4.58/5.16 pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)):(fofType->Prop)
% 4.58/5.16 pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 pair_u0:=(inn n_2):(fofType->fofType)
% 4.58/5.16 pairis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2))))
% 4.58/5.16 pdofnt:=(fun (X0:fofType)=> (pdofrp (rpofnt X0))):(fofType->fofType)
% 4.58/5.16 pdofrp:=(fun (X0:fofType)=> ((rp_df ((rp_pl X0) d_1rp)) d_1rp)):(fofType->fofType)
% 4.58/5.16 perm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injseq X0) X1) X2)) (((surjseq X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->fofType)
% 4.58/5.16 plusdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_pd X0) X1)))))):fofType
% 4.58/5.16 plusfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_pf X0) X1)))))):fofType
% 4.58/5.16 pofrp:=(fun (X0:fofType)=> (realof (pdofrp X0))):(fofType->fofType)
% 4.58/5.16 pos:=(fun (X0:fofType)=> ((l_some dif) (propp X0))):(fofType->Prop)
% 4.58/5.16 posd:=(fun (X0:fofType)=> ((rp_more (stm X0)) (std X0))):(fofType->Prop)
% 4.58/5.16 power:(fofType->fofType)
% 4.58/5.16 pr1:=(fun (X0:fofType)=> rpofp):(fofType->(fofType->fofType))
% 4.58/5.16 prod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((prodprop X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 prodprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_ts X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.58/5.16 prodprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((prodprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj)):(fofType->fofType)
% 4.58/5.16 proj0_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0)))
% 4.58/5.16 proj0_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0))
% 4.58/5.16 proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 4.58/5.16 proj1_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))
% 4.58/5.16 proj1_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1))
% 4.58/5.16 proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 4.58/5.16 proj_Sigma_eta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)))
% 4.58/5.16 proofsirrelevant:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->((all_of (fun (X5:fofType)=> ((in X5) real))) (fun (X5:fofType)=> ((intrl X5)->(((r_lessis X1) X5)->(((r_lessis X5) X0)->(((r_is X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))))))))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 prop1:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3)))):(Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.58/5.16 prop1d:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (posd X1)) (posd X2)) ((rp_eq X0) ((rp_md X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 prop1t:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((nt_is ((ap X0) ((ap suct) X1))) ((ap suct) ((ap X0) X1)))))):(fofType->Prop)
% 4.58/5.16 prop2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))
% 4.58/5.16 prop2d:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) ((prop1d X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 prop2t:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (prop1t X1))):(fofType->(fofType->Prop))
% 4.58/5.16 prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->Prop)
% 4.58/5.16 propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.58/5.16 propn:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (negd X1))):(fofType->(fofType->Prop))
% 4.58/5.16 propp:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (posd X1))):(fofType->(fofType->Prop))
% 4.58/5.16 ps1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> rpofp):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 r_0:=(realof ((rp_df d_1rp) d_1rp)):fofType
% 4.58/5.16 r_all:=(all real):((fofType->Prop)->Prop)
% 4.58/5.16 r_class:=((ecect dif) rp_eq):(fofType->fofType)
% 4.58/5.16 r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))):(Prop->(Prop->Prop))
% 4.58/5.16 r_fixf:=((fixfu dif) rp_eq):(fofType->(fofType->Prop))
% 4.58/5.16 r_in:=(esti real):(fofType->(fofType->Prop))
% 4.58/5.16 r_inn:=(esti dif):(fofType->(fofType->Prop))
% 4.58/5.16 r_is:=(e_is real):(fofType->(fofType->Prop))
% 4.58/5.16 r_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))))))):(fofType->(fofType->Prop))
% 4.58/5.16 r_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_less X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 r_m0:=((indreal real) m0dr):(fofType->fofType)
% 4.58/5.16 r_mn:=(fun (X0:fofType) (X1:fofType)=> ((r_pl X0) (r_m0 X1))):(fofType->(fofType->fofType))
% 4.58/5.16 r_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))))))):(fofType->(fofType->Prop))
% 4.58/5.16 r_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_more X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 r_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 r_one:=(one real):((fofType->Prop)->Prop)
% 4.58/5.16 r_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind real) (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.58/5.16 r_pl:=((indreal2 real) plusdr):(fofType->(fofType->fofType))
% 4.58/5.16 r_schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind real) ((d_5r205_prop3 X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 r_some:=(l_some real):((fofType->Prop)->Prop)
% 4.58/5.16 r_sqrt:=(fun (X0:fofType)=> ((ind real) (fun (X1:fofType)=> ((d_and (d_not (neg X1))) ((r_is ((r_ts X1) X1)) X0))))):(fofType->fofType)
% 4.58/5.16 r_ts:=((indreal2 real) timesdr):(fofType->(fofType->fofType))
% 4.58/5.16 rat:=((ect frac) n_eq):fofType
% 4.58/5.16 ratd:=(fun (X0:fofType)=> ((d_not (zero X0))->(ratrp (rpofpd (absd X0))))):(fofType->Prop)
% 4.58/5.16 ratof:=((ectelt frac) n_eq):(fofType->fofType)
% 4.58/5.16 ratrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (ratd X1))))):(fofType->Prop)
% 4.58/5.16 ratrp:=(((image rat) cut) ((d_Sigma rat) rpofrt)):(fofType->Prop)
% 4.58/5.16 ratset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rt_less X1) X0)))):(fofType->fofType)
% 4.58/5.16 ratt:=((d_Sep cut) ratrp):fofType
% 4.58/5.16 real:=((ect dif) rp_eq):fofType
% 4.58/5.16 realof:=((ectelt dif) rp_eq):(fofType->fofType)
% 4.58/5.16 refis:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1))))
% 4.58/5.16 relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% 4.58/5.16 repl:(fofType->((fofType->fofType)->fofType))
% 4.58/5.16 right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.16 right:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.16 rlofnt:=(fun (X0:fofType)=> (realof (pdofnt X0))):(fofType->fofType)
% 4.58/5.16 rp1:=(fun (X0:fofType)=> ((rp_pl X0) d_1rp)):(fofType->fofType)
% 4.58/5.16 rp_all:=(all cut):((fofType->Prop)->Prop)
% 4.58/5.16 rp_df:=(pair1 cut):(fofType->(fofType->fofType))
% 4.58/5.16 rp_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((diffprop2 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.16 rp_eq:=(fun (X0:fofType) (X1:fofType)=> ((rp_is ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_in:=(esti cut):(fofType->(fofType->Prop))
% 4.58/5.16 rp_is:=(e_is cut):(fofType->(fofType->Prop))
% 4.58/5.16 rp_less:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((urt X0) X2)) ((lrt X1) X2))))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessd X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_less X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_md:=(fun (X0:fofType) (X1:fofType)=> ((rp_pd X0) (m0d X1))):(fofType->(fofType->fofType))
% 4.58/5.16 rp_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.58/5.16 rp_more:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((lrt X0) X2)) ((urt X1) X2))))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_more X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((mored X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_nt_1t:=(nttofnt n_1):fofType
% 4.58/5.16 rp_nt_all:=(all nt_natt):((fofType->Prop)->Prop)
% 4.58/5.16 rp_nt_cond1:=(rp_nt_in rp_nt_1t):(fofType->Prop)
% 4.58/5.16 rp_nt_cond2:=(fun (X0:fofType)=> (rp_nt_all (fun (X1:fofType)=> ((imp ((rp_nt_in X1) X0)) ((rp_nt_in ((ap nt_suct) X1)) X0))))):(fofType->Prop)
% 4.58/5.16 rp_nt_in:=(esti nt_natt):(fofType->(fofType->Prop))
% 4.58/5.16 rp_nt_is:=(e_is nt_natt):(fofType->(fofType->Prop))
% 4.58/5.16 rp_nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_nt_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rp_nt_one:=(one nt_natt):((fofType->Prop)->Prop)
% 4.58/5.16 rp_nt_some:=(l_some nt_natt):((fofType->Prop)->Prop)
% 4.58/5.16 rp_one:=(one cut):((fofType->Prop)->Prop)
% 4.58/5.16 rp_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.58/5.16 rp_pd:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl (stm X0)) (stm X1))) ((rp_pl (std X0)) (std X1)))):(fofType->(fofType->fofType))
% 4.58/5.16 rp_pl:=(fun (X0:fofType) (X1:fofType)=> (cutof ((sum X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 rp_some:=(l_some cut):((fofType->Prop)->Prop)
% 4.58/5.16 rp_td:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl ((rp_ts (stm X0)) (stm X1))) ((rp_ts (std X0)) (std X1)))) ((rp_pl ((rp_ts (stm X0)) (std X1))) ((rp_ts (std X0)) (stm X1))))):(fofType->(fofType->fofType))
% 4.58/5.16 rp_ts:=(fun (X0:fofType) (X1:fofType)=> (cutof ((prod X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.16 rpofn:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (nofrp X1))))):(fofType->fofType)
% 4.58/5.16 rpofnd:=(fun (X0:fofType)=> ((rp_mn (std X0)) (stm X0))):(fofType->fofType)
% 4.58/5.16 rpofnt:=(fun (X0:fofType)=> (rpofrt (rtofn X0))):(fofType->fofType)
% 4.58/5.16 rpofntt:=((e_in cut) natrp):(fofType->fofType)
% 4.58/5.16 rpofp:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (pofrp X1))))):(fofType->fofType)
% 4.58/5.16 rpofpd:=(fun (X0:fofType)=> ((rp_mn (stm X0)) (std X0))):(fofType->fofType)
% 4.58/5.16 rpofrt:=(fun (X0:fofType)=> (cutof (ratset X0))):(fofType->fofType)
% 4.58/5.16 rpofrtt:=((e_in cut) ratrp):(fofType->fofType)
% 4.58/5.16 rt_all:=(all rat):((fofType->Prop)->Prop)
% 4.58/5.16 rt_in:=(esti rat):(fofType->(fofType->Prop))
% 4.58/5.16 rt_is:=(e_is rat):(fofType->(fofType->Prop))
% 4.58/5.16 rt_lb:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((iii1_lbprop X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rt_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))))):(fofType->(fofType->Prop))
% 4.58/5.16 rt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rt_min:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_lb X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop))
% 4.58/5.16 rt_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.58/5.16 rt_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))))):(fofType->(fofType->Prop))
% 4.58/5.16 rt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rt_one:=(one rat):((fofType->Prop)->Prop)
% 4.58/5.16 rt_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.58/5.16 rt_pl:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) plusfrt)):(fofType->(fofType->fofType))
% 4.58/5.16 rt_some:=(l_some rat):((fofType->Prop)->Prop)
% 4.58/5.16 rt_ts:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) timesfrt)):(fofType->(fofType->fofType))
% 4.58/5.16 rt_ub:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((ubprop X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.16 rtc:=(fun (X0:fofType)=> (cutof (sqrtset X0))):(fofType->fofType)
% 4.58/5.16 rtofn:=(fun (X0:fofType)=> (ratof ((n_fr X0) n_1))):(fofType->fofType)
% 4.58/5.16 rtofnt:=((e_in rat) natrt):(fofType->fofType)
% 4.58/5.16 rtofrp:=(((soft rat) cut) ((d_Sigma rat) rpofrt)):(fofType->fofType)
% 4.58/5.16 rtofrtt:=(fun (X0:fofType)=> (rtofrp (rpofrtt X0))):(fofType->fofType)
% 4.58/5.16 rtt_all:=(all ratt):((fofType->Prop)->Prop)
% 4.58/5.16 rtt_is:=(e_is ratt):(fofType->(fofType->Prop))
% 4.58/5.16 rtt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rtt_is X0) X1))):(fofType->(fofType->Prop))
% 4.58/5.17 rtt_one:=(one ratt):((fofType->Prop)->Prop)
% 4.58/5.17 rtt_some:=(l_some ratt):((fofType->Prop)->Prop)
% 4.58/5.17 rttofrp:=((out cut) ratrp):(fofType->fofType)
% 4.58/5.17 rttofrt:=(fun (X0:fofType)=> (rttofrp (rpofrt X0))):(fofType->fofType)
% 4.58/5.17 s01:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_lessis X1) X0)))):(fofType->fofType)
% 4.58/5.17 s02:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_more X1) X0)))):(fofType->fofType)
% 4.58/5.17 s11:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_less X1) X0)))):(fofType->fofType)
% 4.58/5.17 s12:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_moreis X1) X0)))):(fofType->fofType)
% 4.58/5.17 satz100:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.58/5.17 satz100a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.58/5.17 satz101:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_one (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 4.58/5.17 satz101a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_some (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 4.58/5.17 satz101b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_pl X1) X2)) X0)->(((rt_is ((rt_pl X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 4.58/5.17 satz101c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl X1) ((rt_mn X0) X1))) X0))))))
% 4.58/5.17 satz101d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl X1) ((rt_mn X0) X1))))))))
% 4.58/5.17 satz101e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl ((rt_mn X0) X1)) X1)) X0))))))
% 4.58/5.17 satz101f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl ((rt_mn X0) X1)) X1)))))))
% 4.58/5.17 satz101g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_is ((rt_pl X1) X2)) X0)->((rt_is X2) ((rt_mn X0) X1))))))))))
% 4.58/5.17 satz102:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X0) X1)) ((rt_ts X1) X0))))))
% 4.58/5.17 satz103:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts ((rt_ts X0) X1)) X2)) ((rt_ts X0) ((rt_ts X1) X2)))))))))
% 4.58/5.17 satz104:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts X0) ((rt_pl X1) X2))) ((rt_pl ((rt_ts X0) X1)) ((rt_ts X0) X2)))))))))
% 4.58/5.17 satz105a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.58/5.17 satz105b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.58/5.17 satz105c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.58/5.17 satz105d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.58/5.17 satz105e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.58/5.17 satz105f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.58/5.17 satz106a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_more X0) X1))))))))
% 4.58/5.17 satz106b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_is X0) X1))))))))
% 4.58/5.17 satz106c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_less X0) X1))))))))
% 4.58/5.17 satz107:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.58/5.17 satz107a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.58/5.17 satz108a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.58/5.17 satz108b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.58/5.17 satz108c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.58/5.17 satz108d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.58/5.17 satz109:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.58/5.17 satz109a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.58/5.17 satz10:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.58/5.17 satz10a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.58/5.17 satz10b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.58/5.17 satz10c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1)))))))
% 4.58/5.17 satz10d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1)))))))
% 4.58/5.17 satz10e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1))))))
% 4.58/5.17 satz10f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1))))))
% 4.58/5.17 satz10g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1)))))))
% 4.58/5.17 satz10h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1)))))))
% 4.58/5.17 satz10j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1))))))
% 4.58/5.17 satz10k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1))))))
% 4.58/5.17 satz110:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_one (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 4.58/5.17 satz110a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 4.58/5.17 satz110b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->(((rt_is ((rt_ts X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 4.58/5.17 satz110c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X1) ((rt_ov X0) X1))) X0)))))
% 4.58/5.17 satz110d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts X1) ((rt_ov X0) X1)))))))
% 4.58/5.17 satz110e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov X0) X1)) X1)) X0)))))
% 4.58/5.17 satz110f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts ((rt_ov X0) X1)) X1))))))
% 4.58/5.17 satz110g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->((rt_is X2) ((rt_ov X0) X1)))))))))
% 4.58/5.17 satz111a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))->((d_29_ii X0) X1))))))
% 4.58/5.17 satz111b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))->((n_is X0) X1))))))
% 4.58/5.17 satz111c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))->((iii X0) X1))))))
% 4.58/5.17 satz111d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((moref ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.58/5.17 satz111e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is X0) X1)->((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.58/5.17 satz111f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.58/5.17 satz111g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->(n_one (natprop X0)))))
% 4.58/5.17 satz112a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_pf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_pl X0) X1)) n_1))))))
% 4.58/5.17 satz112b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_tf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_ts X0) X1)) n_1))))))
% 4.58/5.17 satz112c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_pl (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_pl X0) X1)))))))))
% 4.58/5.17 satz112d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_pl X0) X1))))))))
% 4.58/5.17 satz112e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_ts (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_ts X0) X1)))))))))
% 4.58/5.17 satz112f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_ts X0) X1))))))))
% 4.58/5.17 satz112g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(((rt_more X0) X1)->(natrt ((rt_mn X0) X1)))))))))
% 4.58/5.17 satz112h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_pl (rtofn X0)) (rtofn X1))) (rtofn ((n_pl X0) X1)))))))
% 4.58/5.17 satz112j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X0)) (rtofn X1))) (rtofn ((n_ts X0) X1)))))))
% 4.58/5.17 satz113a:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((nt_nis ((ap suct) X0)) nt_1t)))
% 4.58/5.17 satz113b:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_is ((ap suct) X0)) ((ap suct) X1))->((nt_is X0) X1))))))
% 4.58/5.17 satz113c:((all_of (fun (X0:fofType)=> ((in X0) (power natt)))) (fun (X0:fofType)=> ((nt_cond1 X0)->((nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((nt_in X1) X0)))))))
% 4.58/5.17 satz114:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((rt_is ((rt_ts (rtofn (den X0))) (ratof X0))) (rtofn (num X0)))))
% 4.58/5.17 satz114a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X1)) (ratof ((n_fr X0) X1)))) (rtofn X0))))))
% 4.58/5.17 satz114b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is (ratof ((n_fr X0) X1))) ((rt_ov (rtofn X0)) (rtofn X1)))))))
% 4.58/5.17 satz114c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ov (rtofn X0)) (rtofn X1))) (ratof ((n_fr X0) X1)))))))
% 4.58/5.17 satz115:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (n_some (fun (X2:fofType)=> ((rt_more ((rt_ts (rtofn X2)) X0)) X1)))))))
% 4.58/5.17 satz115a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and (natrt X2)) ((rt_more ((rt_ts X2) X0)) X1))))))))
% 4.58/5.17 satz116:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) X0)))
% 4.58/5.17 satz117:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_is X0) X1)->((rp_is X1) X0))))))
% 4.58/5.17 satz118:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->(((rp_is X1) X2)->((rp_is X0) X2)))))))))
% 4.58/5.17 satz119:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X2) X1)->((urt X0) X2)))))))))
% 4.58/5.17 satz119a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X1) X2)->((urt X0) X2)))))))))
% 4.58/5.17 satz11:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0))))))
% 4.58/5.17 satz120:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X2) X1)->((lrt X0) X2)))))))))
% 4.58/5.17 satz120a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X1) X2)->((lrt X0) X2)))))))))
% 4.58/5.17 satz121:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_less X1) X0))))))
% 4.58/5.17 satz122:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->((rp_more X1) X0))))))
% 4.58/5.17 satz123:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((orec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.58/5.17 satz123c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->(d_not ((rp_less X0) X1)))))))
% 4.58/5.17 satz123d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->(d_not ((rp_more X0) X1)))))))
% 4.58/5.17 satz123e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_more X0) X1))->((rp_lessis X0) X1))))))
% 4.58/5.17 satz123f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_less X0) X1))->((rp_moreis X0) X1))))))
% 4.58/5.17 satz123g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(d_not ((rp_lessis X0) X1)))))))
% 4.58/5.17 satz123h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(d_not ((rp_moreis X0) X1)))))))
% 4.58/5.17 satz123j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_moreis X0) X1))->((rp_less X0) X1))))))
% 4.58/5.17 satz123k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_lessis X0) X1))->((rp_more X0) X1))))))
% 4.58/5.17 satz124:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->((rp_lessis X1) X0))))))
% 4.58/5.17 satz125:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->((rp_moreis X1) X0))))))
% 4.58/5.17 satz126:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 4.58/5.17 satz127a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 4.58/5.17 satz127b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_lessis X1) X2)->((rp_less X0) X2)))))))))
% 4.58/5.17 satz127c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_moreis X0) X1)->(((rp_more X1) X2)->((rp_more X0) X2)))))))))
% 4.58/5.17 satz127d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_moreis X1) X2)->((rp_more X0) X2)))))))))
% 4.58/5.17 satz128:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X1) X2)->((rp_lessis X0) X2)))))))))
% 4.58/5.17 satz129:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((sum X0) X1))))))
% 4.58/5.17 satz129a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_pl X2) X3)) ((sum X0) X1)))))))))))))
% 4.58/5.17 satz12:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0))))))
% 4.58/5.17 satz130:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_pl X0) X1)) ((rp_pl X1) X0))))))
% 4.58/5.17 satz131:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_pl ((rp_pl X0) X1)) X2)) ((rp_pl X0) ((rp_pl X1) X2)))))))))
% 4.58/5.17 satz132:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (fun (X3:fofType)=> ((d_and ((d_and ((lrt X0) X2)) ((urt X0) X3))) (((d_and ((lrt X0) X2)) ((urt X0) X3))->((rt_is ((rt_mn X3) X2)) X1)))))))))))
% 4.58/5.17 satz132app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (forall (X1:Prop), ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((lrt X0) X3)->((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((urt X0) X4)->(((rt_is ((rt_mn X4) X3)) X2)->X1)))))))->X1))))))
% 4.58/5.17 satz133:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_more ((rp_pl X0) X1)) X0)))))
% 4.58/5.17 satz133a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_less X0) ((rp_pl X0) X1))))))
% 4.58/5.17 satz134:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.58/5.17 satz135b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.58/5.17 satz135c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.58/5.17 satz135d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.58/5.17 satz135e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.58/5.17 satz135f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.58/5.17 satz135g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz135h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 4.58/5.17 satz135j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz135k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 4.58/5.17 satz136a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_more X0) X1))))))))
% 4.58/5.17 satz136b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_is X0) X1))))))))
% 4.58/5.17 satz136c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_less X0) X1))))))))
% 4.58/5.17 satz136d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_more X0) X1))))))))
% 4.58/5.17 satz136e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_is X0) X1))))))))
% 4.58/5.17 satz136f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_less X0) X1))))))))
% 4.58/5.17 satz137:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz137a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz138a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz138b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz138c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz138d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz139:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz139a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.58/5.17 satz13:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0))))))
% 4.58/5.17 satz140:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_one (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 4.58/5.17 satz140a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_some (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 4.58/5.17 satz140b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_pl X1) X2)) X0)->(((rp_is ((rp_pl X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 4.58/5.17 satz140c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl X1) ((rp_mn X0) X1))) X0))))))
% 4.58/5.17 satz140d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl X1) ((rp_mn X0) X1))))))))
% 4.58/5.17 satz140e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl ((rp_mn X0) X1)) X1)) X0))))))
% 4.58/5.17 satz140f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl ((rp_mn X0) X1)) X1)))))))
% 4.58/5.17 satz140g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_is ((rp_pl X1) X2)) X0)->((rp_is X2) ((rp_mn X0) X1))))))))))
% 4.58/5.17 satz140h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(cutprop ((diff X0) X1)))))))
% 4.58/5.17 satz141:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((prod X0) X1))))))
% 4.58/5.17 satz141a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_ts X2) X3)) ((prod X0) X1)))))))))))))
% 4.58/5.17 satz141b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov d_1rt) X1)) X0)) ((rt_ov X0) X1))))))
% 4.58/5.17 satz141c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ov X0) X1)) ((rt_ts ((rt_ov d_1rt) X1)) X0))))))
% 4.58/5.17 satz142:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) ((rp_ts X1) X0))))))
% 4.58/5.17 satz143:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts ((rp_ts X0) X1)) X2)) ((rp_ts X0) ((rp_ts X1) X2)))))))))
% 4.58/5.17 satz144:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts X0) ((rp_pl X1) X2))) ((rp_pl ((rp_ts X0) X1)) ((rp_ts X0) X2)))))))))
% 4.58/5.17 satz145a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.58/5.17 satz145b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.58/5.17 satz145c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.58/5.17 satz145d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.58/5.17 satz145e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.58/5.17 satz145f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.58/5.17 satz145g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz145h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 4.58/5.17 satz145j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz145k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 4.58/5.17 satz146a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_more X0) X1))))))))
% 4.58/5.17 satz146b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_is X0) X1))))))))
% 4.58/5.17 satz146c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_less X0) X1))))))))
% 4.58/5.17 satz146d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_more X0) X1))))))))
% 4.58/5.17 satz146e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_is X0) X1))))))))
% 4.58/5.17 satz146f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_less X0) X1))))))))
% 4.58/5.17 satz147:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz147a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz148a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz148b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz148c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz148d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz149:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz149a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.58/5.17 satz14:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0))))))
% 4.58/5.17 satz150:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (cutprop (ratset X0))))
% 4.58/5.17 satz151:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) d_1rp)) X0)))
% 4.58/5.17 satz151a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts X0) d_1rp))))
% 4.58/5.17 satz151b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts d_1rp) X0)) X0)))
% 4.58/5.17 satz151c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts d_1rp) X0))))
% 4.58/5.17 satz152:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_some (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) d_1rp)))))
% 4.58/5.17 satz153:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_one (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 4.58/5.17 satz153a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 4.58/5.17 satz153b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->(((rp_is ((rp_ts X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 4.58/5.17 satz153c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) ((rp_ov X0) X1))) X0)))))
% 4.58/5.17 satz153d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts X1) ((rp_ov X0) X1)))))))
% 4.58/5.17 satz153e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts ((rp_ov X0) X1)) X1)) X0)))))
% 4.58/5.17 satz153f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts ((rp_ov X0) X1)) X1))))))
% 4.58/5.17 satz153g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->((rp_is X2) ((rp_ov X0) X1)))))))))
% 4.58/5.17 satz154a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_more (rpofrt X0)) (rpofrt X1)))))))
% 4.58/5.17 satz154b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rp_is (rpofrt X0)) (rpofrt X1)))))))
% 4.58/5.17 satz154c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rp_less (rpofrt X0)) (rpofrt X1)))))))
% 4.58/5.17 satz154d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_more (rpofrt X0)) (rpofrt X1))->((rt_more X0) X1))))))
% 4.58/5.17 satz154e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_is (rpofrt X0)) (rpofrt X1))->((rt_is X0) X1))))))
% 4.58/5.17 satz154f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X0)) (rpofrt X1))->((rt_less X0) X1))))))
% 4.58/5.17 satz155a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_pl X0) X1))) ((rp_pl (rpofrt X0)) (rpofrt X1)))))))
% 4.58/5.17 satz155b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_is (rpofrt ((rt_mn X0) X1))) ((rp_mn (rpofrt X0)) (rpofrt X1))))))))
% 4.58/5.17 satz155c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ts X0) X1))) ((rp_ts (rpofrt X0)) (rpofrt X1)))))))
% 4.58/5.17 satz155d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ov X0) X1))) ((rp_ov (rpofrt X0)) (rpofrt X1)))))))
% 4.58/5.17 satz155e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_pl X0) X1))) ((rp_pl (rpofnt X0)) (rpofnt X1)))))))
% 4.58/5.17 satz155f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_ts X0) X1))) ((rp_ts (rpofnt X0)) (rpofnt X1)))))))
% 4.58/5.17 satz156a:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((rp_nt_nis ((ap nt_suct) X0)) rp_nt_1t)))
% 4.58/5.17 satz156b:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> (((rp_nt_is ((ap nt_suct) X0)) ((ap nt_suct) X1))->((rp_nt_is X0) X1))))))
% 4.58/5.17 satz156c:((all_of (fun (X0:fofType)=> ((in X0) (power nt_natt)))) (fun (X0:fofType)=> ((rp_nt_cond1 X0)->((rp_nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> ((rp_nt_in X1) X0)))))))
% 4.58/5.17 satz157a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->((rt_min ((d_Sep rat) (urt X0))) (rtofrp X0)))))
% 4.58/5.17 satz157b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->(rt_some (rt_min ((d_Sep rat) (urt X0)))))))
% 4.58/5.17 satz157c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_min ((d_Sep rat) (urt X0))) X1)->((rp_is X0) (rpofrt X1)))))))
% 4.58/5.17 satz157d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rt_some (rt_min ((d_Sep rat) (urt X0))))->(ratrp X0))))
% 4.58/5.17 satz158a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((rp_less (rpofrt X1)) X0))))))
% 4.58/5.17 satz158b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((rp_moreis (rpofrt X1)) X0))))))
% 4.58/5.17 satz158c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X1)) X0)->((lrt X0) X1))))))
% 4.58/5.17 satz158d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_moreis (rpofrt X1)) X0)->((urt X0) X1))))))
% 4.58/5.17 satz159:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rp_less X0) (rpofrt X2))) ((rp_less (rpofrt X2)) X1)))))))))
% 4.58/5.17 satz159a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rp_some (fun (X2:fofType)=> (((and3 (ratrp X2)) ((rp_less X0) X2)) ((rp_less X2) X1)))))))))
% 4.58/5.17 satz159app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(forall (X2:Prop), (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rp_less X0) (rpofrt X3))->(((rp_less (rpofrt X3)) X1)->X2))))->X2)))))))
% 4.58/5.17 satz15:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 4.58/5.17 satz160:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(rt_some (fun (X3:fofType)=> (rt_some (fun (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2)))))))))))))
% 4.58/5.17 satz160app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(forall (X3:Prop), (((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((rp_more (rpofrt X4)) X0)->((all_of (fun (X5:fofType)=> ((in X5) rat))) (fun (X5:fofType)=> (((rp_more (rpofrt X5)) X1)->(((rt_is ((rt_ts X4) X5)) X2)->X3)))))))->X3)))))))))
% 4.58/5.17 satz161:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_one (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))))
% 4.58/5.17 satz162:(rp_some irratrp)
% 4.58/5.17 satz163:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) X0)))
% 4.58/5.17 satz164:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is X1) X0))))))
% 4.58/5.17 satz165:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->(((r_is X1) X2)->((r_is X0) X2)))))))))
% 4.58/5.17 satz166a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(pos (abs X0)))))
% 4.58/5.17 satz166b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (abs X0)))))
% 4.58/5.17 satz166c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 4.58/5.17 satz166d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 4.58/5.17 satz166e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_nis X0) r_0)->(pos (abs X0)))))
% 4.58/5.17 satz166f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (abs X0)) r_0))))
% 4.58/5.17 satz167:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((orec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.58/5.17 satz167a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((or3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.58/5.17 satz167b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((ec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.58/5.17 satz167c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->(d_not ((r_less X0) X1)))))))
% 4.58/5.17 satz167d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->(d_not ((r_more X0) X1)))))))
% 4.58/5.17 satz167e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_more X0) X1))->((r_lessis X0) X1))))))
% 4.58/5.17 satz167f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_less X0) X1))->((r_moreis X0) X1))))))
% 4.58/5.17 satz167g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(d_not ((r_lessis X0) X1)))))))
% 4.58/5.17 satz167h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(d_not ((r_moreis X0) X1)))))))
% 4.58/5.17 satz167j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_moreis X0) X1))->((r_less X0) X1))))))
% 4.58/5.17 satz167k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_lessis X0) X1))->((r_more X0) X1))))))
% 4.58/5.17 satz168a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->((r_lessis X1) X0))))))
% 4.58/5.17 satz168b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->((r_moreis X1) X0))))))
% 4.58/5.17 satz169a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->((r_more X0) r_0))))
% 4.58/5.17 satz169b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_more X0) r_0)->(pos X0))))
% 4.58/5.17 satz169c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->((r_less X0) r_0))))
% 4.58/5.17 satz169d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_less X0) r_0)->(neg X0))))
% 4.58/5.17 satz16a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 4.58/5.17 satz16b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2)))))))))
% 4.58/5.17 satz16c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2)))))))))
% 4.58/5.17 satz16d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2)))))))))
% 4.58/5.17 satz170:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_moreis (abs X0)) r_0)))
% 4.58/5.17 satz170a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (d_not (neg (abs X0)))))
% 4.58/5.17 satz171:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_less X1) X2)->((r_less X0) X2)))))))))
% 4.58/5.17 satz172a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_less X1) X2)->((r_less X0) X2)))))))))
% 4.58/5.17 satz172b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_lessis X1) X2)->((r_less X0) X2)))))))))
% 4.58/5.17 satz172c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_moreis X0) X1)->(((r_more X1) X2)->((r_more X0) X2)))))))))
% 4.58/5.17 satz172d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->(((r_moreis X1) X2)->((r_more X0) X2)))))))))
% 4.58/5.17 satz173:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_lessis X1) X2)->((r_lessis X0) X2)))))))))
% 4.58/5.17 satz174:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((intrl X0)->(ratrl X0))))
% 4.58/5.17 satz175:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X0) X1)) ((r_pl X1) X0))))))
% 4.58/5.17 satz176a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(neg (r_m0 X0)))))
% 4.58/5.17 satz176b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (r_m0 X0)) r_0))))
% 4.58/5.17 satz176c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (r_m0 X0)))))
% 4.58/5.17 satz176d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg (r_m0 X0))->(pos X0))))
% 4.58/5.17 satz176e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is (r_m0 X0)) r_0)->((r_is X0) r_0))))
% 4.58/5.17 satz176f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos (r_m0 X0))->(neg X0))))
% 4.58/5.17 satz177:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (r_m0 (r_m0 X0))) X0)))
% 4.58/5.17 satz177a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) (r_m0 (r_m0 X0)))))
% 4.58/5.17 satz177b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is (r_m0 X0)) X1))))))
% 4.58/5.17 satz177c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is X1) (r_m0 X0)))))))
% 4.58/5.17 satz177d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) X1)->((r_is X0) (r_m0 X1)))))))
% 4.58/5.17 satz177e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) X1)->((r_is (r_m0 X1)) X0))))))
% 4.58/5.17 satz178:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs (r_m0 X0))) (abs X0))))
% 4.58/5.17 satz178a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs X0)) (abs (r_m0 X0)))))
% 4.58/5.17 satz179:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl X0) (r_m0 X0))) r_0)))
% 4.58/5.17 satz179a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl (r_m0 X0)) X0)) r_0)))
% 4.58/5.17 satz17:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((lessis X1) X2)->((lessis X0) X2)))))))))
% 4.58/5.17 satz180:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_pl X0) X1))) ((r_pl (r_m0 X0)) (r_m0 X1)))))))
% 4.58/5.17 satz180a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl (r_m0 X0)) (r_m0 X1))) (r_m0 ((r_pl X0) X1)))))))
% 4.58/5.17 satz181:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_mn X0) X1))) ((r_mn X1) X0))))))
% 4.58/5.17 satz181a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_mn X0) X1)) (r_m0 ((r_mn X1) X0)))))))
% 4.58/5.17 satz182a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_mn X0) X1))->((r_more X0) X1))))))
% 4.58/5.17 satz182b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_mn X0) X1)) r_0)->((r_is X0) X1))))))
% 4.58/5.17 satz182c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_mn X0) X1))->((r_less X0) X1))))))
% 4.58/5.17 satz182d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(pos ((r_mn X0) X1)))))))
% 4.58/5.17 satz182e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is ((r_mn X0) X1)) r_0))))))
% 4.58/5.17 satz182f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(neg ((r_mn X0) X1)))))))
% 4.58/5.17 satz183a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->((r_less (r_m0 X0)) (r_m0 X1)))))))
% 4.58/5.17 satz183b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is (r_m0 X0)) (r_m0 X1)))))))
% 4.58/5.17 satz183c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->((r_more (r_m0 X0)) (r_m0 X1)))))))
% 4.58/5.17 satz183d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less (r_m0 X0)) (r_m0 X1))->((r_more X0) X1))))))
% 4.58/5.17 satz183e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) (r_m0 X1))->((r_is X0) X1))))))
% 4.58/5.17 satz183f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more (r_m0 X0)) (r_m0 X1))->((r_less X0) X1))))))
% 4.58/5.17 satz184:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (r_some (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))))))))
% 4.58/5.17 satz185:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((r_is ((r_pl ((r_mn X0) X1)) ((r_mn X2) X3))) ((r_mn ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))
% 4.58/5.17 satz186:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_pl ((r_pl X0) X1)) X2)) ((r_pl X0) ((r_pl X1) X2)))))))))
% 4.58/5.17 satz187:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_one (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0)))))))
% 4.58/5.17 satz187a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X1) ((r_mn X0) X1))) X0)))))
% 4.58/5.17 satz187b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0)))))))
% 4.58/5.17 satz187c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is ((r_mn X0) X1)) X2))))))))
% 4.58/5.17 satz187d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is X2) ((r_mn X0) X1)))))))))
% 4.58/5.17 satz187e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is ((r_mn X0) X1)) X2))))))))
% 4.58/5.17 satz187f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is X2) ((r_mn X0) X1)))))))))
% 4.58/5.17 satz188a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X0) X2)) ((r_pl X1) X2))->((r_more X0) X1))))))))
% 4.58/5.17 satz188b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X0) X2)) ((r_pl X1) X2))->((r_is X0) X1))))))))
% 4.58/5.17 satz188c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X0) X2)) ((r_pl X1) X2))->((r_less X0) X1))))))))
% 4.58/5.17 satz188d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 4.58/5.17 satz188e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 4.58/5.17 satz188f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 4.58/5.17 satz188g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X2) X0)) ((r_pl X2) X1))->((r_more X0) X1))))))))
% 4.58/5.17 satz188h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X0)) ((r_pl X2) X1))->((r_is X0) X1))))))))
% 4.58/5.17 satz188j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X2) X0)) ((r_pl X2) X1))->((r_less X0) X1))))))))
% 4.58/5.17 satz188k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 4.58/5.17 satz188l:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 4.58/5.17 satz188m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 4.58/5.17 satz188n:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz188o:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X2) X0)) ((r_pl X3) X1))))))))))))
% 4.58/5.17 satz188p:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz188q:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X2) X0)) ((r_pl X3) X1))))))))))))
% 4.58/5.17 satz189:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz189a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz18:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0)))))
% 4.58/5.17 satz18a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1))))))
% 4.58/5.17 satz18b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0)))
% 4.58/5.17 satz18c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0))))
% 4.58/5.17 satz190a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz190b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_moreis X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz190c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz190d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_lessis X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz191:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_moreis X2) X3)->((r_moreis ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz191a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_lessis X2) X3)->((r_lessis ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.58/5.17 satz192a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) r_0)->((r_is ((r_ts X0) X1)) r_0))))))
% 4.58/5.17 satz192b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X1) r_0)->((r_is ((r_ts X0) X1)) r_0))))))
% 4.58/5.17 satz192c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_ts X0) X1)) r_0)->((l_or ((r_is X0) r_0)) ((r_is X1) r_0)))))))
% 4.58/5.17 satz192d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X0) r_0)->(((r_nis X1) r_0)->((r_nis ((r_ts X0) X1)) r_0)))))))
% 4.58/5.17 satz193:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (abs ((r_ts X0) X1))) ((r_ts (abs X0)) (abs X1)))))))
% 4.58/5.17 satz193a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (abs X0)) (abs X1))) (abs ((r_ts X0) X1)))))))
% 4.58/5.17 satz194:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts X1) X0))))))
% 4.58/5.17 satz195:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts X0) d_1rl)) X0)))
% 4.58/5.17 satz195a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts X0) d_1rl))))
% 4.58/5.17 satz195b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts d_1rl) X0)) X0)))
% 4.58/5.17 satz195c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts d_1rl) X0))))
% 4.58/5.17 satz196a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))))))))
% 4.58/5.17 satz196b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))))))))
% 4.58/5.17 satz196c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((neg X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))))))))
% 4.58/5.17 satz196d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((pos X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))))))))
% 4.58/5.17 satz196e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1))))))))))
% 4.58/5.17 satz196f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))))
% 4.58/5.17 satz196g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1))))))))
% 4.58/5.17 satz196h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))
% 4.58/5.17 satz197a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) (r_m0 ((r_ts X0) X1)))))))
% 4.58/5.17 satz197b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) (r_m0 ((r_ts X0) X1)))))))
% 4.58/5.17 satz197c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) ((r_ts X0) (r_m0 X1)))))))
% 4.58/5.17 satz197d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) ((r_ts (r_m0 X0)) X1))))))
% 4.58/5.17 satz197e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts (r_m0 X0)) X1))))))
% 4.58/5.17 satz197f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts X0) (r_m0 X1)))))))
% 4.58/5.17 satz198:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) (r_m0 X1))) ((r_ts X0) X1))))))
% 4.58/5.17 satz198a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts (r_m0 X0)) (r_m0 X1)))))))
% 4.58/5.17 satz199:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts ((r_ts X0) X1)) X2)) ((r_ts X0) ((r_ts X1) X2)))))))))
% 4.58/5.17 satz19a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.58/5.17 satz19b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.58/5.17 satz19c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.58/5.17 satz19d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.58/5.17 satz19e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.58/5.17 satz19f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.58/5.17 satz19g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz19h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 4.58/5.17 satz19j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz19k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 4.58/5.17 satz19l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.58/5.17 satz19m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.58/5.17 satz19n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.58/5.17 satz19o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.58/5.17 satz1:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1)))))))
% 4.58/5.17 satz201:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_pl X1) X2))) ((r_pl ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 4.58/5.17 satz202:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_mn X1) X2))) ((r_mn ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 4.58/5.17 satz203a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.58/5.17 satz203b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X0) X2)) ((r_ts X1) X2)))))))))
% 4.58/5.17 satz203c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.58/5.17 satz203d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.58/5.17 satz203e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X2) X0)) ((r_ts X2) X1)))))))))
% 4.58/5.17 satz203f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.58/5.17 satz203g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.58/5.17 satz203j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.58/5.17 satz203k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.58/5.17 satz203m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.58/5.17 satz204:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_one (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 4.58/5.17 satz204a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_some (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 4.58/5.17 satz204b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is ((r_ts X1) X2)) X0)->(((r_is ((r_ts X1) X3)) X0)->((r_is X2) X3))))))))))))
% 4.58/5.17 satz204c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts X1) ((r_ov X0) X1))) X0))))))
% 4.58/5.17 satz204d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts X1) ((r_ov X0) X1))))))))
% 4.58/5.17 satz204e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts ((r_ov X0) X1)) X1)) X0))))))
% 4.58/5.17 satz204f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts ((r_ov X0) X1)) X1)))))))
% 4.58/5.17 satz204g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_nis X1) r_0)->(((r_is ((r_ts X1) X2)) X0)->((r_is X2) ((r_ov X0) X1))))))))))
% 4.58/5.17 satz205:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->(r_one (fun (X2:fofType)=> ((d_and (r_all (fun (X3:fofType)=> (((r_less X3) X2)->((r_in X3) X0))))) (r_all (fun (X3:fofType)=> (((r_more X3) X2)->((r_in X3) X1)))))))))))))))
% 4.58/5.17 satz205a:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X2) ((r_schnitt X0) X1))->((r_in X2) X0))))))))))))
% 4.58/5.17 satz205b:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X2) ((r_schnitt X0) X1))->((r_in X2) X1))))))))))))
% 4.58/5.17 satz20a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1))))))))
% 4.58/5.17 satz20b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1))))))))
% 4.58/5.17 satz20c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1))))))))
% 4.58/5.17 satz20d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1))))))))
% 4.58/5.17 satz20e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1))))))))
% 4.58/5.17 satz20f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1))))))))
% 4.58/5.17 satz21:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz21a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz22a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz22b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz22c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz22d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz23:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz23a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.58/5.17 satz24:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1)))
% 4.58/5.17 satz24a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1))
% 4.58/5.17 satz24b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1)))
% 4.58/5.17 satz24c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0))))
% 4.58/5.17 satz25:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1)))))))
% 4.58/5.17 satz25a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0)))))))
% 4.58/5.17 satz25b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0))))))
% 4.58/5.17 satz25c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0))))))
% 4.58/5.17 satz26:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0))))))
% 4.58/5.17 satz26a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0))))))
% 4.58/5.17 satz26b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0))))))
% 4.58/5.17 satz26c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0))))))
% 4.58/5.17 satz27:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0))))
% 4.58/5.17 satz27a:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0))))
% 4.58/5.17 satz28:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))))))
% 4.58/5.17 satz28a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0)))
% 4.58/5.17 satz28b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0))))))
% 4.58/5.17 satz28c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0)))
% 4.58/5.17 satz28d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1))))))
% 4.58/5.17 satz28e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1))))
% 4.58/5.17 satz28f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1)))))))
% 4.58/5.17 satz28g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0))))
% 4.58/5.17 satz28h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1))))))
% 4.58/5.17 satz29:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))))))
% 4.58/5.17 satz2:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 4.58/5.17 satz30:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))))))))
% 4.58/5.17 satz31:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))))))))
% 4.58/5.17 satz32a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.58/5.17 satz32b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.58/5.17 satz32c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.58/5.17 satz32d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.58/5.17 satz32e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.58/5.17 satz32f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.58/5.17 satz32g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz32h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 4.58/5.17 satz32j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz32k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 4.58/5.17 satz32l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.58/5.17 satz32m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.58/5.17 satz32n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.58/5.17 satz32o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.58/5.17 satz33a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1))))))))
% 4.58/5.17 satz33b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1))))))))
% 4.58/5.17 satz33c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1))))))))
% 4.58/5.17 satz34:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz34a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz35a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz35b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz35c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz35d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz36:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz36a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.58/5.17 satz37:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0)))
% 4.58/5.17 satz38:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0))))))
% 4.58/5.17 satz39:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2)))))))))
% 4.58/5.17 satz3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 4.58/5.17 satz3a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 4.58/5.17 satz40:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1)))))))
% 4.58/5.17 satz40a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0)))))
% 4.58/5.17 satz40b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.58/5.17 satz40c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1))))))))
% 4.58/5.17 satz41:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.58/5.17 satz41a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.58/5.17 satz41b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.58/5.17 satz41c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1)))))))
% 4.58/5.17 satz41d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1)))))))
% 4.58/5.17 satz41e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1))))))
% 4.58/5.17 satz41f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1))))))
% 4.58/5.17 satz41g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1)))))))
% 4.58/5.17 satz41h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1)))))))
% 4.58/5.17 satz41j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1))))))
% 4.58/5.17 satz41k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1))))))
% 4.58/5.17 satz42:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0))))))
% 4.58/5.17 satz43:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0))))))
% 4.58/5.17 satz44:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3))))))))))))
% 4.58/5.17 satz45:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3))))))))))))
% 4.58/5.17 satz46:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3))))))))))))
% 4.58/5.17 satz47:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3))))))))))))
% 4.58/5.17 satz48:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0))))))
% 4.58/5.17 satz49:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0))))))
% 4.58/5.17 satz4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2))))))))))
% 4.58/5.17 satz4a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0))))
% 4.58/5.17 satz4b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1)))))))
% 4.58/5.17 satz4c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0))))
% 4.58/5.17 satz4d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1)))))))
% 4.58/5.17 satz4e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1))))
% 4.58/5.17 satz4f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1)))))))
% 4.58/5.17 satz4g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0))))
% 4.58/5.17 satz4h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1))))))
% 4.58/5.17 satz50:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 4.58/5.17 satz51a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 4.58/5.17 satz51b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2)))))))))
% 4.58/5.17 satz51c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2)))))))))
% 4.58/5.17 satz51d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2)))))))))
% 4.58/5.17 satz52:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lesseq X1) X2)->((lesseq X0) X2)))))))))
% 4.58/5.17 satz53:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0)))))
% 4.58/5.17 satz54:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0)))))
% 4.58/5.17 satz55:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1)))))))))
% 4.58/5.17 satz56:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz57:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2))))))))
% 4.58/5.17 satz57a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2)))))))))
% 4.58/5.17 satz58:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_pf X0) X1)) ((n_pf X1) X0))))))
% 4.58/5.17 satz59:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2)))))))))
% 4.58/5.17 satz5:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))))))))
% 4.58/5.17 satz60:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((moref ((n_pf X0) X1)) X0)))))
% 4.58/5.17 satz60a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((lessf X0) ((n_pf X0) X1))))))
% 4.58/5.17 satz61:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.58/5.17 satz62b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.58/5.17 satz62c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.58/5.17 satz62d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.58/5.17 satz62e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.58/5.17 satz62f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.58/5.17 satz62g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz62h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 4.58/5.17 satz62j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz62k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 4.58/5.17 satz63a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1))))))))
% 4.58/5.17 satz63b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1))))))))
% 4.58/5.17 satz63c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1))))))))
% 4.58/5.17 satz63d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1))))))))
% 4.58/5.17 satz63e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1))))))))
% 4.58/5.17 satz63f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1))))))))
% 4.58/5.17 satz64:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz64a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz65a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz65b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz65c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz65d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz66:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz66a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.58/5.17 satz67a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0))))))))
% 4.58/5.17 satz67b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 4.58/5.17 satz67d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1))))))))
% 4.58/5.17 satz67e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1))))))))))
% 4.58/5.17 satz68:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz69:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_tf X0) X1)) ((n_tf X1) X0))))))
% 4.58/5.17 satz6:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))))))
% 4.58/5.17 satz70:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2)))))))))
% 4.58/5.17 satz71:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2)))))))))
% 4.58/5.17 satz72a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.58/5.17 satz72b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.58/5.17 satz72c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.58/5.17 satz72d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.58/5.17 satz72e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.58/5.17 satz72f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.58/5.17 satz72g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz72h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 4.58/5.17 satz72j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz72k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 4.58/5.17 satz73a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1))))))))
% 4.58/5.17 satz73b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1))))))))
% 4.58/5.17 satz73c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1))))))))
% 4.58/5.17 satz73d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1))))))))
% 4.58/5.17 satz73e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1))))))))
% 4.58/5.17 satz73f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1))))))))
% 4.58/5.17 satz74:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz74a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz75a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz75b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz75c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz75d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz76:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz76a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.58/5.17 satz77a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0)))))))
% 4.58/5.17 satz77b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 4.58/5.17 satz78:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0)))
% 4.58/5.17 satz79:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0))))))
% 4.58/5.17 satz7:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))))
% 4.58/5.17 satz80:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2)))))))))
% 4.58/5.17 satz81:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.58/5.17 satz81a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.58/5.17 satz81b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.58/5.17 satz81c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1)))))))
% 4.58/5.17 satz81d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1)))))))
% 4.58/5.17 satz81e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1))))))
% 4.58/5.17 satz81f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1))))))
% 4.58/5.17 satz81g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1)))))))
% 4.58/5.17 satz81h:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(d_not ((rt_moreis X0) X1)))))))
% 4.58/5.17 satz81j:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_moreis X0) X1))->((rt_less X0) X1))))))
% 4.58/5.17 satz81k:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_lessis X0) X1))->((rt_more X0) X1))))))
% 4.58/5.17 satz82:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0))))))
% 4.58/5.17 satz83:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0))))))
% 4.58/5.17 satz84:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->((rt_lessis X1) X0))))))
% 4.58/5.17 satz85:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->((rt_moreis X1) X0))))))
% 4.58/5.17 satz86:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 4.58/5.17 satz87a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 4.58/5.17 satz87b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_lessis X1) X2)->((rt_less X0) X2)))))))))
% 4.58/5.17 satz87c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_moreis X0) X1)->(((rt_more X1) X2)->((rt_more X0) X2)))))))))
% 4.58/5.17 satz87d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_moreis X1) X2)->((rt_more X0) X2)))))))))
% 4.58/5.17 satz88:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X1) X2)->((rt_lessis X0) X2)))))))))
% 4.58/5.17 satz89:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_more X1) X0)))))
% 4.58/5.17 satz8:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2)))))))))
% 4.58/5.17 satz8a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2))))))))
% 4.58/5.17 satz8b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))))))
% 4.58/5.17 satz90:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_less X1) X0)))))
% 4.58/5.17 satz91:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rt_less X0) X2)) ((rt_less X2) X1)))))))))
% 4.58/5.17 satz92:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_pl X0) X1)) ((rt_pl X1) X0))))))
% 4.58/5.17 satz93:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_pl ((rt_pl X0) X1)) X2)) ((rt_pl X0) ((rt_pl X1) X2)))))))))
% 4.58/5.17 satz94:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_more ((rt_pl X0) X1)) X0)))))
% 4.58/5.17 satz94a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_less X0) ((rt_pl X0) X1))))))
% 4.58/5.17 satz95:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.58/5.17 satz96b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.58/5.17 satz96c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.58/5.17 satz96d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.58/5.17 satz96e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.58/5.17 satz96f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.58/5.17 satz97a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_more X0) X1))))))))
% 4.58/5.17 satz97b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_is X0) X1))))))))
% 4.58/5.17 satz97c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_less X0) X1))))))))
% 4.58/5.17 satz98:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.58/5.17 satz98a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.58/5.17 satz99a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.58/5.17 satz99b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.58/5.17 satz99c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.58/5.17 satz99d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.58/5.17 satz9:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2)))))))))
% 4.58/5.17 satz9a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 4.58/5.17 satz9b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 4.58/5.17 sc1:=(fun (X0:fofType)=> ((d_Sep cut) (fun (X1:fofType)=> ((r_in (pofrp X1)) X0)))):(fofType->fofType)
% 4.58/5.17 schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) ((d_5p205_prop3 X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.17 schnittprop:=(fun (X0:fofType) (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((d_and ((rp_in X2) X0)) ((lrt X2) X1))))):(fofType->(fofType->Prop))
% 4.58/5.17 schnittset:=(fun (X0:fofType)=> ((d_Sep rat) (schnittprop X0))):(fofType->fofType)
% 4.58/5.17 second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)):(fofType->(fofType->fofType))
% 4.58/5.17 second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 second_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1))))))
% 4.58/5.17 secondis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3))))))
% 4.58/5.17 seq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Pi real) (fun (X3:fofType)=> (((if (intrl X3)) (((if ((r_lessis X1) X3)) (((if ((r_lessis X3) X0)) X2) (ordsucc emptyset))) (ordsucc emptyset))) (ordsucc emptyset))))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 set_ext:(forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1))))
% 4.58/5.17 setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))):(fofType->(fofType->fofType))
% 4.58/5.17 setof_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0)))))
% 4.58/5.17 setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))):(fofType->(fofType->fofType))
% 4.58/5.17 shift_n1:=(fun (X0:fofType) (X1:fofType)=> (inn ((shiftl X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 shift_n2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rlofnt (((shift_n1 X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 shift_ns:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ap X2) (((shiftr X0) X1) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.17 shift_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((r_is X3) ((ap X2) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.58/5.17 shift_ul:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((shiftl X2) X1)):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 shiftf:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X4:fofType)=> ((ap X3) (((shiftr X0) X1) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.17 shiftl1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((shiftl X0) X1)) (((shift_ul X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 shiftl:=(fun (X0:fofType) (X1:fofType)=> (ntofrl ((r_mn ((r_pl X0) d_1rl)) X1))):(fofType->(fofType->fofType))
% 4.58/5.17 shiftr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((r_mn ((r_pl (((shift_n2 X0) X1) X2)) X1)) d_1rl)):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 shiftseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X3:fofType)=> (((shiftl1 X0) X1) ((((shift_ns X0) X1) X2) X3))))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 singlet_u0:=(inn n_1):(fofType->fofType)
% 4.58/5.17 snt:=(fun (X0:fofType) (X1:fofType)=> (cutof (schnittset X0))):(fofType->(fofType->fofType))
% 4.58/5.17 soft:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.17 sq1:=(fun (X0:fofType)=> ((rp_ts X0) X0)):(fofType->fofType)
% 4.58/5.17 sqrt:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))):(fofType->fofType)
% 4.58/5.17 sqrtset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rp_less ((rp_ts (rpofrt X1)) (rpofrt X1))) X0)))):(fofType->fofType)
% 4.58/5.17 srp:=(fun (X0:fofType)=> (sqrt (rpofpd X0))):(fofType->fofType)
% 4.58/5.17 st_disj:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.17 stc:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((schnitt (sc1 X0)) (sc1 X1))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 std:=(second1 cut):(fofType->fofType)
% 4.58/5.17 stm:=(first1 cut):(fofType->fofType)
% 4.58/5.17 stp:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (pofrp (((stc X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 subrelation:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (R':(A->(B->Prop)))=> (forall (x:A) (y:B), (((R x) y)->((R' x) y)))):(forall (A:Type) (B:Type), ((A->(B->Prop))->((A->(B->Prop))->Prop)))
% 4.58/5.17 suc_p:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat)))))
% 4.58/5.17 suct:=((d_Sigma natt) (fun (X0:fofType)=> (ntofn (ordsucc (nofnt X0))))):fofType
% 4.58/5.17 sum:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((sumprop X0) X1))):(fofType->(fofType->fofType))
% 4.58/5.17 sumprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_pl X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.58/5.17 sumprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((sumprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.17 surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.17 surjseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((((imseq X0) X1) X2) X3))))))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.17 times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->fofType)
% 4.58/5.17 timesdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_td X0) X1)))))):fofType
% 4.58/5.17 timesfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_tf X0) X1)))))):fofType
% 4.58/5.17 tofs:=(fun (X0:fofType) (X1:fofType)=> ap):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.58/5.17 u01:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X2) ((rt_pl X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.58/5.17 ubprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_moreis X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.58/5.17 ul1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((shiftl1 X0) X1)):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.58/5.17 um10:=(fun (X0:fofType)=> ((rt_mn (rtofn X0)) d_1rt)):(fofType->fofType)
% 4.58/5.17 um1:=(fun (X0:fofType)=> (nofrt (um10 X0))):(fofType->fofType)
% 4.58/5.17 union:(fofType->fofType)
% 4.58/5.17 unique:=(fun (A:Type) (P:(A->Prop)) (x:A)=> ((and (P x)) (forall (x':A), ((P x')->(((eq A) x) x'))))):(forall (A:Type), ((A->Prop)->(A->Prop)))
% 4.65/5.26 unique_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R x) y))))))=> ((((dependent_unique_choice A) (fun (x2:A)=> B)) R) x)):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R x) y)))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% 4.65/5.26 univof:(fofType->fofType)
% 4.65/5.26 unmore:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4))))))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 urt:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_in X1) (lcl X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 wel:=(fun (X0:Prop)=> (d_not (d_not X0))):(Prop->Prop)
% 4.65/5.26 wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 wissel_wb:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 xi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2))))
% 4.65/5.26 xmy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_mn (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 xout:=(fun (X0:fofType)=> ((outn X0) X0)):(fofType->fofType)
% 4.65/5.26 xpy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_pl (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 xrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_xm X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 xty:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_ts (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 yrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_ym X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 zero:=(fun (X0:fofType)=> ((rp_is (stm X0)) (std X0))):(fofType->Prop)
% 4.65/5.26 zeta:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((((ite ((rp_less (((d_5160_fr X0) X1) X2)) d_1rp)) cut) (((d_5160_fr X0) X1) X2)) d_1rp)):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 ---termcontext
% 4.65/5.26 [[[False:Prop
% 4.65/5.26 False_rect:(forall (P:Type), (False->P))
% 4.65/5.26 I:True
% 4.65/5.26 NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% 4.65/5.26 True:Prop
% 4.65/5.26 _TPTP_proj1:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj)):(fofType->fofType)
% 4.65/5.26 abs:=((indreal real) absdr):(fofType->fofType)
% 4.65/5.26 absd:=(fun (X0:fofType)=> ((((ite (negd X0)) dif) ((rp_df (std X0)) (stm X0))) X0)):(fofType->fofType)
% 4.65/5.26 absdr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (absd X0)))):fofType
% 4.65/5.26 all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))):(fofType->((fofType->Prop)->Prop))
% 4.65/5.26 all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))):((fofType->Prop)->((fofType->Prop)->Prop))
% 4.65/5.26 amone:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3)))))))):(fofType->((fofType->Prop)->Prop))
% 4.65/5.26 and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.65/5.26 and:(Prop->(Prop->Prop))
% 4.65/5.26 and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 4.65/5.26 and_rect:=(fun (A:Prop) (B:Prop) (P:Type) (X:(A->(B->P))) (H:((and A) B))=> ((X (((proj1 A) B) H)) (((proj2 A) B) H))):(forall (A:Prop) (B:Prop) (P:Type), ((A->(B->P))->(((and A) B)->P)))
% 4.65/5.26 anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->Prop)))
% 4.65/5.26 ap:=(fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1)):(fofType->(fofType->fofType))
% 4.65/5.26 ap_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))
% 4.65/5.26 apb1:=(fun (X0:fofType) (X1:fofType)=> (rpofpd ((rp_pd X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 arpi:=(fun (X0:fofType)=> ((rp_ov d_1rp) (rpofpd X0))):(fofType->fofType)
% 4.65/5.26 atb3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd ((rp_td X0) X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 beta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2))))
% 4.65/5.26 bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 changef:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.65/5.26 chi:=(fun (X0:fofType) (X1:fofType)=> (cutof ((diff X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% 4.65/5.26 choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% 4.65/5.26 class:=((ecect frac) n_eq):(fofType->fofType)
% 4.65/5.26 classic:(forall (P:Prop), ((or P) (not P)))
% 4.65/5.26 classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 4.65/5.26 cond1:=(n_in n_1):(fofType->Prop)
% 4.65/5.26 cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))):(fofType->Prop)
% 4.65/5.26 conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 4.65/5.26 cut:=((d_Sep (power rat)) cutprop):fofType
% 4.65/5.26 cutof:=((out (power rat)) cutprop):(fofType->fofType)
% 4.65/5.26 cutprop1:=(fun (X0:fofType)=> ((d_and (cutprop1a X0)) (cutprop1b X0))):(fofType->Prop)
% 4.65/5.26 cutprop1a:=(nonempty rat):(fofType->Prop)
% 4.65/5.26 cutprop1b:=(fun (X0:fofType)=> (d_not (rt_all (fun (X1:fofType)=> ((rt_in X1) X0))))):(fofType->Prop)
% 4.65/5.26 cutprop2:=(fun (X0:fofType)=> (rt_all (fun (X1:fofType)=> ((imp ((rt_in X1) X0)) ((cutprop2a X0) X1))))):(fofType->Prop)
% 4.65/5.26 cutprop2a:=(fun (X0:fofType) (X1:fofType)=> (rt_all (fun (X2:fofType)=> ((imp (d_not ((rt_in X2) X0))) ((rt_less X1) X2))))):(fofType->(fofType->Prop))
% 4.65/5.26 cutprop3:=(fun (X0:fofType)=> (d_not (rt_some (max X0)))):(fofType->Prop)
% 4.65/5.26 cutprop:=(fun (X0:fofType)=> (((and3 (cutprop1 X0)) (cutprop2 X0)) (cutprop3 X0))):(fofType->Prop)
% 4.65/5.26 d161_s:=(fun (X0:fofType)=> (pdofrp (srp X0))):(fofType->fofType)
% 4.65/5.26 d_10_prop1:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))
% 4.65/5.26 d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2)))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 4.65/5.26 d_1df:=(pdofrp d_1rp):fofType
% 4.65/5.26 d_1out:=(fun (X0:fofType)=> ((outn X0) n_1)):(fofType->fofType)
% 4.65/5.26 d_1rl:=(realof d_1df):fofType
% 4.65/5.26 d_1rp:=(rpofrt d_1rt):fofType
% 4.65/5.26 d_1rt:=(rtofn n_1):fofType
% 4.65/5.26 d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->fofType)
% 4.65/5.26 d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0)):(fofType->Prop)
% 4.65/5.26 d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))):(fofType->Prop)
% 4.65/5.26 d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))):(fofType->fofType)
% 4.65/5.26 d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))):(fofType->Prop)
% 4.65/5.26 d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_25_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))):(fofType->(fofType->Prop))
% 4.65/5.26 d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_29_prop1:=(fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_2rl:=((r_pl d_1rl) d_1rl):fofType
% 4.65/5.26 d_2x0:=(fun (X0:fofType)=> ((rt_pl X0) X0)):(fofType->fofType)
% 4.65/5.26 d_3129_z1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X0) ((rt_pl X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 d_3132_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((lrt X0) X1)) ((urt X0) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_3132_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((rt_is ((rt_mn X3) X2)) X1)):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 d_3132_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((d_3132_prop1 X0) X2) X3)) ((((d_3132_prop1 X0) X2) X3)->((((d_3132_prop2 X0) X1) X2) X3)))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 d_3132_prop4:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (((d_3132_prop3 X0) X1) X2))))):(fofType->(fofType->Prop))
% 4.65/5.26 d_3132_u0:=(fun (X0:fofType) (X1:fofType)=> ((rt_pl X1) X0)):(fofType->(fofType->fofType))
% 4.65/5.26 d_3132_v0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (um10 X2)) X0))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 d_3132_w0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (rtofn X2)) X0))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 d_367_vo:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))):(fofType->(fofType->fofType))
% 4.65/5.26 d_367_w:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 d_3r184_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_3r184_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_some ((d_3r184_prop1 X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_3r184_prop3:=(fun (X0:fofType)=> (r_some (d_3r184_prop2 X0))):(fofType->Prop)
% 4.65/5.26 d_4141_v0:=(fun (X0:fofType) (X1:fofType)=> ((rt_ts ((rt_ov d_1rt) X1)) X0)):(fofType->(fofType->fofType))
% 4.65/5.26 d_4144_x2:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_moreis X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.65/5.26 d_4152_chi:=(fun (X0:fofType)=> (cutof (inv X0))):(fofType->fofType)
% 4.65/5.26 d_4153_chi:=(fun (X0:fofType) (X1:fofType)=> ((rp_ts X1) X0)):(fofType->(fofType->fofType))
% 4.65/5.26 d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))):(fofType->fofType)
% 4.65/5.26 d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0)):fofType
% 4.65/5.26 d_428_prop1:=(fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))):(fofType->(fofType->Prop))
% 4.65/5.26 d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->Prop)
% 4.65/5.26 d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))):(fofType->(fofType->Prop))
% 4.65/5.26 d_430_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_431_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_477_v:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 d_5113_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nt_in (ntofn X1)) X0)):(fofType->(fofType->Prop))
% 4.65/5.26 d_5156_prop1:=(fun (X0:fofType) (X1:fofType)=> ((rp_nt_in (nttofnt X1)) X0)):(fofType->(fofType->Prop))
% 4.65/5.26 d_5157_s1:=(fun (X0:fofType)=> ((d_Sep rat) (urt X0))):(fofType->fofType)
% 4.65/5.26 d_5160_dn:=(fun (X0:fofType) (X1:fofType)=> ((rp_pl ((rp_pl X0) X1)) d_1rp)):(fofType->(fofType->fofType))
% 4.65/5.26 d_5160_fr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_ov (((d_5160_nm X0) X1) X2)) ((d_5160_dn X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 d_5160_nm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_mn (rpofrt X2)) ((rp_ts X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 d_5160_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.65/5.26 d_5160_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((d_5160_prop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_5160_xr:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((rt_ov X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 d_5160_y0:=(fun (X0:fofType)=> X0):(fofType->fofType)
% 4.65/5.26 d_5160_yr:=(fun (X0:fofType)=> (rpofrt (d_5160_y0 X0))):(fofType->fofType)
% 4.65/5.26 d_5161_dn:=(fun (X0:fofType)=> ((rp_pl (rpofrt X0)) ((rp_pl (rpofrt X0)) d_1rp))):(fofType->fofType)
% 4.65/5.26 d_5161_fr:=(fun (X0:fofType) (X1:fofType)=> ((rp_ov ((d_5161_nm X0) X1)) (d_5161_dn X1))):(fofType->(fofType->fofType))
% 4.65/5.26 d_5161_max:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_more X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType))
% 4.65/5.26 d_5161_min:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_less X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType))
% 4.65/5.26 d_5161_nm:=(fun (X0:fofType) (X1:fofType)=> ((rp_mn X0) ((rp_ts (rpofrt X1)) (rpofrt X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 d_5161_xm:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_more X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.65/5.26 d_5161_ym:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_less X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.65/5.26 d_5162_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_eq ((n_tf ((n_fr X1) X0)) ((n_fr X1) X0))) ((n_fr (ordsucc n_1)) n_1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_5162_prop2:=(fun (X0:fofType)=> (n_some (d_5162_prop1 X0))):(fofType->Prop)
% 4.65/5.26 d_5162_prop3:=(n_some d_5162_prop2):Prop
% 4.65/5.26 d_5162_x0:=(rtofrp ksi):fofType
% 4.65/5.26 d_5162_y:=((ind nat) (min d_5162_prop2)):fofType
% 4.65/5.26 d_527_q:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (X0 (ntofn X1))):((fofType->Prop)->(fofType->Prop))
% 4.65/5.26 d_54_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (nofnt ((ap X0) (ntofn X1)))))):(fofType->fofType)
% 4.65/5.26 d_54_gt:=(fun (X0:fofType)=> ((d_Sigma natt) (fun (X1:fofType)=> (ntofn ((ap X0) (nofnt X1)))))):(fofType->fofType)
% 4.65/5.26 d_54_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc (nofnt X0)))) (d_24_prop1 X1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_59_i:=(fun (X0:fofType) (X1:fofType)=> ((n_is (nofnt X0)) (nofnt X1))):(fofType->(fofType->Prop))
% 4.65/5.26 d_59_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X0)) (nofnt X1)))):(fofType->(fofType->Prop))
% 4.65/5.26 d_59_iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X1)) (nofnt X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 d_5p205_prop1:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_less X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop))
% 4.65/5.26 d_5p205_prop2:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_more X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop))
% 4.65/5.26 d_5p205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5p205_prop1 X0) X2)) ((d_5p205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_5r205_prop1:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_less X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop))
% 4.65/5.26 d_5r205_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_more X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop))
% 4.65/5.26 d_5r205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5r205_prop1 X0) X2)) ((d_5r205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 d_5r205_sp1:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_in (r_m0 X1)) X0)))):(fofType->fofType)
% 4.65/5.26 d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1))):((fofType->((fofType->fofType)->fofType))->(fofType->fofType))
% 4.65/5.26 d_In_rec_G:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))):((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))
% 4.65/5.26 d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1)):(fofType->fofType)
% 4.65/5.26 d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))):(fofType->fofType)
% 4.65/5.26 d_Pi:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))))):(fofType->((fofType->fofType)->fofType))
% 4.65/5.26 d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))):(fofType->Prop)
% 4.65/5.26 d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))):(fofType->((fofType->Prop)->((fofType->fofType)->fofType)))
% 4.65/5.26 d_Repl_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0)))))):(fofType->Prop)
% 4.65/5.26 d_Sep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset)):(fofType->((fofType->Prop)->fofType))
% 4.65/5.26 d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))):(fofType->((fofType->fofType)->fofType))
% 4.65/5.26 d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0)):(fofType->fofType)
% 4.65/5.26 d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))):(fofType->(fofType->Prop))
% 4.65/5.26 d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))):(fofType->Prop)
% 4.65/5.26 d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))):(fofType->fofType)
% 4.65/5.26 d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))):(fofType->Prop)
% 4.65/5.26 d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))):(Prop->(Prop->Prop))
% 4.65/5.26 d_not:=(fun (X0:Prop)=> ((imp X0) False)):(Prop->Prop)
% 4.65/5.26 d_pair:=(fun (X0:fofType) (X1:fofType)=> pair):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 den:=(second1 nat):(fofType->fofType)
% 4.65/5.26 dependent_unique_choice:(forall (A:Type) (B:(A->Type)) (R:(forall (x:A), ((B x)->Prop))), ((forall (x:A), ((ex (B x)) ((unique (B x)) (fun (y:(B x))=> ((R x) y)))))->((ex (forall (x:A), (B x))) (fun (f:(forall (x:A), (B x)))=> (forall (x:A), ((R x) (f x)))))))
% 4.65/5.26 dif:=(pair1type cut):fofType
% 4.65/5.26 diff:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((rp_diffprop X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 diffprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((rt_more X1) X2)) (((rt_more X1) X2)->((rt_is X0) ((rt_mn X1) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 diffprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((urt X1) X4)) (((diffprop1 X2) X3) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.65/5.26 diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 e_fisi:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3)))))))
% 4.65/5.26 e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2):(fofType->((fofType->Prop)->(fofType->fofType)))
% 4.65/5.26 e_in_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 4.65/5.26 e_inp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2)))))
% 4.65/5.26 e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 e_isp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3))))))))
% 4.65/5.26 e_pair_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1)))))))))
% 4.65/5.26 ec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0))):(Prop->(Prop->(Prop->Prop)))
% 4.65/5.26 ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.65/5.26 ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.65/5.26 ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.65/5.26 ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->fofType))
% 4.65/5.26 ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.65/5.26 ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.65/5.26 empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))):(fofType->(fofType->Prop))
% 4.65/5.26 emptyset:fofType
% 4.65/5.26 eps:((fofType->Prop)->fofType)
% 4.65/5.26 eq:=(fun (T:Type) (a:T) (b:T)=> (forall (P:(T->Prop)), ((P a)->(P b)))):(forall (T:Type), (T->(T->Prop)))
% 4.65/5.26 eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% 4.65/5.26 eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% 4.65/5.26 eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% 4.65/5.26 eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 4.65/5.26 eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 4.65/5.26 esti:=(fun (X0:fofType)=> in):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 estie:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2)))))
% 4.65/5.26 estii:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1))))))
% 4.65/5.26 eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% 4.65/5.26 eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% 4.65/5.26 ex:(forall (A:Type), ((A->Prop)->Prop))
% 4.65/5.26 ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% 4.65/5.26 ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% 4.65/5.26 famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))):(fofType->((fofType->fofType)->fofType))
% 4.65/5.26 first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)):(fofType->(fofType->fofType))
% 4.65/5.26 first:=(fun (X0:fofType) (X1:fofType)=> proj0):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 first_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 4.65/5.26 firstis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2))))))
% 4.65/5.26 fixf2:=((fixfu2 dif) rp_eq):(fofType->(fofType->Prop))
% 4.65/5.26 fixf:=((fixfu2 frac) n_eq):(fofType->(fofType->Prop))
% 4.65/5.26 fixfu2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7))))))))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.65/5.26 fixfu:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.65/5.26 fofType:Type
% 4.65/5.26 frac:=(pair1type nat):fofType
% 4.65/5.26 functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% 4.65/5.26 functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 4.65/5.26 functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% 4.65/5.26 half:=((r_ov d_1rl) d_2rl):fofType
% 4.65/5.26 i1_s:=(d_Sep nat):((fofType->Prop)->fofType)
% 4.65/5.26 if:=(fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2)))))):(Prop->(fofType->(fofType->fofType)))
% 4.65/5.26 if_i_0:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2)))
% 4.65/5.26 if_i_1:(forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1)))
% 4.65/5.26 if_i_correct:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2))))
% 4.65/5.26 if_i_or:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2)))
% 4.65/5.26 iff:=(fun (A:Prop) (B:Prop)=> ((and (A->B)) (B->A))):(Prop->(Prop->Prop))
% 4.65/5.26 iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 4.65/5.26 iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 4.65/5.26 iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 4.65/5.26 iii1_lbprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_lessis X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))):(fofType->(fofType->Prop))
% 4.65/5.26 iiia_x0:=(fun (X0:fofType)=> (rtofn (ntofrp X0))):(fofType->fofType)
% 4.65/5.26 iiit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X1) X0))):(fofType->(fofType->Prop))
% 4.65/5.26 iit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 image:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1)):(Prop->(Prop->Prop))
% 4.65/5.26 improp:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and (((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))) ((((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))->(((((shift_prop1 X0) X1) X2) X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.65/5.26 imseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (r_some ((((improp X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 in:(fofType->(fofType->Prop))
% 4.65/5.26 incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))):(fofType->((fofType->Prop)->fofType))
% 4.65/5.26 ind_p:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0)))))
% 4.65/5.26 indeq2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))
% 4.65/5.26 indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 4.65/5.26 indrat:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 indreal2:=((indeq2 dif) rp_eq):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 indreal:=((indeq dif) rp_eq):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 inf:=(esti frac):(fofType->(fofType->Prop))
% 4.65/5.26 inj_h:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.65/5.26 injective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4))))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 injseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->(((r_is ((ap X2) X3)) ((ap X2) X4))->((r_is X3) X4))))))))))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType))
% 4.65/5.26 inseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->(((and3 (intrl ((ap X2) X3))) ((r_lessis X1) ((ap X2) X3))) ((r_lessis ((ap X2) X3)) X0)))))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 intd:=(fun (X0:fofType)=> ((l_or (zero X0)) (natd (absd X0)))):(fofType->Prop)
% 4.65/5.26 intd_a3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X0))):(fofType->(fofType->fofType))
% 4.65/5.26 intd_b2:=(fun (X0:fofType)=> (rpofpd (m0d X0))):(fofType->fofType)
% 4.65/5.26 intd_b3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X1))):(fofType->(fofType->fofType))
% 4.65/5.26 intrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (intd X1))))):(fofType->Prop)
% 4.65/5.26 inv:=(fun (X0:fofType)=> ((d_Sep rat) (invprop X0))):(fofType->fofType)
% 4.65/5.26 inverse:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset)))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 invprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((urt X0) X2)) ((rt_less X2) X1))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 invprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 ((urt X0) X2)) (rt_some ((invprop1 X0) X2))) ((rt_is X1) ((rt_ov d_1rt) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 invprop:=(fun (X0:fofType) (X1:fofType)=> (rt_some ((invprop2 X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 irratd:=(fun (X0:fofType)=> (d_not (ratd X0))):(fofType->Prop)
% 4.65/5.26 irratrl:=(fun (X0:fofType)=> (d_not (ratrl X0))):(fofType->Prop)
% 4.65/5.26 irratrp:=(fun (X0:fofType)=> (d_not (ratrp X0))):(fofType->Prop)
% 4.65/5.26 is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)):(fofType->((fofType->Prop)->Prop))
% 4.65/5.26 isseti:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2))))))))
% 4.65/5.26 ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))):(Prop->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 iv4d_ai:=(fun (X0:fofType)=> (pdofrp (arpi X0))):(fofType->fofType)
% 4.65/5.26 iv5d_2:=((rp_pl d_1rp) d_1rp):fofType
% 4.65/5.26 ivr1_nr:=(fun (X0:fofType)=> rpofnd):(fofType->(fofType->fofType))
% 4.65/5.26 ivr1_pr:=(fun (X0:fofType)=> rpofpd):(fofType->(fofType->fofType))
% 4.65/5.26 ivr2_propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 ivr2_propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 ivr2_x0:=(fun (X0:fofType) (X1:fofType)=> (ntofrp ((ivr1_pr X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 ivr2_xn:=(fun (X0:fofType)=> ((((soft nat) real) ((d_Sigma nat) rlofnt)) (rlofnt X0))):(fofType->fofType)
% 4.65/5.26 k_EmptyAx:(((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False)
% 4.65/5.26 k_If_In_01:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset)))))
% 4.65/5.26 k_If_In_then_E:(forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2))))
% 4.65/5.26 k_In_0_1:((in emptyset) (ordsucc emptyset))
% 4.65/5.26 k_In_ind:(forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1))))
% 4.65/5.26 k_Pi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3))))))
% 4.65/5.26 k_PowerE:(forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0)))
% 4.65/5.26 k_PowerEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0)))
% 4.65/5.26 k_PowerI:(forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0))))
% 4.65/5.26 k_ReplEq:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3)))))))
% 4.65/5.26 k_Self_In_Power:(forall (X0:fofType), ((in X0) (power X0)))
% 4.65/5.26 k_SepE1:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0)))
% 4.65/5.26 k_SepE2:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2)))
% 4.65/5.26 k_SepI:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1)))))
% 4.65/5.26 k_Sigma_eta_proj0_proj1:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))))
% 4.65/5.26 k_UnionEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0))))))
% 4.65/5.26 k_UnivOf_In:(forall (X0:fofType), ((in X0) (univof X0)))
% 4.65/5.26 k_UnivOf_ZF_closed:(forall (X0:fofType), (d_ZF_closed (univof X0)))
% 4.65/5.26 k_satz123a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((or3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.65/5.26 k_satz123b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((ec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.65/5.26 k_satz67c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0))))))
% 4.65/5.26 ksi:=((ind cut) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) X0)) (rpofnt (ordsucc n_1))))):fofType
% 4.65/5.26 l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))):(Prop->(Prop->Prop))
% 4.65/5.26 l_et:(forall (X0:Prop), ((wel X0)->X0))
% 4.65/5.26 l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))):(Prop->(Prop->Prop))
% 4.65/5.26 l_or:=(fun (X0:Prop)=> (imp (d_not X0))):(Prop->(Prop->Prop))
% 4.65/5.26 l_some:=(fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1)))):(fofType->((fofType->Prop)->Prop))
% 4.65/5.26 lam_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1))))
% 4.65/5.26 lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))):((fofType->Prop)->(fofType->(fofType->Prop)))
% 4.65/5.26 lcl:=((e_in (power rat)) cutprop):(fofType->fofType)
% 4.65/5.26 left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 left:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 lessd:=(fun (X0:fofType) (X1:fofType)=> ((rp_less ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 lrt:=(fun (X0:fofType) (X1:fofType)=> ((rt_in X1) (lcl X0))):(fofType->(fofType->Prop))
% 4.65/5.26 m0d:=(fun (X0:fofType)=> ((rp_df (std X0)) (stm X0))):(fofType->fofType)
% 4.65/5.26 m0dr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (m0d X0)))):fofType
% 4.65/5.26 max:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_ub X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop))
% 4.65/5.26 min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop))
% 4.65/5.26 mored:=(fun (X0:fofType) (X1:fofType)=> ((rp_more ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 mxy:=(fun (X0:fofType) (X1:fofType)=> ((r_ts half) ((r_pl X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 n1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (negd X1))):(fofType->(fofType->Prop))
% 4.65/5.26 n1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (posd X1))):(fofType->(fofType->Prop))
% 4.65/5.26 nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)):(fofType->(fofType->Prop))
% 4.65/5.26 n_1:=(ordsucc emptyset):fofType
% 4.65/5.26 n_1_p:((is_of n_1) (fun (X0:fofType)=> ((in X0) nat)))
% 4.65/5.26 n_1o:=((outn n_1) n_1):fofType
% 4.65/5.26 n_1t:=((outn n_2) n_1):fofType
% 4.65/5.26 n_2:=((n_pl n_1) n_1):fofType
% 4.65/5.26 n_2t:=((outn n_2) n_2):fofType
% 4.65/5.26 n_all:=(all nat):((fofType->Prop)->Prop)
% 4.65/5.26 n_ax3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1)))
% 4.65/5.26 n_ax4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1))))))
% 4.65/5.26 n_ax5:((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0)))))))
% 4.65/5.26 n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 n_fr:=(pair1 nat):(fofType->(fofType->fofType))
% 4.65/5.26 n_in:=(esti nat):(fofType->(fofType->Prop))
% 4.65/5.26 n_is:=(e_is nat):(fofType->(fofType->Prop))
% 4.65/5.26 n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))):((fofType->Prop)->(fofType->Prop))
% 4.65/5.26 n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 n_one:=(one nat):((fofType->Prop)->Prop)
% 4.65/5.26 n_pf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 n_pl:=(fun (X0:fofType)=> (ap (plus X0))):(fofType->(fofType->fofType))
% 4.65/5.26 n_some:=(l_some nat):((fofType->Prop)->Prop)
% 4.65/5.26 n_tf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 n_ts:=(fun (X0:fofType)=> (ap (times X0))):(fofType->(fofType->fofType))
% 4.65/5.26 nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))):fofType
% 4.65/5.26 nat_1:(nat_p (ordsucc emptyset))
% 4.65/5.26 nat_ind:(forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1))))))
% 4.65/5.26 nat_inv:(forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1))))))))
% 4.65/5.26 nat_ordsucc:(forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0))))
% 4.65/5.26 nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))):(fofType->Prop)
% 4.65/5.26 nat_p_omega:(forall (X0:fofType), ((nat_p X0)->((in X0) omega)))
% 4.65/5.26 natd:=(fun (X0:fofType)=> ((d_and (posd X0)) ((posd X0)->(natrp (rpofpd X0))))):(fofType->Prop)
% 4.65/5.26 natprop:=(fun (X0:fofType) (X1:fofType)=> ((inf ((n_fr X1) n_1)) (class X0))):(fofType->(fofType->Prop))
% 4.65/5.26 natrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (natd X1))))):(fofType->Prop)
% 4.65/5.26 natrp:=(((image nat) cut) ((d_Sigma nat) rpofnt)):(fofType->Prop)
% 4.65/5.26 natrt:=(fun (X0:fofType)=> (n_some (natprop X0))):(fofType->Prop)
% 4.65/5.26 natt:=((d_Sep rat) natrt):fofType
% 4.65/5.26 ndofrp:=(fun (X0:fofType)=> ((rp_df d_1rp) ((rp_pl X0) d_1rp))):(fofType->fofType)
% 4.65/5.26 neg:=(fun (X0:fofType)=> ((l_some dif) (propn X0))):(fofType->Prop)
% 4.65/5.26 negd:=(fun (X0:fofType)=> ((rp_less (stm X0)) (std X0))):(fofType->Prop)
% 4.65/5.26 neq_ordsucc_0:(forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset)))
% 4.65/5.26 nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2)))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 nofnt:=(fun (X0:fofType)=> (nofrt (rtofnt X0))):(fofType->fofType)
% 4.65/5.26 nofrp:=(fun (X0:fofType)=> (realof (ndofrp X0))):(fofType->fofType)
% 4.65/5.26 nofrt:=(fun (X0:fofType)=> ((ind nat) (natprop X0))):(fofType->fofType)
% 4.65/5.26 non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))):(fofType->((fofType->Prop)->(fofType->Prop)))
% 4.65/5.26 nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))):(fofType->(fofType->Prop))
% 4.65/5.26 not:=(fun (P:Prop)=> (P->False)):(Prop->Prop)
% 4.65/5.26 nt_1t:=(ntofn n_1):fofType
% 4.65/5.26 nt_all:=(all natt):((fofType->Prop)->Prop)
% 4.65/5.26 nt_cond1:=(nt_in nt_1t):(fofType->Prop)
% 4.65/5.26 nt_cond2:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((imp ((nt_in X1) X0)) ((nt_in ((ap suct) X1)) X0))))):(fofType->Prop)
% 4.65/5.26 nt_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 nt_in:=(esti natt):(fofType->(fofType->Prop))
% 4.65/5.26 nt_is:=(e_is natt):(fofType->(fofType->Prop))
% 4.65/5.26 nt_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (nt_all (fun (X2:fofType)=> ((imp (X0 X2)) ((nt_lessis X1) X2))))):((fofType->Prop)->(fofType->Prop))
% 4.65/5.26 nt_less:=(fun (X0:fofType) (X1:fofType)=> ((rt_less (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.65/5.26 nt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((rt_lessis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.65/5.26 nt_min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((nt_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop))
% 4.65/5.26 nt_more:=(fun (X0:fofType) (X1:fofType)=> ((rt_more (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.65/5.26 nt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((rt_moreis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.65/5.26 nt_natt:=((d_Sep cut) natrp):fofType
% 4.65/5.26 nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((nt_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 nt_one:=(one natt):((fofType->Prop)->Prop)
% 4.65/5.26 nt_pl:=(fun (X0:fofType) (X1:fofType)=> (ntofrt ((rt_pl (rtofnt X0)) (rtofnt X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 nt_satz15:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> (((nt_less X0) X1)->(((nt_less X1) X2)->((nt_less X0) X2)))))))))
% 4.65/5.26 nt_satz1:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_nis X0) X1)->((nt_nis ((ap suct) X0)) ((ap suct) X1)))))))
% 4.65/5.26 nt_satz21:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) natt))) (fun (X3:fofType)=> (((nt_more X0) X1)->(((nt_more X2) X3)->((nt_more ((nt_pl X0) X2)) ((nt_pl X1) X3))))))))))))
% 4.65/5.26 nt_satz27:(forall (X0:(fofType->Prop)), ((nt_some X0)->(nt_some (nt_min X0))))
% 4.65/5.26 nt_satz4:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((one ((d_Pi natt) (fun (X1:fofType)=> natt))) (fun (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (nt_all (fun (X2:fofType)=> ((nt_is ((ap X1) ((ap suct) X2))) ((ap suct) ((ap X1) X2))))))))))
% 4.65/5.26 nt_satz5:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((nt_is ((nt_pl ((nt_pl X0) X1)) X2)) ((nt_pl X0) ((nt_pl X1) X2)))))))))
% 4.65/5.26 nt_satz9:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((orec3 ((nt_is X0) X1)) (nt_some (fun (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))))) (nt_some (fun (X2:fofType)=> ((nt_is X1) ((nt_pl X0) X2)))))))))
% 4.65/5.26 nt_some:=(l_some natt):((fofType->Prop)->Prop)
% 4.65/5.26 nt_suct:=((d_Sigma nt_natt) (fun (X0:fofType)=> (nttofnt (ordsucc (ntofntt X0))))):fofType
% 4.65/5.26 ntofn:=(fun (X0:fofType)=> (ntofrt (rtofn X0))):(fofType->fofType)
% 4.65/5.26 ntofntt:=(fun (X0:fofType)=> (ntofrp (rpofntt X0))):(fofType->fofType)
% 4.65/5.26 ntofrl:=(((soft nat) real) ((d_Sigma nat) rlofnt)):(fofType->fofType)
% 4.65/5.26 ntofrp:=(((soft nat) cut) ((d_Sigma nat) rpofnt)):(fofType->fofType)
% 4.65/5.26 ntofrt:=((out rat) natrt):(fofType->fofType)
% 4.65/5.26 nttofnt:=(fun (X0:fofType)=> (nttofrp (rpofnt X0))):(fofType->fofType)
% 4.65/5.26 nttofrp:=((out cut) natrp):(fofType->fofType)
% 4.65/5.26 num:=(first1 nat):(fofType->fofType)
% 4.65/5.26 obvious:=((imp False) False):Prop
% 4.65/5.26 omega:=((d_Sep (univof emptyset)) nat_p):fofType
% 4.65/5.26 omega_nat_p:(forall (X0:fofType), (((in X0) omega)->(nat_p X0)))
% 4.65/5.26 one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))):(fofType->((fofType->Prop)->Prop))
% 4.65/5.26 oneax:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1))))
% 4.65/5.26 or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.65/5.26 or:(Prop->(Prop->Prop))
% 4.65/5.26 or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 4.65/5.26 or_first:=(fun (A:Prop) (B:Prop)=> (((((or_ind A) B) ((B->A)->A)) (fun (x:A) (x0:(B->A))=> x)) (fun (x:B) (x0:(B->A))=> (x0 x)))):(forall (A:Prop) (B:Prop), (((or A) B)->((B->A)->A)))
% 4.65/5.26 or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 4.65/5.26 or_introl:(forall (A:Prop) (B:Prop), (A->((or A) B)))
% 4.65/5.26 or_intror:(forall (A:Prop) (B:Prop), (B->((or A) B)))
% 4.65/5.26 or_second:=(fun (A:Prop) (B:Prop) (x:((or A) B))=> (((or_first B) A) (((or_comm_i A) B) x))):(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B)))
% 4.65/5.26 ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0))):(fofType->fofType)
% 4.65/5.26 ordsucc_inj:(forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1)))
% 4.65/5.26 orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.65/5.26 orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))):(Prop->(Prop->Prop))
% 4.65/5.26 otax1:(forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 4.65/5.26 otax2:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2)))))
% 4.65/5.26 out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))):(fofType->((fofType->Prop)->(fofType->fofType)))
% 4.65/5.26 outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType))
% 4.65/5.26 p1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (negd X1))):(fofType->(fofType->Prop))
% 4.65/5.26 p1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (posd X1))):(fofType->(fofType->Prop))
% 4.65/5.26 pair1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2)))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))):(fofType->fofType)
% 4.65/5.26 pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))):(fofType->(fofType->fofType))
% 4.65/5.26 pair_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1))))))
% 4.65/5.26 pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)):(fofType->Prop)
% 4.65/5.26 pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 pair_u0:=(inn n_2):(fofType->fofType)
% 4.65/5.26 pairis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2))))
% 4.65/5.26 pdofnt:=(fun (X0:fofType)=> (pdofrp (rpofnt X0))):(fofType->fofType)
% 4.65/5.26 pdofrp:=(fun (X0:fofType)=> ((rp_df ((rp_pl X0) d_1rp)) d_1rp)):(fofType->fofType)
% 4.65/5.26 perm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injseq X0) X1) X2)) (((surjseq X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->fofType)
% 4.65/5.26 plusdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_pd X0) X1)))))):fofType
% 4.65/5.26 plusfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_pf X0) X1)))))):fofType
% 4.65/5.26 pofrp:=(fun (X0:fofType)=> (realof (pdofrp X0))):(fofType->fofType)
% 4.65/5.26 pos:=(fun (X0:fofType)=> ((l_some dif) (propp X0))):(fofType->Prop)
% 4.65/5.26 posd:=(fun (X0:fofType)=> ((rp_more (stm X0)) (std X0))):(fofType->Prop)
% 4.65/5.26 power:(fofType->fofType)
% 4.65/5.26 pr1:=(fun (X0:fofType)=> rpofp):(fofType->(fofType->fofType))
% 4.65/5.26 prod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((prodprop X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 prodprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_ts X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.65/5.26 prodprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((prodprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj)):(fofType->fofType)
% 4.65/5.26 proj0_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0)))
% 4.65/5.26 proj0_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0))
% 4.65/5.26 proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 4.65/5.26 proj1_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))
% 4.65/5.26 proj1_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1))
% 4.65/5.26 proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 4.65/5.26 proj_Sigma_eta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)))
% 4.65/5.26 proofsirrelevant:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->((all_of (fun (X5:fofType)=> ((in X5) real))) (fun (X5:fofType)=> ((intrl X5)->(((r_lessis X1) X5)->(((r_lessis X5) X0)->(((r_is X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))))))))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 prop1:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3)))):(Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.65/5.26 prop1d:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (posd X1)) (posd X2)) ((rp_eq X0) ((rp_md X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 prop1t:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((nt_is ((ap X0) ((ap suct) X1))) ((ap suct) ((ap X0) X1)))))):(fofType->Prop)
% 4.65/5.26 prop2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))
% 4.65/5.26 prop2d:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) ((prop1d X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 prop2t:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (prop1t X1))):(fofType->(fofType->Prop))
% 4.65/5.26 prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->Prop)
% 4.65/5.26 propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.65/5.26 propn:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (negd X1))):(fofType->(fofType->Prop))
% 4.65/5.26 propp:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (posd X1))):(fofType->(fofType->Prop))
% 4.65/5.26 ps1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> rpofp):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 r_0:=(realof ((rp_df d_1rp) d_1rp)):fofType
% 4.65/5.26 r_all:=(all real):((fofType->Prop)->Prop)
% 4.65/5.26 r_class:=((ecect dif) rp_eq):(fofType->fofType)
% 4.65/5.26 r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))):(Prop->(Prop->Prop))
% 4.65/5.26 r_fixf:=((fixfu dif) rp_eq):(fofType->(fofType->Prop))
% 4.65/5.26 r_in:=(esti real):(fofType->(fofType->Prop))
% 4.65/5.26 r_inn:=(esti dif):(fofType->(fofType->Prop))
% 4.65/5.26 r_is:=(e_is real):(fofType->(fofType->Prop))
% 4.65/5.26 r_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))))))):(fofType->(fofType->Prop))
% 4.65/5.26 r_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_less X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 r_m0:=((indreal real) m0dr):(fofType->fofType)
% 4.65/5.26 r_mn:=(fun (X0:fofType) (X1:fofType)=> ((r_pl X0) (r_m0 X1))):(fofType->(fofType->fofType))
% 4.65/5.26 r_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))))))):(fofType->(fofType->Prop))
% 4.65/5.26 r_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_more X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 r_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 r_one:=(one real):((fofType->Prop)->Prop)
% 4.65/5.26 r_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind real) (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.65/5.26 r_pl:=((indreal2 real) plusdr):(fofType->(fofType->fofType))
% 4.65/5.26 r_schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind real) ((d_5r205_prop3 X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 r_some:=(l_some real):((fofType->Prop)->Prop)
% 4.65/5.26 r_sqrt:=(fun (X0:fofType)=> ((ind real) (fun (X1:fofType)=> ((d_and (d_not (neg X1))) ((r_is ((r_ts X1) X1)) X0))))):(fofType->fofType)
% 4.65/5.26 r_ts:=((indreal2 real) timesdr):(fofType->(fofType->fofType))
% 4.65/5.26 rat:=((ect frac) n_eq):fofType
% 4.65/5.26 ratd:=(fun (X0:fofType)=> ((d_not (zero X0))->(ratrp (rpofpd (absd X0))))):(fofType->Prop)
% 4.65/5.26 ratof:=((ectelt frac) n_eq):(fofType->fofType)
% 4.65/5.26 ratrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (ratd X1))))):(fofType->Prop)
% 4.65/5.26 ratrp:=(((image rat) cut) ((d_Sigma rat) rpofrt)):(fofType->Prop)
% 4.65/5.26 ratset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rt_less X1) X0)))):(fofType->fofType)
% 4.65/5.26 ratt:=((d_Sep cut) ratrp):fofType
% 4.65/5.26 real:=((ect dif) rp_eq):fofType
% 4.65/5.26 realof:=((ectelt dif) rp_eq):(fofType->fofType)
% 4.65/5.26 refis:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1))))
% 4.65/5.26 relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% 4.65/5.26 repl:(fofType->((fofType->fofType)->fofType))
% 4.65/5.26 right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 right:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 rlofnt:=(fun (X0:fofType)=> (realof (pdofnt X0))):(fofType->fofType)
% 4.65/5.26 rp1:=(fun (X0:fofType)=> ((rp_pl X0) d_1rp)):(fofType->fofType)
% 4.65/5.26 rp_all:=(all cut):((fofType->Prop)->Prop)
% 4.65/5.26 rp_df:=(pair1 cut):(fofType->(fofType->fofType))
% 4.65/5.26 rp_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((diffprop2 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 rp_eq:=(fun (X0:fofType) (X1:fofType)=> ((rp_is ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_in:=(esti cut):(fofType->(fofType->Prop))
% 4.65/5.26 rp_is:=(e_is cut):(fofType->(fofType->Prop))
% 4.65/5.26 rp_less:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((urt X0) X2)) ((lrt X1) X2))))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessd X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_less X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_md:=(fun (X0:fofType) (X1:fofType)=> ((rp_pd X0) (m0d X1))):(fofType->(fofType->fofType))
% 4.65/5.26 rp_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.65/5.26 rp_more:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((lrt X0) X2)) ((urt X1) X2))))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_more X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((mored X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_nt_1t:=(nttofnt n_1):fofType
% 4.65/5.26 rp_nt_all:=(all nt_natt):((fofType->Prop)->Prop)
% 4.65/5.26 rp_nt_cond1:=(rp_nt_in rp_nt_1t):(fofType->Prop)
% 4.65/5.26 rp_nt_cond2:=(fun (X0:fofType)=> (rp_nt_all (fun (X1:fofType)=> ((imp ((rp_nt_in X1) X0)) ((rp_nt_in ((ap nt_suct) X1)) X0))))):(fofType->Prop)
% 4.65/5.26 rp_nt_in:=(esti nt_natt):(fofType->(fofType->Prop))
% 4.65/5.26 rp_nt_is:=(e_is nt_natt):(fofType->(fofType->Prop))
% 4.65/5.26 rp_nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_nt_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rp_nt_one:=(one nt_natt):((fofType->Prop)->Prop)
% 4.65/5.26 rp_nt_some:=(l_some nt_natt):((fofType->Prop)->Prop)
% 4.65/5.26 rp_one:=(one cut):((fofType->Prop)->Prop)
% 4.65/5.26 rp_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.65/5.26 rp_pd:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl (stm X0)) (stm X1))) ((rp_pl (std X0)) (std X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 rp_pl:=(fun (X0:fofType) (X1:fofType)=> (cutof ((sum X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 rp_some:=(l_some cut):((fofType->Prop)->Prop)
% 4.65/5.26 rp_td:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl ((rp_ts (stm X0)) (stm X1))) ((rp_ts (std X0)) (std X1)))) ((rp_pl ((rp_ts (stm X0)) (std X1))) ((rp_ts (std X0)) (stm X1))))):(fofType->(fofType->fofType))
% 4.65/5.26 rp_ts:=(fun (X0:fofType) (X1:fofType)=> (cutof ((prod X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 rpofn:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (nofrp X1))))):(fofType->fofType)
% 4.65/5.26 rpofnd:=(fun (X0:fofType)=> ((rp_mn (std X0)) (stm X0))):(fofType->fofType)
% 4.65/5.26 rpofnt:=(fun (X0:fofType)=> (rpofrt (rtofn X0))):(fofType->fofType)
% 4.65/5.26 rpofntt:=((e_in cut) natrp):(fofType->fofType)
% 4.65/5.26 rpofp:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (pofrp X1))))):(fofType->fofType)
% 4.65/5.26 rpofpd:=(fun (X0:fofType)=> ((rp_mn (stm X0)) (std X0))):(fofType->fofType)
% 4.65/5.26 rpofrt:=(fun (X0:fofType)=> (cutof (ratset X0))):(fofType->fofType)
% 4.65/5.26 rpofrtt:=((e_in cut) ratrp):(fofType->fofType)
% 4.65/5.26 rt_all:=(all rat):((fofType->Prop)->Prop)
% 4.65/5.26 rt_in:=(esti rat):(fofType->(fofType->Prop))
% 4.65/5.26 rt_is:=(e_is rat):(fofType->(fofType->Prop))
% 4.65/5.26 rt_lb:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((iii1_lbprop X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rt_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))))):(fofType->(fofType->Prop))
% 4.65/5.26 rt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rt_min:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_lb X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop))
% 4.65/5.26 rt_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.65/5.26 rt_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))))):(fofType->(fofType->Prop))
% 4.65/5.26 rt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rt_one:=(one rat):((fofType->Prop)->Prop)
% 4.65/5.26 rt_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.65/5.26 rt_pl:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) plusfrt)):(fofType->(fofType->fofType))
% 4.65/5.26 rt_some:=(l_some rat):((fofType->Prop)->Prop)
% 4.65/5.26 rt_ts:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) timesfrt)):(fofType->(fofType->fofType))
% 4.65/5.26 rt_ub:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((ubprop X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rtc:=(fun (X0:fofType)=> (cutof (sqrtset X0))):(fofType->fofType)
% 4.65/5.26 rtofn:=(fun (X0:fofType)=> (ratof ((n_fr X0) n_1))):(fofType->fofType)
% 4.65/5.26 rtofnt:=((e_in rat) natrt):(fofType->fofType)
% 4.65/5.26 rtofrp:=(((soft rat) cut) ((d_Sigma rat) rpofrt)):(fofType->fofType)
% 4.65/5.26 rtofrtt:=(fun (X0:fofType)=> (rtofrp (rpofrtt X0))):(fofType->fofType)
% 4.65/5.26 rtt_all:=(all ratt):((fofType->Prop)->Prop)
% 4.65/5.26 rtt_is:=(e_is ratt):(fofType->(fofType->Prop))
% 4.65/5.26 rtt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rtt_is X0) X1))):(fofType->(fofType->Prop))
% 4.65/5.26 rtt_one:=(one ratt):((fofType->Prop)->Prop)
% 4.65/5.26 rtt_some:=(l_some ratt):((fofType->Prop)->Prop)
% 4.65/5.26 rttofrp:=((out cut) ratrp):(fofType->fofType)
% 4.65/5.26 rttofrt:=(fun (X0:fofType)=> (rttofrp (rpofrt X0))):(fofType->fofType)
% 4.65/5.26 s01:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_lessis X1) X0)))):(fofType->fofType)
% 4.65/5.26 s02:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_more X1) X0)))):(fofType->fofType)
% 4.65/5.26 s11:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_less X1) X0)))):(fofType->fofType)
% 4.65/5.26 s12:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_moreis X1) X0)))):(fofType->fofType)
% 4.65/5.26 satz100:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.65/5.26 satz100a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.65/5.26 satz101:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_one (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 4.65/5.26 satz101a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_some (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 4.65/5.26 satz101b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_pl X1) X2)) X0)->(((rt_is ((rt_pl X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 4.65/5.26 satz101c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl X1) ((rt_mn X0) X1))) X0))))))
% 4.65/5.26 satz101d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl X1) ((rt_mn X0) X1))))))))
% 4.65/5.26 satz101e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl ((rt_mn X0) X1)) X1)) X0))))))
% 4.65/5.26 satz101f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl ((rt_mn X0) X1)) X1)))))))
% 4.65/5.26 satz101g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_is ((rt_pl X1) X2)) X0)->((rt_is X2) ((rt_mn X0) X1))))))))))
% 4.65/5.26 satz102:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X0) X1)) ((rt_ts X1) X0))))))
% 4.65/5.26 satz103:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts ((rt_ts X0) X1)) X2)) ((rt_ts X0) ((rt_ts X1) X2)))))))))
% 4.65/5.26 satz104:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts X0) ((rt_pl X1) X2))) ((rt_pl ((rt_ts X0) X1)) ((rt_ts X0) X2)))))))))
% 4.65/5.26 satz105a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.65/5.26 satz105b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.65/5.26 satz105c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.65/5.26 satz105d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.65/5.26 satz105e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.65/5.26 satz105f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.65/5.26 satz106a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_more X0) X1))))))))
% 4.65/5.26 satz106b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_is X0) X1))))))))
% 4.65/5.26 satz106c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_less X0) X1))))))))
% 4.65/5.26 satz107:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.65/5.26 satz107a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.65/5.26 satz108a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.65/5.26 satz108b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.65/5.26 satz108c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.65/5.26 satz108d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.65/5.26 satz109:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.65/5.26 satz109a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.65/5.26 satz10:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.65/5.26 satz10a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.65/5.26 satz10b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.65/5.26 satz10c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1)))))))
% 4.65/5.26 satz10d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1)))))))
% 4.65/5.26 satz10e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1))))))
% 4.65/5.26 satz10f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1))))))
% 4.65/5.26 satz10g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1)))))))
% 4.65/5.26 satz10h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1)))))))
% 4.65/5.26 satz10j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1))))))
% 4.65/5.26 satz10k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1))))))
% 4.65/5.26 satz110:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_one (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 4.65/5.26 satz110a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 4.65/5.26 satz110b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->(((rt_is ((rt_ts X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 4.65/5.26 satz110c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X1) ((rt_ov X0) X1))) X0)))))
% 4.65/5.26 satz110d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts X1) ((rt_ov X0) X1)))))))
% 4.65/5.26 satz110e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov X0) X1)) X1)) X0)))))
% 4.65/5.26 satz110f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts ((rt_ov X0) X1)) X1))))))
% 4.65/5.26 satz110g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->((rt_is X2) ((rt_ov X0) X1)))))))))
% 4.65/5.26 satz111a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))->((d_29_ii X0) X1))))))
% 4.65/5.26 satz111b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))->((n_is X0) X1))))))
% 4.65/5.26 satz111c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))->((iii X0) X1))))))
% 4.65/5.26 satz111d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((moref ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.65/5.26 satz111e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is X0) X1)->((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.65/5.26 satz111f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.65/5.26 satz111g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->(n_one (natprop X0)))))
% 4.65/5.26 satz112a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_pf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_pl X0) X1)) n_1))))))
% 4.65/5.26 satz112b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_tf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_ts X0) X1)) n_1))))))
% 4.65/5.26 satz112c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_pl (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_pl X0) X1)))))))))
% 4.65/5.26 satz112d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_pl X0) X1))))))))
% 4.65/5.26 satz112e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_ts (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_ts X0) X1)))))))))
% 4.65/5.26 satz112f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_ts X0) X1))))))))
% 4.65/5.26 satz112g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(((rt_more X0) X1)->(natrt ((rt_mn X0) X1)))))))))
% 4.65/5.26 satz112h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_pl (rtofn X0)) (rtofn X1))) (rtofn ((n_pl X0) X1)))))))
% 4.65/5.26 satz112j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X0)) (rtofn X1))) (rtofn ((n_ts X0) X1)))))))
% 4.65/5.26 satz113a:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((nt_nis ((ap suct) X0)) nt_1t)))
% 4.65/5.26 satz113b:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_is ((ap suct) X0)) ((ap suct) X1))->((nt_is X0) X1))))))
% 4.65/5.26 satz113c:((all_of (fun (X0:fofType)=> ((in X0) (power natt)))) (fun (X0:fofType)=> ((nt_cond1 X0)->((nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((nt_in X1) X0)))))))
% 4.65/5.26 satz114:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((rt_is ((rt_ts (rtofn (den X0))) (ratof X0))) (rtofn (num X0)))))
% 4.65/5.26 satz114a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X1)) (ratof ((n_fr X0) X1)))) (rtofn X0))))))
% 4.65/5.26 satz114b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is (ratof ((n_fr X0) X1))) ((rt_ov (rtofn X0)) (rtofn X1)))))))
% 4.65/5.26 satz114c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ov (rtofn X0)) (rtofn X1))) (ratof ((n_fr X0) X1)))))))
% 4.65/5.26 satz115:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (n_some (fun (X2:fofType)=> ((rt_more ((rt_ts (rtofn X2)) X0)) X1)))))))
% 4.65/5.26 satz115a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and (natrt X2)) ((rt_more ((rt_ts X2) X0)) X1))))))))
% 4.65/5.26 satz116:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) X0)))
% 4.65/5.26 satz117:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_is X0) X1)->((rp_is X1) X0))))))
% 4.65/5.26 satz118:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->(((rp_is X1) X2)->((rp_is X0) X2)))))))))
% 4.65/5.26 satz119:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X2) X1)->((urt X0) X2)))))))))
% 4.65/5.26 satz119a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X1) X2)->((urt X0) X2)))))))))
% 4.65/5.26 satz11:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0))))))
% 4.65/5.26 satz120:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X2) X1)->((lrt X0) X2)))))))))
% 4.65/5.26 satz120a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X1) X2)->((lrt X0) X2)))))))))
% 4.65/5.26 satz121:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_less X1) X0))))))
% 4.65/5.26 satz122:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->((rp_more X1) X0))))))
% 4.65/5.26 satz123:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((orec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.65/5.26 satz123c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->(d_not ((rp_less X0) X1)))))))
% 4.65/5.26 satz123d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->(d_not ((rp_more X0) X1)))))))
% 4.65/5.26 satz123e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_more X0) X1))->((rp_lessis X0) X1))))))
% 4.65/5.26 satz123f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_less X0) X1))->((rp_moreis X0) X1))))))
% 4.65/5.26 satz123g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(d_not ((rp_lessis X0) X1)))))))
% 4.65/5.26 satz123h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(d_not ((rp_moreis X0) X1)))))))
% 4.65/5.26 satz123j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_moreis X0) X1))->((rp_less X0) X1))))))
% 4.65/5.26 satz123k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_lessis X0) X1))->((rp_more X0) X1))))))
% 4.65/5.26 satz124:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->((rp_lessis X1) X0))))))
% 4.65/5.26 satz125:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->((rp_moreis X1) X0))))))
% 4.65/5.26 satz126:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 4.65/5.26 satz127a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 4.65/5.26 satz127b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_lessis X1) X2)->((rp_less X0) X2)))))))))
% 4.65/5.26 satz127c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_moreis X0) X1)->(((rp_more X1) X2)->((rp_more X0) X2)))))))))
% 4.65/5.26 satz127d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_moreis X1) X2)->((rp_more X0) X2)))))))))
% 4.65/5.26 satz128:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X1) X2)->((rp_lessis X0) X2)))))))))
% 4.65/5.26 satz129:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((sum X0) X1))))))
% 4.65/5.26 satz129a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_pl X2) X3)) ((sum X0) X1)))))))))))))
% 4.65/5.26 satz12:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0))))))
% 4.65/5.26 satz130:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_pl X0) X1)) ((rp_pl X1) X0))))))
% 4.65/5.26 satz131:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_pl ((rp_pl X0) X1)) X2)) ((rp_pl X0) ((rp_pl X1) X2)))))))))
% 4.65/5.26 satz132:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (fun (X3:fofType)=> ((d_and ((d_and ((lrt X0) X2)) ((urt X0) X3))) (((d_and ((lrt X0) X2)) ((urt X0) X3))->((rt_is ((rt_mn X3) X2)) X1)))))))))))
% 4.65/5.26 satz132app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (forall (X1:Prop), ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((lrt X0) X3)->((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((urt X0) X4)->(((rt_is ((rt_mn X4) X3)) X2)->X1)))))))->X1))))))
% 4.65/5.26 satz133:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_more ((rp_pl X0) X1)) X0)))))
% 4.65/5.26 satz133a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_less X0) ((rp_pl X0) X1))))))
% 4.65/5.26 satz134:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.65/5.26 satz135b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.65/5.26 satz135c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.65/5.26 satz135d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.65/5.26 satz135e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.65/5.26 satz135f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.65/5.26 satz135g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz135h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 4.65/5.26 satz135j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz135k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 4.65/5.26 satz136a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_more X0) X1))))))))
% 4.65/5.26 satz136b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_is X0) X1))))))))
% 4.65/5.26 satz136c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_less X0) X1))))))))
% 4.65/5.26 satz136d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_more X0) X1))))))))
% 4.65/5.26 satz136e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_is X0) X1))))))))
% 4.65/5.26 satz136f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_less X0) X1))))))))
% 4.65/5.26 satz137:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz137a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz138a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz138b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz138c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz138d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz139:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz139a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.65/5.26 satz13:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0))))))
% 4.65/5.26 satz140:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_one (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 4.65/5.26 satz140a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_some (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 4.65/5.26 satz140b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_pl X1) X2)) X0)->(((rp_is ((rp_pl X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 4.65/5.26 satz140c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl X1) ((rp_mn X0) X1))) X0))))))
% 4.65/5.26 satz140d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl X1) ((rp_mn X0) X1))))))))
% 4.65/5.26 satz140e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl ((rp_mn X0) X1)) X1)) X0))))))
% 4.65/5.26 satz140f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl ((rp_mn X0) X1)) X1)))))))
% 4.65/5.26 satz140g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_is ((rp_pl X1) X2)) X0)->((rp_is X2) ((rp_mn X0) X1))))))))))
% 4.65/5.26 satz140h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(cutprop ((diff X0) X1)))))))
% 4.65/5.26 satz141:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((prod X0) X1))))))
% 4.65/5.26 satz141a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_ts X2) X3)) ((prod X0) X1)))))))))))))
% 4.65/5.26 satz141b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov d_1rt) X1)) X0)) ((rt_ov X0) X1))))))
% 4.65/5.26 satz141c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ov X0) X1)) ((rt_ts ((rt_ov d_1rt) X1)) X0))))))
% 4.65/5.26 satz142:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) ((rp_ts X1) X0))))))
% 4.65/5.26 satz143:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts ((rp_ts X0) X1)) X2)) ((rp_ts X0) ((rp_ts X1) X2)))))))))
% 4.65/5.26 satz144:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts X0) ((rp_pl X1) X2))) ((rp_pl ((rp_ts X0) X1)) ((rp_ts X0) X2)))))))))
% 4.65/5.26 satz145a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.65/5.26 satz145b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.65/5.26 satz145c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.65/5.26 satz145d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.65/5.26 satz145e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.65/5.26 satz145f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.65/5.26 satz145g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz145h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 4.65/5.26 satz145j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz145k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 4.65/5.26 satz146a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_more X0) X1))))))))
% 4.65/5.26 satz146b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_is X0) X1))))))))
% 4.65/5.26 satz146c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_less X0) X1))))))))
% 4.65/5.26 satz146d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_more X0) X1))))))))
% 4.65/5.26 satz146e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_is X0) X1))))))))
% 4.65/5.26 satz146f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_less X0) X1))))))))
% 4.65/5.26 satz147:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz147a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz148a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz148b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz148c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz148d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz149:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz149a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.65/5.26 satz14:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0))))))
% 4.65/5.26 satz150:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (cutprop (ratset X0))))
% 4.65/5.26 satz151:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) d_1rp)) X0)))
% 4.65/5.26 satz151a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts X0) d_1rp))))
% 4.65/5.26 satz151b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts d_1rp) X0)) X0)))
% 4.65/5.26 satz151c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts d_1rp) X0))))
% 4.65/5.26 satz152:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_some (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) d_1rp)))))
% 4.65/5.26 satz153:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_one (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 4.65/5.26 satz153a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 4.65/5.26 satz153b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->(((rp_is ((rp_ts X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 4.65/5.26 satz153c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) ((rp_ov X0) X1))) X0)))))
% 4.65/5.26 satz153d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts X1) ((rp_ov X0) X1)))))))
% 4.65/5.26 satz153e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts ((rp_ov X0) X1)) X1)) X0)))))
% 4.65/5.26 satz153f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts ((rp_ov X0) X1)) X1))))))
% 4.65/5.26 satz153g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->((rp_is X2) ((rp_ov X0) X1)))))))))
% 4.65/5.26 satz154a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_more (rpofrt X0)) (rpofrt X1)))))))
% 4.65/5.26 satz154b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rp_is (rpofrt X0)) (rpofrt X1)))))))
% 4.65/5.26 satz154c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rp_less (rpofrt X0)) (rpofrt X1)))))))
% 4.65/5.26 satz154d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_more (rpofrt X0)) (rpofrt X1))->((rt_more X0) X1))))))
% 4.65/5.26 satz154e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_is (rpofrt X0)) (rpofrt X1))->((rt_is X0) X1))))))
% 4.65/5.26 satz154f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X0)) (rpofrt X1))->((rt_less X0) X1))))))
% 4.65/5.26 satz155a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_pl X0) X1))) ((rp_pl (rpofrt X0)) (rpofrt X1)))))))
% 4.65/5.26 satz155b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_is (rpofrt ((rt_mn X0) X1))) ((rp_mn (rpofrt X0)) (rpofrt X1))))))))
% 4.65/5.26 satz155c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ts X0) X1))) ((rp_ts (rpofrt X0)) (rpofrt X1)))))))
% 4.65/5.26 satz155d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ov X0) X1))) ((rp_ov (rpofrt X0)) (rpofrt X1)))))))
% 4.65/5.26 satz155e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_pl X0) X1))) ((rp_pl (rpofnt X0)) (rpofnt X1)))))))
% 4.65/5.26 satz155f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_ts X0) X1))) ((rp_ts (rpofnt X0)) (rpofnt X1)))))))
% 4.65/5.26 satz156a:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((rp_nt_nis ((ap nt_suct) X0)) rp_nt_1t)))
% 4.65/5.26 satz156b:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> (((rp_nt_is ((ap nt_suct) X0)) ((ap nt_suct) X1))->((rp_nt_is X0) X1))))))
% 4.65/5.26 satz156c:((all_of (fun (X0:fofType)=> ((in X0) (power nt_natt)))) (fun (X0:fofType)=> ((rp_nt_cond1 X0)->((rp_nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> ((rp_nt_in X1) X0)))))))
% 4.65/5.26 satz157a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->((rt_min ((d_Sep rat) (urt X0))) (rtofrp X0)))))
% 4.65/5.26 satz157b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->(rt_some (rt_min ((d_Sep rat) (urt X0)))))))
% 4.65/5.26 satz157c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_min ((d_Sep rat) (urt X0))) X1)->((rp_is X0) (rpofrt X1)))))))
% 4.65/5.26 satz157d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rt_some (rt_min ((d_Sep rat) (urt X0))))->(ratrp X0))))
% 4.65/5.26 satz158a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((rp_less (rpofrt X1)) X0))))))
% 4.65/5.26 satz158b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((rp_moreis (rpofrt X1)) X0))))))
% 4.65/5.26 satz158c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X1)) X0)->((lrt X0) X1))))))
% 4.65/5.26 satz158d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_moreis (rpofrt X1)) X0)->((urt X0) X1))))))
% 4.65/5.26 satz159:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rp_less X0) (rpofrt X2))) ((rp_less (rpofrt X2)) X1)))))))))
% 4.65/5.26 satz159a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rp_some (fun (X2:fofType)=> (((and3 (ratrp X2)) ((rp_less X0) X2)) ((rp_less X2) X1)))))))))
% 4.65/5.26 satz159app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(forall (X2:Prop), (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rp_less X0) (rpofrt X3))->(((rp_less (rpofrt X3)) X1)->X2))))->X2)))))))
% 4.65/5.26 satz15:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 4.65/5.26 satz160:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(rt_some (fun (X3:fofType)=> (rt_some (fun (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2)))))))))))))
% 4.65/5.26 satz160app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(forall (X3:Prop), (((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((rp_more (rpofrt X4)) X0)->((all_of (fun (X5:fofType)=> ((in X5) rat))) (fun (X5:fofType)=> (((rp_more (rpofrt X5)) X1)->(((rt_is ((rt_ts X4) X5)) X2)->X3)))))))->X3)))))))))
% 4.65/5.26 satz161:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_one (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))))
% 4.65/5.26 satz162:(rp_some irratrp)
% 4.65/5.26 satz163:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) X0)))
% 4.65/5.26 satz164:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is X1) X0))))))
% 4.65/5.26 satz165:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->(((r_is X1) X2)->((r_is X0) X2)))))))))
% 4.65/5.26 satz166a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(pos (abs X0)))))
% 4.65/5.26 satz166b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (abs X0)))))
% 4.65/5.26 satz166c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 4.65/5.26 satz166d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 4.65/5.26 satz166e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_nis X0) r_0)->(pos (abs X0)))))
% 4.65/5.26 satz166f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (abs X0)) r_0))))
% 4.65/5.26 satz167:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((orec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.65/5.26 satz167a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((or3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.65/5.26 satz167b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((ec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.65/5.26 satz167c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->(d_not ((r_less X0) X1)))))))
% 4.65/5.26 satz167d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->(d_not ((r_more X0) X1)))))))
% 4.65/5.26 satz167e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_more X0) X1))->((r_lessis X0) X1))))))
% 4.65/5.26 satz167f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_less X0) X1))->((r_moreis X0) X1))))))
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% 4.65/5.26 satz169b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_more X0) r_0)->(pos X0))))
% 4.65/5.26 satz169c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->((r_less X0) r_0))))
% 4.65/5.26 satz169d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_less X0) r_0)->(neg X0))))
% 4.65/5.26 satz16a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
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% 4.65/5.26 satz170:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_moreis (abs X0)) r_0)))
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% 4.65/5.26 satz172c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_moreis X0) X1)->(((r_more X1) X2)->((r_more X0) X2)))))))))
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% 4.65/5.26 satz173:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_lessis X1) X2)->((r_lessis X0) X2)))))))))
% 4.65/5.26 satz174:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((intrl X0)->(ratrl X0))))
% 4.65/5.26 satz175:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X0) X1)) ((r_pl X1) X0))))))
% 4.65/5.26 satz176a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(neg (r_m0 X0)))))
% 4.65/5.26 satz176b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (r_m0 X0)) r_0))))
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% 4.65/5.26 satz176d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg (r_m0 X0))->(pos X0))))
% 4.65/5.26 satz176e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is (r_m0 X0)) r_0)->((r_is X0) r_0))))
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% 4.65/5.26 satz177a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) (r_m0 (r_m0 X0)))))
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% 4.65/5.26 satz178:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs (r_m0 X0))) (abs X0))))
% 4.65/5.26 satz178a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs X0)) (abs (r_m0 X0)))))
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% 4.65/5.26 satz179a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl (r_m0 X0)) X0)) r_0)))
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% 4.65/5.26 satz188f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 4.65/5.26 satz188g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X2) X0)) ((r_pl X2) X1))->((r_more X0) X1))))))))
% 4.65/5.26 satz188h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X0)) ((r_pl X2) X1))->((r_is X0) X1))))))))
% 4.65/5.26 satz188j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X2) X0)) ((r_pl X2) X1))->((r_less X0) X1))))))))
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% 4.65/5.26 satz188l:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 4.65/5.26 satz188m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 4.65/5.26 satz188n:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz188o:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X2) X0)) ((r_pl X3) X1))))))))))))
% 4.65/5.26 satz188p:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz188q:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X2) X0)) ((r_pl X3) X1))))))))))))
% 4.65/5.26 satz189:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz189a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz18:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0)))))
% 4.65/5.26 satz18a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1))))))
% 4.65/5.26 satz18b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0)))
% 4.65/5.26 satz18c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0))))
% 4.65/5.26 satz190a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz190b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_moreis X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz190c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz190d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_lessis X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz191:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_moreis X2) X3)->((r_moreis ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz191a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_lessis X2) X3)->((r_lessis ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.65/5.26 satz192a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) r_0)->((r_is ((r_ts X0) X1)) r_0))))))
% 4.65/5.26 satz192b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X1) r_0)->((r_is ((r_ts X0) X1)) r_0))))))
% 4.65/5.26 satz192c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_ts X0) X1)) r_0)->((l_or ((r_is X0) r_0)) ((r_is X1) r_0)))))))
% 4.65/5.26 satz192d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X0) r_0)->(((r_nis X1) r_0)->((r_nis ((r_ts X0) X1)) r_0)))))))
% 4.65/5.26 satz193:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (abs ((r_ts X0) X1))) ((r_ts (abs X0)) (abs X1)))))))
% 4.65/5.26 satz193a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (abs X0)) (abs X1))) (abs ((r_ts X0) X1)))))))
% 4.65/5.26 satz194:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts X1) X0))))))
% 4.65/5.26 satz195:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts X0) d_1rl)) X0)))
% 4.65/5.26 satz195a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts X0) d_1rl))))
% 4.65/5.26 satz195b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts d_1rl) X0)) X0)))
% 4.65/5.26 satz195c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts d_1rl) X0))))
% 4.65/5.26 satz196a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))))))))
% 4.65/5.26 satz196b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))))))))
% 4.65/5.26 satz196c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((neg X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))))))))
% 4.65/5.26 satz196d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((pos X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))))))))
% 4.65/5.26 satz196e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1))))))))))
% 4.65/5.26 satz196f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))))
% 4.65/5.26 satz196g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1))))))))
% 4.65/5.26 satz196h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))
% 4.65/5.26 satz197a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) (r_m0 ((r_ts X0) X1)))))))
% 4.65/5.26 satz197b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) (r_m0 ((r_ts X0) X1)))))))
% 4.65/5.26 satz197c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) ((r_ts X0) (r_m0 X1)))))))
% 4.65/5.26 satz197d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) ((r_ts (r_m0 X0)) X1))))))
% 4.65/5.26 satz197e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts (r_m0 X0)) X1))))))
% 4.65/5.26 satz197f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts X0) (r_m0 X1)))))))
% 4.65/5.26 satz198:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) (r_m0 X1))) ((r_ts X0) X1))))))
% 4.65/5.26 satz198a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts (r_m0 X0)) (r_m0 X1)))))))
% 4.65/5.26 satz199:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts ((r_ts X0) X1)) X2)) ((r_ts X0) ((r_ts X1) X2)))))))))
% 4.65/5.26 satz19a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.65/5.26 satz19b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.65/5.26 satz19c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.65/5.26 satz19d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.65/5.26 satz19e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.65/5.26 satz19f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.65/5.26 satz19g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz19h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 4.65/5.26 satz19j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz19k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 4.65/5.26 satz19l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.65/5.26 satz19m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.65/5.26 satz19n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.65/5.26 satz19o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.65/5.26 satz1:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1)))))))
% 4.65/5.26 satz201:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_pl X1) X2))) ((r_pl ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 4.65/5.26 satz202:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_mn X1) X2))) ((r_mn ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 4.65/5.26 satz203a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.65/5.26 satz203b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X0) X2)) ((r_ts X1) X2)))))))))
% 4.65/5.26 satz203c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.65/5.26 satz203d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.65/5.26 satz203e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X2) X0)) ((r_ts X2) X1)))))))))
% 4.65/5.26 satz203f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.65/5.26 satz203g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.65/5.26 satz203j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.65/5.26 satz203k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.65/5.26 satz203m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.65/5.26 satz204:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_one (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 4.65/5.26 satz204a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_some (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 4.65/5.26 satz204b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is ((r_ts X1) X2)) X0)->(((r_is ((r_ts X1) X3)) X0)->((r_is X2) X3))))))))))))
% 4.65/5.26 satz204c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts X1) ((r_ov X0) X1))) X0))))))
% 4.65/5.26 satz204d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts X1) ((r_ov X0) X1))))))))
% 4.65/5.26 satz204e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts ((r_ov X0) X1)) X1)) X0))))))
% 4.65/5.26 satz204f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts ((r_ov X0) X1)) X1)))))))
% 4.65/5.26 satz204g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_nis X1) r_0)->(((r_is ((r_ts X1) X2)) X0)->((r_is X2) ((r_ov X0) X1))))))))))
% 4.65/5.26 satz205:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->(r_one (fun (X2:fofType)=> ((d_and (r_all (fun (X3:fofType)=> (((r_less X3) X2)->((r_in X3) X0))))) (r_all (fun (X3:fofType)=> (((r_more X3) X2)->((r_in X3) X1)))))))))))))))
% 4.65/5.26 satz205a:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X2) ((r_schnitt X0) X1))->((r_in X2) X0))))))))))))
% 4.65/5.26 satz205b:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X2) ((r_schnitt X0) X1))->((r_in X2) X1))))))))))))
% 4.65/5.26 satz20a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1))))))))
% 4.65/5.26 satz20b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1))))))))
% 4.65/5.26 satz20c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1))))))))
% 4.65/5.26 satz20d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1))))))))
% 4.65/5.26 satz20e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1))))))))
% 4.65/5.26 satz20f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1))))))))
% 4.65/5.26 satz21:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz21a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz22a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz22b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz22c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz22d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz23:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz23a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.65/5.26 satz24:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1)))
% 4.65/5.26 satz24a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1))
% 4.65/5.26 satz24b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1)))
% 4.65/5.26 satz24c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0))))
% 4.65/5.26 satz25:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1)))))))
% 4.65/5.26 satz25a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0)))))))
% 4.65/5.26 satz25b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0))))))
% 4.65/5.26 satz25c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0))))))
% 4.65/5.26 satz26:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0))))))
% 4.65/5.26 satz26a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0))))))
% 4.65/5.26 satz26b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0))))))
% 4.65/5.26 satz26c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0))))))
% 4.65/5.26 satz27:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0))))
% 4.65/5.26 satz27a:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0))))
% 4.65/5.26 satz28:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))))))
% 4.65/5.26 satz28a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0)))
% 4.65/5.26 satz28b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0))))))
% 4.65/5.26 satz28c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0)))
% 4.65/5.26 satz28d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1))))))
% 4.65/5.26 satz28e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1))))
% 4.65/5.26 satz28f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1)))))))
% 4.65/5.26 satz28g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0))))
% 4.65/5.26 satz28h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1))))))
% 4.65/5.26 satz29:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))))))
% 4.65/5.26 satz2:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 4.65/5.26 satz30:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))))))))
% 4.65/5.26 satz31:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))))))))
% 4.65/5.26 satz32a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.65/5.26 satz32b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.65/5.26 satz32c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.65/5.26 satz32d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.65/5.26 satz32e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.65/5.26 satz32f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.65/5.26 satz32g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz32h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 4.65/5.26 satz32j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz32k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 4.65/5.26 satz32l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.65/5.26 satz32m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.65/5.26 satz32n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.65/5.26 satz32o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.65/5.26 satz33a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1))))))))
% 4.65/5.26 satz33b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1))))))))
% 4.65/5.26 satz33c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1))))))))
% 4.65/5.26 satz34:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz34a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz35a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz35b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz35c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz35d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz36:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz36a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.65/5.26 satz37:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0)))
% 4.65/5.26 satz38:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0))))))
% 4.65/5.26 satz39:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2)))))))))
% 4.65/5.26 satz3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 4.65/5.26 satz3a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 4.65/5.26 satz40:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1)))))))
% 4.65/5.26 satz40a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0)))))
% 4.65/5.26 satz40b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.65/5.26 satz40c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1))))))))
% 4.65/5.26 satz41:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.65/5.26 satz41a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.65/5.26 satz41b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.65/5.26 satz41c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1)))))))
% 4.65/5.26 satz41d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1)))))))
% 4.65/5.26 satz41e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1))))))
% 4.65/5.26 satz41f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1))))))
% 4.65/5.26 satz41g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1)))))))
% 4.65/5.26 satz41h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1)))))))
% 4.65/5.26 satz41j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1))))))
% 4.65/5.26 satz41k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1))))))
% 4.65/5.26 satz42:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0))))))
% 4.65/5.26 satz43:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0))))))
% 4.65/5.26 satz44:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3))))))))))))
% 4.65/5.26 satz45:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3))))))))))))
% 4.65/5.26 satz46:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3))))))))))))
% 4.65/5.26 satz47:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3))))))))))))
% 4.65/5.26 satz48:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0))))))
% 4.65/5.26 satz49:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0))))))
% 4.65/5.26 satz4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2))))))))))
% 4.65/5.26 satz4a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0))))
% 4.65/5.26 satz4b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1)))))))
% 4.65/5.26 satz4c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0))))
% 4.65/5.26 satz4d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1)))))))
% 4.65/5.26 satz4e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1))))
% 4.65/5.26 satz4f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1)))))))
% 4.65/5.26 satz4g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0))))
% 4.65/5.26 satz4h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1))))))
% 4.65/5.26 satz50:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 4.65/5.26 satz51a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 4.65/5.26 satz51b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2)))))))))
% 4.65/5.26 satz51c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2)))))))))
% 4.65/5.26 satz51d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2)))))))))
% 4.65/5.26 satz52:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lesseq X1) X2)->((lesseq X0) X2)))))))))
% 4.65/5.26 satz53:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0)))))
% 4.65/5.26 satz54:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0)))))
% 4.65/5.26 satz55:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1)))))))))
% 4.65/5.26 satz56:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz57:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2))))))))
% 4.65/5.26 satz57a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2)))))))))
% 4.65/5.26 satz58:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_pf X0) X1)) ((n_pf X1) X0))))))
% 4.65/5.26 satz59:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2)))))))))
% 4.65/5.26 satz5:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))))))))
% 4.65/5.26 satz60:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((moref ((n_pf X0) X1)) X0)))))
% 4.65/5.26 satz60a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((lessf X0) ((n_pf X0) X1))))))
% 4.65/5.26 satz61:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.65/5.26 satz62b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.65/5.26 satz62c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.65/5.26 satz62d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.65/5.26 satz62e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.65/5.26 satz62f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.65/5.26 satz62g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz62h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 4.65/5.26 satz62j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz62k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 4.65/5.26 satz63a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1))))))))
% 4.65/5.26 satz63b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1))))))))
% 4.65/5.26 satz63c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1))))))))
% 4.65/5.26 satz63d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1))))))))
% 4.65/5.26 satz63e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1))))))))
% 4.65/5.26 satz63f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1))))))))
% 4.65/5.26 satz64:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz64a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz65a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz65b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz65c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz65d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz66:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz66a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.65/5.26 satz67a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0))))))))
% 4.65/5.26 satz67b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 4.65/5.26 satz67d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1))))))))
% 4.65/5.26 satz67e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1))))))))))
% 4.65/5.26 satz68:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz69:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_tf X0) X1)) ((n_tf X1) X0))))))
% 4.65/5.26 satz6:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))))))
% 4.65/5.26 satz70:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2)))))))))
% 4.65/5.26 satz71:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2)))))))))
% 4.65/5.26 satz72a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.65/5.26 satz72b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.65/5.26 satz72c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.65/5.26 satz72d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.65/5.26 satz72e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.65/5.26 satz72f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.65/5.26 satz72g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz72h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 4.65/5.26 satz72j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz72k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 4.65/5.26 satz73a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1))))))))
% 4.65/5.26 satz73b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1))))))))
% 4.65/5.26 satz73c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1))))))))
% 4.65/5.26 satz73d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1))))))))
% 4.65/5.26 satz73e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1))))))))
% 4.65/5.26 satz73f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1))))))))
% 4.65/5.26 satz74:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz74a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz75a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz75b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz75c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz75d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz76:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz76a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.65/5.26 satz77a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0)))))))
% 4.65/5.26 satz77b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 4.65/5.26 satz78:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0)))
% 4.65/5.26 satz79:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0))))))
% 4.65/5.26 satz7:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))))
% 4.65/5.26 satz80:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2)))))))))
% 4.65/5.26 satz81:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.65/5.26 satz81a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.65/5.26 satz81b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.65/5.26 satz81c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1)))))))
% 4.65/5.26 satz81d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1)))))))
% 4.65/5.26 satz81e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1))))))
% 4.65/5.26 satz81f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1))))))
% 4.65/5.26 satz81g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1)))))))
% 4.65/5.26 satz81h:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(d_not ((rt_moreis X0) X1)))))))
% 4.65/5.26 satz81j:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_moreis X0) X1))->((rt_less X0) X1))))))
% 4.65/5.26 satz81k:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_lessis X0) X1))->((rt_more X0) X1))))))
% 4.65/5.26 satz82:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0))))))
% 4.65/5.26 satz83:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0))))))
% 4.65/5.26 satz84:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->((rt_lessis X1) X0))))))
% 4.65/5.26 satz85:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->((rt_moreis X1) X0))))))
% 4.65/5.26 satz86:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 4.65/5.26 satz87a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 4.65/5.26 satz87b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_lessis X1) X2)->((rt_less X0) X2)))))))))
% 4.65/5.26 satz87c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_moreis X0) X1)->(((rt_more X1) X2)->((rt_more X0) X2)))))))))
% 4.65/5.26 satz87d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_moreis X1) X2)->((rt_more X0) X2)))))))))
% 4.65/5.26 satz88:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X1) X2)->((rt_lessis X0) X2)))))))))
% 4.65/5.26 satz89:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_more X1) X0)))))
% 4.65/5.26 satz8:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2)))))))))
% 4.65/5.26 satz8a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2))))))))
% 4.65/5.26 satz8b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))))))
% 4.65/5.26 satz90:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_less X1) X0)))))
% 4.65/5.26 satz91:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rt_less X0) X2)) ((rt_less X2) X1)))))))))
% 4.65/5.26 satz92:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_pl X0) X1)) ((rt_pl X1) X0))))))
% 4.65/5.26 satz93:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_pl ((rt_pl X0) X1)) X2)) ((rt_pl X0) ((rt_pl X1) X2)))))))))
% 4.65/5.26 satz94:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_more ((rt_pl X0) X1)) X0)))))
% 4.65/5.26 satz94a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_less X0) ((rt_pl X0) X1))))))
% 4.65/5.26 satz95:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.65/5.26 satz96b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.65/5.26 satz96c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.65/5.26 satz96d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.65/5.26 satz96e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.65/5.26 satz96f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.65/5.26 satz97a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_more X0) X1))))))))
% 4.65/5.26 satz97b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_is X0) X1))))))))
% 4.65/5.26 satz97c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_less X0) X1))))))))
% 4.65/5.26 satz98:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.65/5.26 satz98a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.65/5.26 satz99a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.65/5.26 satz99b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.65/5.26 satz99c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.65/5.26 satz99d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.65/5.26 satz9:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2)))))))))
% 4.65/5.26 satz9a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 4.65/5.26 satz9b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 4.65/5.26 sc1:=(fun (X0:fofType)=> ((d_Sep cut) (fun (X1:fofType)=> ((r_in (pofrp X1)) X0)))):(fofType->fofType)
% 4.65/5.26 schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) ((d_5p205_prop3 X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 schnittprop:=(fun (X0:fofType) (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((d_and ((rp_in X2) X0)) ((lrt X2) X1))))):(fofType->(fofType->Prop))
% 4.65/5.26 schnittset:=(fun (X0:fofType)=> ((d_Sep rat) (schnittprop X0))):(fofType->fofType)
% 4.65/5.26 second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)):(fofType->(fofType->fofType))
% 4.65/5.26 second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 second_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1))))))
% 4.65/5.26 secondis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3))))))
% 4.65/5.26 seq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Pi real) (fun (X3:fofType)=> (((if (intrl X3)) (((if ((r_lessis X1) X3)) (((if ((r_lessis X3) X0)) X2) (ordsucc emptyset))) (ordsucc emptyset))) (ordsucc emptyset))))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 set_ext:(forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1))))
% 4.65/5.26 setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 setof_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0)))))
% 4.65/5.26 setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))):(fofType->(fofType->fofType))
% 4.65/5.26 shift_n1:=(fun (X0:fofType) (X1:fofType)=> (inn ((shiftl X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 shift_n2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rlofnt (((shift_n1 X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 shift_ns:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ap X2) (((shiftr X0) X1) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 shift_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((r_is X3) ((ap X2) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.65/5.26 shift_ul:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((shiftl X2) X1)):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 shiftf:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X4:fofType)=> ((ap X3) (((shiftr X0) X1) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 shiftl1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((shiftl X0) X1)) (((shift_ul X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 shiftl:=(fun (X0:fofType) (X1:fofType)=> (ntofrl ((r_mn ((r_pl X0) d_1rl)) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 shiftr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((r_mn ((r_pl (((shift_n2 X0) X1) X2)) X1)) d_1rl)):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 shiftseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X3:fofType)=> (((shiftl1 X0) X1) ((((shift_ns X0) X1) X2) X3))))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 singlet_u0:=(inn n_1):(fofType->fofType)
% 4.65/5.26 snt:=(fun (X0:fofType) (X1:fofType)=> (cutof (schnittset X0))):(fofType->(fofType->fofType))
% 4.65/5.26 soft:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 sq1:=(fun (X0:fofType)=> ((rp_ts X0) X0)):(fofType->fofType)
% 4.65/5.26 sqrt:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))):(fofType->fofType)
% 4.65/5.26 sqrtset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rp_less ((rp_ts (rpofrt X1)) (rpofrt X1))) X0)))):(fofType->fofType)
% 4.65/5.26 srp:=(fun (X0:fofType)=> (sqrt (rpofpd X0))):(fofType->fofType)
% 4.65/5.26 st_disj:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 stc:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((schnitt (sc1 X0)) (sc1 X1))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 std:=(second1 cut):(fofType->fofType)
% 4.65/5.26 stm:=(first1 cut):(fofType->fofType)
% 4.65/5.26 stp:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (pofrp (((stc X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 subrelation:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (R':(A->(B->Prop)))=> (forall (x:A) (y:B), (((R x) y)->((R' x) y)))):(forall (A:Type) (B:Type), ((A->(B->Prop))->((A->(B->Prop))->Prop)))
% 4.65/5.26 suc_p:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat)))))
% 4.65/5.26 suct:=((d_Sigma natt) (fun (X0:fofType)=> (ntofn (ordsucc (nofnt X0))))):fofType
% 4.65/5.26 sum:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((sumprop X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 sumprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_pl X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.65/5.26 sumprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((sumprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 surjseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((((imseq X0) X1) X2) X3))))))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->fofType)
% 4.65/5.26 timesdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_td X0) X1)))))):fofType
% 4.65/5.26 timesfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_tf X0) X1)))))):fofType
% 4.65/5.26 tofs:=(fun (X0:fofType) (X1:fofType)=> ap):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 u01:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X2) ((rt_pl X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 ubprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_moreis X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.65/5.26 ul1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((shiftl1 X0) X1)):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.65/5.26 um10:=(fun (X0:fofType)=> ((rt_mn (rtofn X0)) d_1rt)):(fofType->fofType)
% 4.65/5.26 um1:=(fun (X0:fofType)=> (nofrt (um10 X0))):(fofType->fofType)
% 4.65/5.26 union:(fofType->fofType)
% 4.65/5.26 unique:=(fun (A:Type) (P:(A->Prop)) (x:A)=> ((and (P x)) (forall (x':A), ((P x')->(((eq A) x) x'))))):(forall (A:Type), ((A->Prop)->(A->Prop)))
% 4.65/5.26 unique_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R x) y))))))=> ((((dependent_unique_choice A) (fun (x2:A)=> B)) R) x)):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R x) y)))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% 4.65/5.26 univof:(fofType->fofType)
% 4.65/5.26 unmore:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4))))))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 urt:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_in X1) (lcl X0)))):(fofType->(fofType->Prop))
% 4.65/5.26 wel:=(fun (X0:Prop)=> (d_not (d_not X0))):(Prop->Prop)
% 4.65/5.26 wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.65/5.26 wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 wissel_wb:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.65/5.26 xi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2))))
% 4.65/5.26 xmy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_mn (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 xout:=(fun (X0:fofType)=> ((outn X0) X0)):(fofType->fofType)
% 4.65/5.26 xpy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_pl (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 xrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_xm X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 xty:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_ts (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.65/5.26 yrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_ym X0) X1))):(fofType->(fofType->fofType))
% 4.65/5.26 zero:=(fun (X0:fofType)=> ((rp_is (stm X0)) (std X0))):(fofType->Prop)
% 4.65/5.26 zeta:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((((ite ((rp_less (((d_5160_fr X0) X1) X2)) d_1rp)) cut) (((d_5160_fr X0) X1) X2)) d_1rp)):(fofType->(fofType->(fofType->fofType)))]X0:fofType
% 4.78/5.35 X1:(fofType->Prop)
% 4.78/5.35 X2:fofType]x:((is_of X2) (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1))))]x0:fofType
% 4.78/5.35 ---subcontext
% 4.78/5.35 [False:Prop
% 4.78/5.35 False_rect:(forall (P:Type), (False->P))
% 4.78/5.35 I:True
% 4.78/5.35 NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% 4.78/5.35 True:Prop
% 4.78/5.35 _TPTP_proj1:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj)):(fofType->fofType)
% 4.78/5.35 abs:=((indreal real) absdr):(fofType->fofType)
% 4.78/5.35 absd:=(fun (X0:fofType)=> ((((ite (negd X0)) dif) ((rp_df (std X0)) (stm X0))) X0)):(fofType->fofType)
% 4.78/5.35 absdr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (absd X0)))):fofType
% 4.78/5.35 all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))):(fofType->((fofType->Prop)->Prop))
% 4.78/5.35 all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))):((fofType->Prop)->((fofType->Prop)->Prop))
% 4.78/5.35 amone:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3)))))))):(fofType->((fofType->Prop)->Prop))
% 4.78/5.35 and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.78/5.35 and:(Prop->(Prop->Prop))
% 4.78/5.35 and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 4.78/5.35 and_rect:=(fun (A:Prop) (B:Prop) (P:Type) (X:(A->(B->P))) (H:((and A) B))=> ((X (((proj1 A) B) H)) (((proj2 A) B) H))):(forall (A:Prop) (B:Prop) (P:Type), ((A->(B->P))->(((and A) B)->P)))
% 4.78/5.35 anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->Prop)))
% 4.78/5.35 ap:=(fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1)):(fofType->(fofType->fofType))
% 4.78/5.35 ap_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))
% 4.78/5.35 apb1:=(fun (X0:fofType) (X1:fofType)=> (rpofpd ((rp_pd X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 arpi:=(fun (X0:fofType)=> ((rp_ov d_1rp) (rpofpd X0))):(fofType->fofType)
% 4.78/5.35 atb3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd ((rp_td X0) X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 beta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2))))
% 4.78/5.35 bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 changef:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.78/5.35 chi:=(fun (X0:fofType) (X1:fofType)=> (cutof ((diff X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% 4.78/5.35 choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% 4.78/5.35 class:=((ecect frac) n_eq):(fofType->fofType)
% 4.78/5.35 classic:(forall (P:Prop), ((or P) (not P)))
% 4.78/5.35 classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 4.78/5.35 cond1:=(n_in n_1):(fofType->Prop)
% 4.78/5.35 cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))):(fofType->Prop)
% 4.78/5.35 conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 4.78/5.35 cut:=((d_Sep (power rat)) cutprop):fofType
% 4.78/5.35 cutof:=((out (power rat)) cutprop):(fofType->fofType)
% 4.78/5.35 cutprop1:=(fun (X0:fofType)=> ((d_and (cutprop1a X0)) (cutprop1b X0))):(fofType->Prop)
% 4.78/5.35 cutprop1a:=(nonempty rat):(fofType->Prop)
% 4.78/5.35 cutprop1b:=(fun (X0:fofType)=> (d_not (rt_all (fun (X1:fofType)=> ((rt_in X1) X0))))):(fofType->Prop)
% 4.78/5.35 cutprop2:=(fun (X0:fofType)=> (rt_all (fun (X1:fofType)=> ((imp ((rt_in X1) X0)) ((cutprop2a X0) X1))))):(fofType->Prop)
% 4.78/5.35 cutprop2a:=(fun (X0:fofType) (X1:fofType)=> (rt_all (fun (X2:fofType)=> ((imp (d_not ((rt_in X2) X0))) ((rt_less X1) X2))))):(fofType->(fofType->Prop))
% 4.78/5.35 cutprop3:=(fun (X0:fofType)=> (d_not (rt_some (max X0)))):(fofType->Prop)
% 4.78/5.35 cutprop:=(fun (X0:fofType)=> (((and3 (cutprop1 X0)) (cutprop2 X0)) (cutprop3 X0))):(fofType->Prop)
% 4.78/5.35 d161_s:=(fun (X0:fofType)=> (pdofrp (srp X0))):(fofType->fofType)
% 4.78/5.35 d_10_prop1:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))
% 4.78/5.35 d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2)))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 4.78/5.35 d_1df:=(pdofrp d_1rp):fofType
% 4.78/5.35 d_1out:=(fun (X0:fofType)=> ((outn X0) n_1)):(fofType->fofType)
% 4.78/5.35 d_1rl:=(realof d_1df):fofType
% 4.78/5.35 d_1rp:=(rpofrt d_1rt):fofType
% 4.78/5.35 d_1rt:=(rtofn n_1):fofType
% 4.78/5.35 d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->fofType)
% 4.78/5.35 d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0)):(fofType->Prop)
% 4.78/5.35 d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))):(fofType->Prop)
% 4.78/5.35 d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))):(fofType->fofType)
% 4.78/5.35 d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))):(fofType->Prop)
% 4.78/5.35 d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_25_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))):(fofType->(fofType->Prop))
% 4.78/5.35 d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_29_prop1:=(fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_2rl:=((r_pl d_1rl) d_1rl):fofType
% 4.78/5.35 d_2x0:=(fun (X0:fofType)=> ((rt_pl X0) X0)):(fofType->fofType)
% 4.78/5.35 d_3129_z1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X0) ((rt_pl X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 d_3132_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((lrt X0) X1)) ((urt X0) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_3132_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((rt_is ((rt_mn X3) X2)) X1)):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 d_3132_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((d_3132_prop1 X0) X2) X3)) ((((d_3132_prop1 X0) X2) X3)->((((d_3132_prop2 X0) X1) X2) X3)))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 d_3132_prop4:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (((d_3132_prop3 X0) X1) X2))))):(fofType->(fofType->Prop))
% 4.78/5.35 d_3132_u0:=(fun (X0:fofType) (X1:fofType)=> ((rt_pl X1) X0)):(fofType->(fofType->fofType))
% 4.78/5.35 d_3132_v0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (um10 X2)) X0))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 d_3132_w0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (rtofn X2)) X0))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 d_367_vo:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))):(fofType->(fofType->fofType))
% 4.78/5.35 d_367_w:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 d_3r184_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_3r184_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_some ((d_3r184_prop1 X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_3r184_prop3:=(fun (X0:fofType)=> (r_some (d_3r184_prop2 X0))):(fofType->Prop)
% 4.78/5.35 d_4141_v0:=(fun (X0:fofType) (X1:fofType)=> ((rt_ts ((rt_ov d_1rt) X1)) X0)):(fofType->(fofType->fofType))
% 4.78/5.35 d_4144_x2:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_moreis X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.78/5.35 d_4152_chi:=(fun (X0:fofType)=> (cutof (inv X0))):(fofType->fofType)
% 4.78/5.35 d_4153_chi:=(fun (X0:fofType) (X1:fofType)=> ((rp_ts X1) X0)):(fofType->(fofType->fofType))
% 4.78/5.35 d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))):(fofType->fofType)
% 4.78/5.35 d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0)):fofType
% 4.78/5.35 d_428_prop1:=(fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))):(fofType->(fofType->Prop))
% 4.78/5.35 d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->Prop)
% 4.78/5.35 d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))):(fofType->(fofType->Prop))
% 4.78/5.35 d_430_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_431_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_477_v:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 d_5113_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nt_in (ntofn X1)) X0)):(fofType->(fofType->Prop))
% 4.78/5.35 d_5156_prop1:=(fun (X0:fofType) (X1:fofType)=> ((rp_nt_in (nttofnt X1)) X0)):(fofType->(fofType->Prop))
% 4.78/5.35 d_5157_s1:=(fun (X0:fofType)=> ((d_Sep rat) (urt X0))):(fofType->fofType)
% 4.78/5.35 d_5160_dn:=(fun (X0:fofType) (X1:fofType)=> ((rp_pl ((rp_pl X0) X1)) d_1rp)):(fofType->(fofType->fofType))
% 4.78/5.35 d_5160_fr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_ov (((d_5160_nm X0) X1) X2)) ((d_5160_dn X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 d_5160_nm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_mn (rpofrt X2)) ((rp_ts X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 d_5160_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.78/5.35 d_5160_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((d_5160_prop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_5160_xr:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((rt_ov X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 d_5160_y0:=(fun (X0:fofType)=> X0):(fofType->fofType)
% 4.78/5.35 d_5160_yr:=(fun (X0:fofType)=> (rpofrt (d_5160_y0 X0))):(fofType->fofType)
% 4.78/5.35 d_5161_dn:=(fun (X0:fofType)=> ((rp_pl (rpofrt X0)) ((rp_pl (rpofrt X0)) d_1rp))):(fofType->fofType)
% 4.78/5.35 d_5161_fr:=(fun (X0:fofType) (X1:fofType)=> ((rp_ov ((d_5161_nm X0) X1)) (d_5161_dn X1))):(fofType->(fofType->fofType))
% 4.78/5.35 d_5161_max:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_more X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType))
% 4.78/5.35 d_5161_min:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_less X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType))
% 4.78/5.35 d_5161_nm:=(fun (X0:fofType) (X1:fofType)=> ((rp_mn X0) ((rp_ts (rpofrt X1)) (rpofrt X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 d_5161_xm:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_more X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.78/5.35 d_5161_ym:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_less X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.78/5.35 d_5162_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_eq ((n_tf ((n_fr X1) X0)) ((n_fr X1) X0))) ((n_fr (ordsucc n_1)) n_1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_5162_prop2:=(fun (X0:fofType)=> (n_some (d_5162_prop1 X0))):(fofType->Prop)
% 4.78/5.35 d_5162_prop3:=(n_some d_5162_prop2):Prop
% 4.78/5.35 d_5162_x0:=(rtofrp ksi):fofType
% 4.78/5.35 d_5162_y:=((ind nat) (min d_5162_prop2)):fofType
% 4.78/5.35 d_527_q:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (X0 (ntofn X1))):((fofType->Prop)->(fofType->Prop))
% 4.78/5.35 d_54_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (nofnt ((ap X0) (ntofn X1)))))):(fofType->fofType)
% 4.78/5.35 d_54_gt:=(fun (X0:fofType)=> ((d_Sigma natt) (fun (X1:fofType)=> (ntofn ((ap X0) (nofnt X1)))))):(fofType->fofType)
% 4.78/5.35 d_54_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc (nofnt X0)))) (d_24_prop1 X1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_59_i:=(fun (X0:fofType) (X1:fofType)=> ((n_is (nofnt X0)) (nofnt X1))):(fofType->(fofType->Prop))
% 4.78/5.35 d_59_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X0)) (nofnt X1)))):(fofType->(fofType->Prop))
% 4.78/5.35 d_59_iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X1)) (nofnt X0)))):(fofType->(fofType->Prop))
% 4.78/5.35 d_5p205_prop1:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_less X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop))
% 4.78/5.35 d_5p205_prop2:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_more X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop))
% 4.78/5.35 d_5p205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5p205_prop1 X0) X2)) ((d_5p205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_5r205_prop1:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_less X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop))
% 4.78/5.35 d_5r205_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_more X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop))
% 4.78/5.35 d_5r205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5r205_prop1 X0) X2)) ((d_5r205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 d_5r205_sp1:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_in (r_m0 X1)) X0)))):(fofType->fofType)
% 4.78/5.35 d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1))):((fofType->((fofType->fofType)->fofType))->(fofType->fofType))
% 4.78/5.35 d_In_rec_G:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))):((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))
% 4.78/5.35 d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1)):(fofType->fofType)
% 4.78/5.35 d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))):(fofType->fofType)
% 4.78/5.35 d_Pi:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))))):(fofType->((fofType->fofType)->fofType))
% 4.78/5.35 d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))):(fofType->Prop)
% 4.78/5.35 d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))):(fofType->((fofType->Prop)->((fofType->fofType)->fofType)))
% 4.78/5.35 d_Repl_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0)))))):(fofType->Prop)
% 4.78/5.35 d_Sep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset)):(fofType->((fofType->Prop)->fofType))
% 4.78/5.35 d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))):(fofType->((fofType->fofType)->fofType))
% 4.78/5.35 d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0)):(fofType->fofType)
% 4.78/5.35 d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))):(fofType->(fofType->Prop))
% 4.78/5.35 d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))):(fofType->Prop)
% 4.78/5.35 d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))):(fofType->fofType)
% 4.78/5.35 d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))):(fofType->Prop)
% 4.78/5.35 d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))):(Prop->(Prop->Prop))
% 4.78/5.35 d_not:=(fun (X0:Prop)=> ((imp X0) False)):(Prop->Prop)
% 4.78/5.35 d_pair:=(fun (X0:fofType) (X1:fofType)=> pair):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 den:=(second1 nat):(fofType->fofType)
% 4.78/5.35 dependent_unique_choice:(forall (A:Type) (B:(A->Type)) (R:(forall (x:A), ((B x)->Prop))), ((forall (x:A), ((ex (B x)) ((unique (B x)) (fun (y:(B x))=> ((R x) y)))))->((ex (forall (x:A), (B x))) (fun (f:(forall (x:A), (B x)))=> (forall (x:A), ((R x) (f x)))))))
% 4.78/5.35 dif:=(pair1type cut):fofType
% 4.78/5.35 diff:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((rp_diffprop X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 diffprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((rt_more X1) X2)) (((rt_more X1) X2)->((rt_is X0) ((rt_mn X1) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 diffprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((urt X1) X4)) (((diffprop1 X2) X3) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.78/5.35 diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 e_fisi:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3)))))))
% 4.78/5.35 e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2):(fofType->((fofType->Prop)->(fofType->fofType)))
% 4.78/5.35 e_in_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 4.78/5.35 e_inp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2)))))
% 4.78/5.35 e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 e_isp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3))))))))
% 4.78/5.35 e_pair_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1)))))))))
% 4.78/5.35 ec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0))):(Prop->(Prop->(Prop->Prop)))
% 4.78/5.35 ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.78/5.35 ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.78/5.35 ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.78/5.35 ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->fofType))
% 4.78/5.35 ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.78/5.35 ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.78/5.35 empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))):(fofType->(fofType->Prop))
% 4.78/5.35 emptyset:fofType
% 4.78/5.35 eps:((fofType->Prop)->fofType)
% 4.78/5.35 eq:=(fun (T:Type) (a:T) (b:T)=> (forall (P:(T->Prop)), ((P a)->(P b)))):(forall (T:Type), (T->(T->Prop)))
% 4.78/5.35 eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% 4.78/5.35 eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% 4.78/5.35 eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% 4.78/5.35 eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 4.78/5.35 eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 4.78/5.35 esti:=(fun (X0:fofType)=> in):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 estie:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2)))))
% 4.78/5.35 estii:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1))))))
% 4.78/5.35 eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% 4.78/5.35 eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% 4.78/5.35 ex:(forall (A:Type), ((A->Prop)->Prop))
% 4.78/5.35 ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% 4.78/5.35 ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% 4.78/5.35 famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))):(fofType->((fofType->fofType)->fofType))
% 4.78/5.35 first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)):(fofType->(fofType->fofType))
% 4.78/5.35 first:=(fun (X0:fofType) (X1:fofType)=> proj0):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 first_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 4.78/5.35 firstis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2))))))
% 4.78/5.35 fixf2:=((fixfu2 dif) rp_eq):(fofType->(fofType->Prop))
% 4.78/5.35 fixf:=((fixfu2 frac) n_eq):(fofType->(fofType->Prop))
% 4.78/5.35 fixfu2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7))))))))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.78/5.35 fixfu:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.78/5.35 fofType:Type
% 4.78/5.35 frac:=(pair1type nat):fofType
% 4.78/5.35 functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% 4.78/5.35 functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 4.78/5.35 functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% 4.78/5.35 half:=((r_ov d_1rl) d_2rl):fofType
% 4.78/5.35 i1_s:=(d_Sep nat):((fofType->Prop)->fofType)
% 4.78/5.35 if:=(fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2)))))):(Prop->(fofType->(fofType->fofType)))
% 4.78/5.35 if_i_0:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2)))
% 4.78/5.35 if_i_1:(forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1)))
% 4.78/5.35 if_i_correct:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2))))
% 4.78/5.35 if_i_or:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2)))
% 4.78/5.35 iff:=(fun (A:Prop) (B:Prop)=> ((and (A->B)) (B->A))):(Prop->(Prop->Prop))
% 4.78/5.35 iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 4.78/5.35 iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 4.78/5.35 iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 4.78/5.35 iii1_lbprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_lessis X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))):(fofType->(fofType->Prop))
% 4.78/5.35 iiia_x0:=(fun (X0:fofType)=> (rtofn (ntofrp X0))):(fofType->fofType)
% 4.78/5.35 iiit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X1) X0))):(fofType->(fofType->Prop))
% 4.78/5.35 iit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 image:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1)):(Prop->(Prop->Prop))
% 4.78/5.35 improp:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and (((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))) ((((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))->(((((shift_prop1 X0) X1) X2) X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.78/5.35 imseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (r_some ((((improp X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 in:(fofType->(fofType->Prop))
% 4.78/5.35 incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))):(fofType->((fofType->Prop)->fofType))
% 4.78/5.35 ind_p:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0)))))
% 4.78/5.35 indeq2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))
% 4.78/5.35 indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 4.78/5.35 indrat:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 indreal2:=((indeq2 dif) rp_eq):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 indreal:=((indeq dif) rp_eq):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 inf:=(esti frac):(fofType->(fofType->Prop))
% 4.78/5.35 inj_h:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.78/5.35 injective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4))))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 injseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->(((r_is ((ap X2) X3)) ((ap X2) X4))->((r_is X3) X4))))))))))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType))
% 4.78/5.35 inseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->(((and3 (intrl ((ap X2) X3))) ((r_lessis X1) ((ap X2) X3))) ((r_lessis ((ap X2) X3)) X0)))))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 intd:=(fun (X0:fofType)=> ((l_or (zero X0)) (natd (absd X0)))):(fofType->Prop)
% 4.78/5.35 intd_a3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X0))):(fofType->(fofType->fofType))
% 4.78/5.35 intd_b2:=(fun (X0:fofType)=> (rpofpd (m0d X0))):(fofType->fofType)
% 4.78/5.35 intd_b3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X1))):(fofType->(fofType->fofType))
% 4.78/5.35 intrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (intd X1))))):(fofType->Prop)
% 4.78/5.35 inv:=(fun (X0:fofType)=> ((d_Sep rat) (invprop X0))):(fofType->fofType)
% 4.78/5.35 inverse:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset)))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 invprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((urt X0) X2)) ((rt_less X2) X1))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 invprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 ((urt X0) X2)) (rt_some ((invprop1 X0) X2))) ((rt_is X1) ((rt_ov d_1rt) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 invprop:=(fun (X0:fofType) (X1:fofType)=> (rt_some ((invprop2 X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 irratd:=(fun (X0:fofType)=> (d_not (ratd X0))):(fofType->Prop)
% 4.78/5.35 irratrl:=(fun (X0:fofType)=> (d_not (ratrl X0))):(fofType->Prop)
% 4.78/5.35 irratrp:=(fun (X0:fofType)=> (d_not (ratrp X0))):(fofType->Prop)
% 4.78/5.35 is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)):(fofType->((fofType->Prop)->Prop))
% 4.78/5.35 isseti:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2))))))))
% 4.78/5.35 ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))):(Prop->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 iv4d_ai:=(fun (X0:fofType)=> (pdofrp (arpi X0))):(fofType->fofType)
% 4.78/5.35 iv5d_2:=((rp_pl d_1rp) d_1rp):fofType
% 4.78/5.35 ivr1_nr:=(fun (X0:fofType)=> rpofnd):(fofType->(fofType->fofType))
% 4.78/5.35 ivr1_pr:=(fun (X0:fofType)=> rpofpd):(fofType->(fofType->fofType))
% 4.78/5.35 ivr2_propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 ivr2_propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 ivr2_x0:=(fun (X0:fofType) (X1:fofType)=> (ntofrp ((ivr1_pr X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 ivr2_xn:=(fun (X0:fofType)=> ((((soft nat) real) ((d_Sigma nat) rlofnt)) (rlofnt X0))):(fofType->fofType)
% 4.78/5.35 k_EmptyAx:(((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False)
% 4.78/5.35 k_If_In_01:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset)))))
% 4.78/5.35 k_If_In_then_E:(forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2))))
% 4.78/5.35 k_In_0_1:((in emptyset) (ordsucc emptyset))
% 4.78/5.35 k_In_ind:(forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1))))
% 4.78/5.35 k_Pi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3))))))
% 4.78/5.35 k_PowerE:(forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0)))
% 4.78/5.35 k_PowerEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0)))
% 4.78/5.35 k_PowerI:(forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0))))
% 4.78/5.35 k_ReplEq:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3)))))))
% 4.78/5.35 k_Self_In_Power:(forall (X0:fofType), ((in X0) (power X0)))
% 4.78/5.35 k_SepE1:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0)))
% 4.78/5.35 k_SepE2:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2)))
% 4.78/5.35 k_SepI:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1)))))
% 4.78/5.35 k_Sigma_eta_proj0_proj1:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))))
% 4.78/5.35 k_UnionEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0))))))
% 4.78/5.35 k_UnivOf_In:(forall (X0:fofType), ((in X0) (univof X0)))
% 4.78/5.35 k_UnivOf_ZF_closed:(forall (X0:fofType), (d_ZF_closed (univof X0)))
% 4.78/5.35 k_satz123a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((or3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.78/5.35 k_satz123b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((ec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.78/5.35 k_satz67c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0))))))
% 4.78/5.35 ksi:=((ind cut) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) X0)) (rpofnt (ordsucc n_1))))):fofType
% 4.78/5.35 l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))):(Prop->(Prop->Prop))
% 4.78/5.35 l_et:(forall (X0:Prop), ((wel X0)->X0))
% 4.78/5.35 l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))):(Prop->(Prop->Prop))
% 4.78/5.35 l_or:=(fun (X0:Prop)=> (imp (d_not X0))):(Prop->(Prop->Prop))
% 4.78/5.35 l_some:=(fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1)))):(fofType->((fofType->Prop)->Prop))
% 4.78/5.35 lam_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1))))
% 4.78/5.35 lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))):((fofType->Prop)->(fofType->(fofType->Prop)))
% 4.78/5.35 lcl:=((e_in (power rat)) cutprop):(fofType->fofType)
% 4.78/5.35 left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 left:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 lessd:=(fun (X0:fofType) (X1:fofType)=> ((rp_less ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.78/5.35 lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.78/5.35 lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 lrt:=(fun (X0:fofType) (X1:fofType)=> ((rt_in X1) (lcl X0))):(fofType->(fofType->Prop))
% 4.78/5.35 m0d:=(fun (X0:fofType)=> ((rp_df (std X0)) (stm X0))):(fofType->fofType)
% 4.78/5.35 m0dr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (m0d X0)))):fofType
% 4.78/5.35 max:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_ub X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop))
% 4.78/5.35 min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop))
% 4.78/5.35 mored:=(fun (X0:fofType) (X1:fofType)=> ((rp_more ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.78/5.35 moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.78/5.35 moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 mxy:=(fun (X0:fofType) (X1:fofType)=> ((r_ts half) ((r_pl X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 n1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (negd X1))):(fofType->(fofType->Prop))
% 4.78/5.35 n1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (posd X1))):(fofType->(fofType->Prop))
% 4.78/5.35 nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)):(fofType->(fofType->Prop))
% 4.78/5.35 n_1:=(ordsucc emptyset):fofType
% 4.78/5.35 n_1_p:((is_of n_1) (fun (X0:fofType)=> ((in X0) nat)))
% 4.78/5.35 n_1o:=((outn n_1) n_1):fofType
% 4.78/5.35 n_1t:=((outn n_2) n_1):fofType
% 4.78/5.35 n_2:=((n_pl n_1) n_1):fofType
% 4.78/5.35 n_2t:=((outn n_2) n_2):fofType
% 4.78/5.35 n_all:=(all nat):((fofType->Prop)->Prop)
% 4.78/5.35 n_ax3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1)))
% 4.78/5.35 n_ax4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1))))))
% 4.78/5.35 n_ax5:((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0)))))))
% 4.78/5.35 n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.78/5.35 n_fr:=(pair1 nat):(fofType->(fofType->fofType))
% 4.78/5.35 n_in:=(esti nat):(fofType->(fofType->Prop))
% 4.78/5.35 n_is:=(e_is nat):(fofType->(fofType->Prop))
% 4.78/5.35 n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))):((fofType->Prop)->(fofType->Prop))
% 4.78/5.35 n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 n_one:=(one nat):((fofType->Prop)->Prop)
% 4.78/5.35 n_pf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 n_pl:=(fun (X0:fofType)=> (ap (plus X0))):(fofType->(fofType->fofType))
% 4.78/5.35 n_some:=(l_some nat):((fofType->Prop)->Prop)
% 4.78/5.35 n_tf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 n_ts:=(fun (X0:fofType)=> (ap (times X0))):(fofType->(fofType->fofType))
% 4.78/5.35 nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))):fofType
% 4.78/5.35 nat_1:(nat_p (ordsucc emptyset))
% 4.78/5.35 nat_ind:(forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1))))))
% 4.78/5.35 nat_inv:(forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1))))))))
% 4.78/5.35 nat_ordsucc:(forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0))))
% 4.78/5.35 nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))):(fofType->Prop)
% 4.78/5.35 nat_p_omega:(forall (X0:fofType), ((nat_p X0)->((in X0) omega)))
% 4.78/5.35 natd:=(fun (X0:fofType)=> ((d_and (posd X0)) ((posd X0)->(natrp (rpofpd X0))))):(fofType->Prop)
% 4.78/5.35 natprop:=(fun (X0:fofType) (X1:fofType)=> ((inf ((n_fr X1) n_1)) (class X0))):(fofType->(fofType->Prop))
% 4.78/5.35 natrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (natd X1))))):(fofType->Prop)
% 4.78/5.35 natrp:=(((image nat) cut) ((d_Sigma nat) rpofnt)):(fofType->Prop)
% 4.78/5.35 natrt:=(fun (X0:fofType)=> (n_some (natprop X0))):(fofType->Prop)
% 4.78/5.35 natt:=((d_Sep rat) natrt):fofType
% 4.78/5.35 ndofrp:=(fun (X0:fofType)=> ((rp_df d_1rp) ((rp_pl X0) d_1rp))):(fofType->fofType)
% 4.78/5.35 neg:=(fun (X0:fofType)=> ((l_some dif) (propn X0))):(fofType->Prop)
% 4.78/5.35 negd:=(fun (X0:fofType)=> ((rp_less (stm X0)) (std X0))):(fofType->Prop)
% 4.78/5.35 neq_ordsucc_0:(forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset)))
% 4.78/5.35 nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2)))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 nofnt:=(fun (X0:fofType)=> (nofrt (rtofnt X0))):(fofType->fofType)
% 4.78/5.35 nofrp:=(fun (X0:fofType)=> (realof (ndofrp X0))):(fofType->fofType)
% 4.78/5.35 nofrt:=(fun (X0:fofType)=> ((ind nat) (natprop X0))):(fofType->fofType)
% 4.78/5.35 non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))):(fofType->((fofType->Prop)->(fofType->Prop)))
% 4.78/5.35 nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))):(fofType->(fofType->Prop))
% 4.78/5.35 not:=(fun (P:Prop)=> (P->False)):(Prop->Prop)
% 4.78/5.35 nt_1t:=(ntofn n_1):fofType
% 4.78/5.35 nt_all:=(all natt):((fofType->Prop)->Prop)
% 4.78/5.35 nt_cond1:=(nt_in nt_1t):(fofType->Prop)
% 4.78/5.35 nt_cond2:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((imp ((nt_in X1) X0)) ((nt_in ((ap suct) X1)) X0))))):(fofType->Prop)
% 4.78/5.35 nt_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 nt_in:=(esti natt):(fofType->(fofType->Prop))
% 4.78/5.35 nt_is:=(e_is natt):(fofType->(fofType->Prop))
% 4.78/5.35 nt_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (nt_all (fun (X2:fofType)=> ((imp (X0 X2)) ((nt_lessis X1) X2))))):((fofType->Prop)->(fofType->Prop))
% 4.78/5.35 nt_less:=(fun (X0:fofType) (X1:fofType)=> ((rt_less (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.78/5.35 nt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((rt_lessis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.78/5.35 nt_min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((nt_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop))
% 4.78/5.35 nt_more:=(fun (X0:fofType) (X1:fofType)=> ((rt_more (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.78/5.35 nt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((rt_moreis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.78/5.35 nt_natt:=((d_Sep cut) natrp):fofType
% 4.78/5.35 nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((nt_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 nt_one:=(one natt):((fofType->Prop)->Prop)
% 4.78/5.35 nt_pl:=(fun (X0:fofType) (X1:fofType)=> (ntofrt ((rt_pl (rtofnt X0)) (rtofnt X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 nt_satz15:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> (((nt_less X0) X1)->(((nt_less X1) X2)->((nt_less X0) X2)))))))))
% 4.78/5.35 nt_satz1:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_nis X0) X1)->((nt_nis ((ap suct) X0)) ((ap suct) X1)))))))
% 4.78/5.35 nt_satz21:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) natt))) (fun (X3:fofType)=> (((nt_more X0) X1)->(((nt_more X2) X3)->((nt_more ((nt_pl X0) X2)) ((nt_pl X1) X3))))))))))))
% 4.78/5.35 nt_satz27:(forall (X0:(fofType->Prop)), ((nt_some X0)->(nt_some (nt_min X0))))
% 4.78/5.35 nt_satz4:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((one ((d_Pi natt) (fun (X1:fofType)=> natt))) (fun (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (nt_all (fun (X2:fofType)=> ((nt_is ((ap X1) ((ap suct) X2))) ((ap suct) ((ap X1) X2))))))))))
% 4.78/5.35 nt_satz5:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((nt_is ((nt_pl ((nt_pl X0) X1)) X2)) ((nt_pl X0) ((nt_pl X1) X2)))))))))
% 4.78/5.35 nt_satz9:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((orec3 ((nt_is X0) X1)) (nt_some (fun (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))))) (nt_some (fun (X2:fofType)=> ((nt_is X1) ((nt_pl X0) X2)))))))))
% 4.78/5.35 nt_some:=(l_some natt):((fofType->Prop)->Prop)
% 4.78/5.35 nt_suct:=((d_Sigma nt_natt) (fun (X0:fofType)=> (nttofnt (ordsucc (ntofntt X0))))):fofType
% 4.78/5.35 ntofn:=(fun (X0:fofType)=> (ntofrt (rtofn X0))):(fofType->fofType)
% 4.78/5.35 ntofntt:=(fun (X0:fofType)=> (ntofrp (rpofntt X0))):(fofType->fofType)
% 4.78/5.35 ntofrl:=(((soft nat) real) ((d_Sigma nat) rlofnt)):(fofType->fofType)
% 4.78/5.35 ntofrp:=(((soft nat) cut) ((d_Sigma nat) rpofnt)):(fofType->fofType)
% 4.78/5.35 ntofrt:=((out rat) natrt):(fofType->fofType)
% 4.78/5.35 nttofnt:=(fun (X0:fofType)=> (nttofrp (rpofnt X0))):(fofType->fofType)
% 4.78/5.35 nttofrp:=((out cut) natrp):(fofType->fofType)
% 4.78/5.35 num:=(first1 nat):(fofType->fofType)
% 4.78/5.35 obvious:=((imp False) False):Prop
% 4.78/5.35 omega:=((d_Sep (univof emptyset)) nat_p):fofType
% 4.78/5.35 omega_nat_p:(forall (X0:fofType), (((in X0) omega)->(nat_p X0)))
% 4.78/5.35 one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))):(fofType->((fofType->Prop)->Prop))
% 4.78/5.35 oneax:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1))))
% 4.78/5.35 or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.78/5.35 or:(Prop->(Prop->Prop))
% 4.78/5.35 or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 4.78/5.35 or_first:=(fun (A:Prop) (B:Prop)=> (((((or_ind A) B) ((B->A)->A)) (fun (x:A) (x0:(B->A))=> x)) (fun (x:B) (x0:(B->A))=> (x0 x)))):(forall (A:Prop) (B:Prop), (((or A) B)->((B->A)->A)))
% 4.78/5.35 or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 4.78/5.35 or_introl:(forall (A:Prop) (B:Prop), (A->((or A) B)))
% 4.78/5.35 or_intror:(forall (A:Prop) (B:Prop), (B->((or A) B)))
% 4.78/5.35 or_second:=(fun (A:Prop) (B:Prop) (x:((or A) B))=> (((or_first B) A) (((or_comm_i A) B) x))):(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B)))
% 4.78/5.35 ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0))):(fofType->fofType)
% 4.78/5.35 ordsucc_inj:(forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1)))
% 4.78/5.35 orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.78/5.35 orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))):(Prop->(Prop->Prop))
% 4.78/5.35 otax1:(forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 4.78/5.35 otax2:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2)))))
% 4.78/5.35 out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))):(fofType->((fofType->Prop)->(fofType->fofType)))
% 4.78/5.35 outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType))
% 4.78/5.35 p1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (negd X1))):(fofType->(fofType->Prop))
% 4.78/5.35 p1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (posd X1))):(fofType->(fofType->Prop))
% 4.78/5.35 pair1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2)))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))):(fofType->fofType)
% 4.78/5.35 pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))):(fofType->(fofType->fofType))
% 4.78/5.35 pair_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1))))))
% 4.78/5.35 pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)):(fofType->Prop)
% 4.78/5.35 pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 pair_u0:=(inn n_2):(fofType->fofType)
% 4.78/5.35 pairis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2))))
% 4.78/5.35 pdofnt:=(fun (X0:fofType)=> (pdofrp (rpofnt X0))):(fofType->fofType)
% 4.78/5.35 pdofrp:=(fun (X0:fofType)=> ((rp_df ((rp_pl X0) d_1rp)) d_1rp)):(fofType->fofType)
% 4.78/5.35 perm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injseq X0) X1) X2)) (((surjseq X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->fofType)
% 4.78/5.35 plusdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_pd X0) X1)))))):fofType
% 4.78/5.35 plusfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_pf X0) X1)))))):fofType
% 4.78/5.35 pofrp:=(fun (X0:fofType)=> (realof (pdofrp X0))):(fofType->fofType)
% 4.78/5.35 pos:=(fun (X0:fofType)=> ((l_some dif) (propp X0))):(fofType->Prop)
% 4.78/5.35 posd:=(fun (X0:fofType)=> ((rp_more (stm X0)) (std X0))):(fofType->Prop)
% 4.78/5.35 power:(fofType->fofType)
% 4.78/5.35 pr1:=(fun (X0:fofType)=> rpofp):(fofType->(fofType->fofType))
% 4.78/5.35 prod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((prodprop X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 prodprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_ts X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.78/5.35 prodprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((prodprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj)):(fofType->fofType)
% 4.78/5.35 proj0_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0)))
% 4.78/5.35 proj0_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0))
% 4.78/5.35 proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 4.78/5.35 proj1_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))
% 4.78/5.35 proj1_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1))
% 4.78/5.35 proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 4.78/5.35 proj_Sigma_eta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)))
% 4.78/5.35 proofsirrelevant:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->((all_of (fun (X5:fofType)=> ((in X5) real))) (fun (X5:fofType)=> ((intrl X5)->(((r_lessis X1) X5)->(((r_lessis X5) X0)->(((r_is X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))))))))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 prop1:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3)))):(Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.78/5.35 prop1d:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (posd X1)) (posd X2)) ((rp_eq X0) ((rp_md X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 prop1t:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((nt_is ((ap X0) ((ap suct) X1))) ((ap suct) ((ap X0) X1)))))):(fofType->Prop)
% 4.78/5.35 prop2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))
% 4.78/5.35 prop2d:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) ((prop1d X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 prop2t:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (prop1t X1))):(fofType->(fofType->Prop))
% 4.78/5.35 prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->Prop)
% 4.78/5.35 propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.78/5.35 propn:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (negd X1))):(fofType->(fofType->Prop))
% 4.78/5.35 propp:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (posd X1))):(fofType->(fofType->Prop))
% 4.78/5.35 ps1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> rpofp):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 r_0:=(realof ((rp_df d_1rp) d_1rp)):fofType
% 4.78/5.35 r_all:=(all real):((fofType->Prop)->Prop)
% 4.78/5.35 r_class:=((ecect dif) rp_eq):(fofType->fofType)
% 4.78/5.35 r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))):(Prop->(Prop->Prop))
% 4.78/5.35 r_fixf:=((fixfu dif) rp_eq):(fofType->(fofType->Prop))
% 4.78/5.35 r_in:=(esti real):(fofType->(fofType->Prop))
% 4.78/5.35 r_inn:=(esti dif):(fofType->(fofType->Prop))
% 4.78/5.35 r_is:=(e_is real):(fofType->(fofType->Prop))
% 4.78/5.35 r_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))))))):(fofType->(fofType->Prop))
% 4.78/5.35 r_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_less X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 r_m0:=((indreal real) m0dr):(fofType->fofType)
% 4.78/5.35 r_mn:=(fun (X0:fofType) (X1:fofType)=> ((r_pl X0) (r_m0 X1))):(fofType->(fofType->fofType))
% 4.78/5.35 r_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))))))):(fofType->(fofType->Prop))
% 4.78/5.35 r_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_more X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 r_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 r_one:=(one real):((fofType->Prop)->Prop)
% 4.78/5.35 r_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind real) (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.78/5.35 r_pl:=((indreal2 real) plusdr):(fofType->(fofType->fofType))
% 4.78/5.35 r_schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind real) ((d_5r205_prop3 X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 r_some:=(l_some real):((fofType->Prop)->Prop)
% 4.78/5.35 r_sqrt:=(fun (X0:fofType)=> ((ind real) (fun (X1:fofType)=> ((d_and (d_not (neg X1))) ((r_is ((r_ts X1) X1)) X0))))):(fofType->fofType)
% 4.78/5.35 r_ts:=((indreal2 real) timesdr):(fofType->(fofType->fofType))
% 4.78/5.35 rat:=((ect frac) n_eq):fofType
% 4.78/5.35 ratd:=(fun (X0:fofType)=> ((d_not (zero X0))->(ratrp (rpofpd (absd X0))))):(fofType->Prop)
% 4.78/5.35 ratof:=((ectelt frac) n_eq):(fofType->fofType)
% 4.78/5.35 ratrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (ratd X1))))):(fofType->Prop)
% 4.78/5.35 ratrp:=(((image rat) cut) ((d_Sigma rat) rpofrt)):(fofType->Prop)
% 4.78/5.35 ratset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rt_less X1) X0)))):(fofType->fofType)
% 4.78/5.35 ratt:=((d_Sep cut) ratrp):fofType
% 4.78/5.35 real:=((ect dif) rp_eq):fofType
% 4.78/5.35 realof:=((ectelt dif) rp_eq):(fofType->fofType)
% 4.78/5.35 refis:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1))))
% 4.78/5.35 relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% 4.78/5.35 repl:(fofType->((fofType->fofType)->fofType))
% 4.78/5.35 right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.35 right:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.35 rlofnt:=(fun (X0:fofType)=> (realof (pdofnt X0))):(fofType->fofType)
% 4.78/5.35 rp1:=(fun (X0:fofType)=> ((rp_pl X0) d_1rp)):(fofType->fofType)
% 4.78/5.35 rp_all:=(all cut):((fofType->Prop)->Prop)
% 4.78/5.35 rp_df:=(pair1 cut):(fofType->(fofType->fofType))
% 4.78/5.35 rp_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((diffprop2 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.35 rp_eq:=(fun (X0:fofType) (X1:fofType)=> ((rp_is ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_in:=(esti cut):(fofType->(fofType->Prop))
% 4.78/5.35 rp_is:=(e_is cut):(fofType->(fofType->Prop))
% 4.78/5.35 rp_less:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((urt X0) X2)) ((lrt X1) X2))))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessd X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_less X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_md:=(fun (X0:fofType) (X1:fofType)=> ((rp_pd X0) (m0d X1))):(fofType->(fofType->fofType))
% 4.78/5.35 rp_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.78/5.35 rp_more:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((lrt X0) X2)) ((urt X1) X2))))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_more X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((mored X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_nt_1t:=(nttofnt n_1):fofType
% 4.78/5.35 rp_nt_all:=(all nt_natt):((fofType->Prop)->Prop)
% 4.78/5.35 rp_nt_cond1:=(rp_nt_in rp_nt_1t):(fofType->Prop)
% 4.78/5.35 rp_nt_cond2:=(fun (X0:fofType)=> (rp_nt_all (fun (X1:fofType)=> ((imp ((rp_nt_in X1) X0)) ((rp_nt_in ((ap nt_suct) X1)) X0))))):(fofType->Prop)
% 4.78/5.35 rp_nt_in:=(esti nt_natt):(fofType->(fofType->Prop))
% 4.78/5.35 rp_nt_is:=(e_is nt_natt):(fofType->(fofType->Prop))
% 4.78/5.35 rp_nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_nt_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rp_nt_one:=(one nt_natt):((fofType->Prop)->Prop)
% 4.78/5.35 rp_nt_some:=(l_some nt_natt):((fofType->Prop)->Prop)
% 4.78/5.35 rp_one:=(one cut):((fofType->Prop)->Prop)
% 4.78/5.35 rp_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.78/5.35 rp_pd:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl (stm X0)) (stm X1))) ((rp_pl (std X0)) (std X1)))):(fofType->(fofType->fofType))
% 4.78/5.35 rp_pl:=(fun (X0:fofType) (X1:fofType)=> (cutof ((sum X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 rp_some:=(l_some cut):((fofType->Prop)->Prop)
% 4.78/5.35 rp_td:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl ((rp_ts (stm X0)) (stm X1))) ((rp_ts (std X0)) (std X1)))) ((rp_pl ((rp_ts (stm X0)) (std X1))) ((rp_ts (std X0)) (stm X1))))):(fofType->(fofType->fofType))
% 4.78/5.35 rp_ts:=(fun (X0:fofType) (X1:fofType)=> (cutof ((prod X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.35 rpofn:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (nofrp X1))))):(fofType->fofType)
% 4.78/5.35 rpofnd:=(fun (X0:fofType)=> ((rp_mn (std X0)) (stm X0))):(fofType->fofType)
% 4.78/5.35 rpofnt:=(fun (X0:fofType)=> (rpofrt (rtofn X0))):(fofType->fofType)
% 4.78/5.35 rpofntt:=((e_in cut) natrp):(fofType->fofType)
% 4.78/5.35 rpofp:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (pofrp X1))))):(fofType->fofType)
% 4.78/5.35 rpofpd:=(fun (X0:fofType)=> ((rp_mn (stm X0)) (std X0))):(fofType->fofType)
% 4.78/5.35 rpofrt:=(fun (X0:fofType)=> (cutof (ratset X0))):(fofType->fofType)
% 4.78/5.35 rpofrtt:=((e_in cut) ratrp):(fofType->fofType)
% 4.78/5.35 rt_all:=(all rat):((fofType->Prop)->Prop)
% 4.78/5.35 rt_in:=(esti rat):(fofType->(fofType->Prop))
% 4.78/5.35 rt_is:=(e_is rat):(fofType->(fofType->Prop))
% 4.78/5.35 rt_lb:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((iii1_lbprop X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rt_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))))):(fofType->(fofType->Prop))
% 4.78/5.35 rt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rt_min:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_lb X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop))
% 4.78/5.35 rt_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.78/5.35 rt_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))))):(fofType->(fofType->Prop))
% 4.78/5.35 rt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rt_one:=(one rat):((fofType->Prop)->Prop)
% 4.78/5.35 rt_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.78/5.35 rt_pl:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) plusfrt)):(fofType->(fofType->fofType))
% 4.78/5.35 rt_some:=(l_some rat):((fofType->Prop)->Prop)
% 4.78/5.35 rt_ts:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) timesfrt)):(fofType->(fofType->fofType))
% 4.78/5.35 rt_ub:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((ubprop X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rtc:=(fun (X0:fofType)=> (cutof (sqrtset X0))):(fofType->fofType)
% 4.78/5.35 rtofn:=(fun (X0:fofType)=> (ratof ((n_fr X0) n_1))):(fofType->fofType)
% 4.78/5.35 rtofnt:=((e_in rat) natrt):(fofType->fofType)
% 4.78/5.35 rtofrp:=(((soft rat) cut) ((d_Sigma rat) rpofrt)):(fofType->fofType)
% 4.78/5.35 rtofrtt:=(fun (X0:fofType)=> (rtofrp (rpofrtt X0))):(fofType->fofType)
% 4.78/5.35 rtt_all:=(all ratt):((fofType->Prop)->Prop)
% 4.78/5.35 rtt_is:=(e_is ratt):(fofType->(fofType->Prop))
% 4.78/5.35 rtt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rtt_is X0) X1))):(fofType->(fofType->Prop))
% 4.78/5.35 rtt_one:=(one ratt):((fofType->Prop)->Prop)
% 4.78/5.35 rtt_some:=(l_some ratt):((fofType->Prop)->Prop)
% 4.78/5.35 rttofrp:=((out cut) ratrp):(fofType->fofType)
% 4.78/5.35 rttofrt:=(fun (X0:fofType)=> (rttofrp (rpofrt X0))):(fofType->fofType)
% 4.78/5.35 s01:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_lessis X1) X0)))):(fofType->fofType)
% 4.78/5.35 s02:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_more X1) X0)))):(fofType->fofType)
% 4.78/5.35 s11:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_less X1) X0)))):(fofType->fofType)
% 4.78/5.35 s12:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_moreis X1) X0)))):(fofType->fofType)
% 4.78/5.35 satz100:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.78/5.35 satz100a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.78/5.35 satz101:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_one (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 4.78/5.35 satz101a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_some (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 4.78/5.35 satz101b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_pl X1) X2)) X0)->(((rt_is ((rt_pl X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 4.78/5.35 satz101c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl X1) ((rt_mn X0) X1))) X0))))))
% 4.78/5.35 satz101d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl X1) ((rt_mn X0) X1))))))))
% 4.78/5.35 satz101e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl ((rt_mn X0) X1)) X1)) X0))))))
% 4.78/5.35 satz101f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl ((rt_mn X0) X1)) X1)))))))
% 4.78/5.35 satz101g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_is ((rt_pl X1) X2)) X0)->((rt_is X2) ((rt_mn X0) X1))))))))))
% 4.78/5.35 satz102:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X0) X1)) ((rt_ts X1) X0))))))
% 4.78/5.35 satz103:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts ((rt_ts X0) X1)) X2)) ((rt_ts X0) ((rt_ts X1) X2)))))))))
% 4.78/5.35 satz104:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts X0) ((rt_pl X1) X2))) ((rt_pl ((rt_ts X0) X1)) ((rt_ts X0) X2)))))))))
% 4.78/5.35 satz105a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.78/5.35 satz105b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.78/5.35 satz105c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.78/5.35 satz105d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.78/5.35 satz105e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.78/5.35 satz105f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.78/5.35 satz106a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_more X0) X1))))))))
% 4.78/5.35 satz106b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_is X0) X1))))))))
% 4.78/5.35 satz106c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_less X0) X1))))))))
% 4.78/5.35 satz107:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.78/5.35 satz107a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.78/5.35 satz108a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.78/5.35 satz108b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.78/5.35 satz108c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.78/5.35 satz108d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.78/5.35 satz109:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.78/5.35 satz109a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.78/5.35 satz10:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.78/5.35 satz10a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.78/5.35 satz10b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.78/5.35 satz10c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1)))))))
% 4.78/5.35 satz10d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1)))))))
% 4.78/5.35 satz10e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1))))))
% 4.78/5.35 satz10f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1))))))
% 4.78/5.35 satz10g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1)))))))
% 4.78/5.35 satz10h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1)))))))
% 4.78/5.35 satz10j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1))))))
% 4.78/5.35 satz10k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1))))))
% 4.78/5.35 satz110:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_one (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 4.78/5.35 satz110a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 4.78/5.35 satz110b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->(((rt_is ((rt_ts X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 4.78/5.35 satz110c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X1) ((rt_ov X0) X1))) X0)))))
% 4.78/5.35 satz110d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts X1) ((rt_ov X0) X1)))))))
% 4.78/5.35 satz110e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov X0) X1)) X1)) X0)))))
% 4.78/5.35 satz110f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts ((rt_ov X0) X1)) X1))))))
% 4.78/5.35 satz110g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->((rt_is X2) ((rt_ov X0) X1)))))))))
% 4.78/5.35 satz111a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))->((d_29_ii X0) X1))))))
% 4.78/5.35 satz111b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))->((n_is X0) X1))))))
% 4.78/5.35 satz111c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))->((iii X0) X1))))))
% 4.78/5.35 satz111d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((moref ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.78/5.35 satz111e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is X0) X1)->((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.78/5.35 satz111f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.78/5.35 satz111g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->(n_one (natprop X0)))))
% 4.78/5.35 satz112a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_pf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_pl X0) X1)) n_1))))))
% 4.78/5.35 satz112b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_tf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_ts X0) X1)) n_1))))))
% 4.78/5.35 satz112c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_pl (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_pl X0) X1)))))))))
% 4.78/5.35 satz112d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_pl X0) X1))))))))
% 4.78/5.35 satz112e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_ts (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_ts X0) X1)))))))))
% 4.78/5.35 satz112f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_ts X0) X1))))))))
% 4.78/5.35 satz112g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(((rt_more X0) X1)->(natrt ((rt_mn X0) X1)))))))))
% 4.78/5.35 satz112h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_pl (rtofn X0)) (rtofn X1))) (rtofn ((n_pl X0) X1)))))))
% 4.78/5.35 satz112j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X0)) (rtofn X1))) (rtofn ((n_ts X0) X1)))))))
% 4.78/5.35 satz113a:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((nt_nis ((ap suct) X0)) nt_1t)))
% 4.78/5.35 satz113b:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_is ((ap suct) X0)) ((ap suct) X1))->((nt_is X0) X1))))))
% 4.78/5.35 satz113c:((all_of (fun (X0:fofType)=> ((in X0) (power natt)))) (fun (X0:fofType)=> ((nt_cond1 X0)->((nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((nt_in X1) X0)))))))
% 4.78/5.35 satz114:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((rt_is ((rt_ts (rtofn (den X0))) (ratof X0))) (rtofn (num X0)))))
% 4.78/5.35 satz114a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X1)) (ratof ((n_fr X0) X1)))) (rtofn X0))))))
% 4.78/5.35 satz114b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is (ratof ((n_fr X0) X1))) ((rt_ov (rtofn X0)) (rtofn X1)))))))
% 4.78/5.35 satz114c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ov (rtofn X0)) (rtofn X1))) (ratof ((n_fr X0) X1)))))))
% 4.78/5.35 satz115:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (n_some (fun (X2:fofType)=> ((rt_more ((rt_ts (rtofn X2)) X0)) X1)))))))
% 4.78/5.35 satz115a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and (natrt X2)) ((rt_more ((rt_ts X2) X0)) X1))))))))
% 4.78/5.35 satz116:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) X0)))
% 4.78/5.35 satz117:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_is X0) X1)->((rp_is X1) X0))))))
% 4.78/5.35 satz118:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->(((rp_is X1) X2)->((rp_is X0) X2)))))))))
% 4.78/5.35 satz119:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X2) X1)->((urt X0) X2)))))))))
% 4.78/5.35 satz119a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X1) X2)->((urt X0) X2)))))))))
% 4.78/5.35 satz11:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0))))))
% 4.78/5.35 satz120:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X2) X1)->((lrt X0) X2)))))))))
% 4.78/5.35 satz120a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X1) X2)->((lrt X0) X2)))))))))
% 4.78/5.35 satz121:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_less X1) X0))))))
% 4.78/5.35 satz122:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->((rp_more X1) X0))))))
% 4.78/5.35 satz123:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((orec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.78/5.35 satz123c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->(d_not ((rp_less X0) X1)))))))
% 4.78/5.35 satz123d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->(d_not ((rp_more X0) X1)))))))
% 4.78/5.35 satz123e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_more X0) X1))->((rp_lessis X0) X1))))))
% 4.78/5.35 satz123f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_less X0) X1))->((rp_moreis X0) X1))))))
% 4.78/5.35 satz123g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(d_not ((rp_lessis X0) X1)))))))
% 4.78/5.35 satz123h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(d_not ((rp_moreis X0) X1)))))))
% 4.78/5.35 satz123j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_moreis X0) X1))->((rp_less X0) X1))))))
% 4.78/5.35 satz123k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_lessis X0) X1))->((rp_more X0) X1))))))
% 4.78/5.35 satz124:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->((rp_lessis X1) X0))))))
% 4.78/5.35 satz125:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->((rp_moreis X1) X0))))))
% 4.78/5.35 satz126:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 4.78/5.35 satz127a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 4.78/5.35 satz127b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_lessis X1) X2)->((rp_less X0) X2)))))))))
% 4.78/5.35 satz127c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_moreis X0) X1)->(((rp_more X1) X2)->((rp_more X0) X2)))))))))
% 4.78/5.35 satz127d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_moreis X1) X2)->((rp_more X0) X2)))))))))
% 4.78/5.35 satz128:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X1) X2)->((rp_lessis X0) X2)))))))))
% 4.78/5.35 satz129:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((sum X0) X1))))))
% 4.78/5.35 satz129a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_pl X2) X3)) ((sum X0) X1)))))))))))))
% 4.78/5.35 satz12:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0))))))
% 4.78/5.35 satz130:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_pl X0) X1)) ((rp_pl X1) X0))))))
% 4.78/5.35 satz131:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_pl ((rp_pl X0) X1)) X2)) ((rp_pl X0) ((rp_pl X1) X2)))))))))
% 4.78/5.35 satz132:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (fun (X3:fofType)=> ((d_and ((d_and ((lrt X0) X2)) ((urt X0) X3))) (((d_and ((lrt X0) X2)) ((urt X0) X3))->((rt_is ((rt_mn X3) X2)) X1)))))))))))
% 4.78/5.35 satz132app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (forall (X1:Prop), ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((lrt X0) X3)->((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((urt X0) X4)->(((rt_is ((rt_mn X4) X3)) X2)->X1)))))))->X1))))))
% 4.78/5.35 satz133:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_more ((rp_pl X0) X1)) X0)))))
% 4.78/5.35 satz133a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_less X0) ((rp_pl X0) X1))))))
% 4.78/5.35 satz134:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.78/5.35 satz135b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.78/5.35 satz135c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.78/5.35 satz135d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.78/5.35 satz135e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.78/5.35 satz135f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.78/5.35 satz135g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz135h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 4.78/5.35 satz135j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz135k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 4.78/5.35 satz136a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_more X0) X1))))))))
% 4.78/5.35 satz136b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_is X0) X1))))))))
% 4.78/5.35 satz136c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_less X0) X1))))))))
% 4.78/5.35 satz136d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_more X0) X1))))))))
% 4.78/5.35 satz136e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_is X0) X1))))))))
% 4.78/5.35 satz136f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_less X0) X1))))))))
% 4.78/5.35 satz137:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz137a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz138a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz138b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz138c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz138d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz139:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz139a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.78/5.35 satz13:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0))))))
% 4.78/5.35 satz140:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_one (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 4.78/5.35 satz140a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_some (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 4.78/5.35 satz140b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_pl X1) X2)) X0)->(((rp_is ((rp_pl X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 4.78/5.35 satz140c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl X1) ((rp_mn X0) X1))) X0))))))
% 4.78/5.35 satz140d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl X1) ((rp_mn X0) X1))))))))
% 4.78/5.35 satz140e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl ((rp_mn X0) X1)) X1)) X0))))))
% 4.78/5.35 satz140f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl ((rp_mn X0) X1)) X1)))))))
% 4.78/5.35 satz140g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_is ((rp_pl X1) X2)) X0)->((rp_is X2) ((rp_mn X0) X1))))))))))
% 4.78/5.35 satz140h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(cutprop ((diff X0) X1)))))))
% 4.78/5.35 satz141:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((prod X0) X1))))))
% 4.78/5.35 satz141a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_ts X2) X3)) ((prod X0) X1)))))))))))))
% 4.78/5.35 satz141b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov d_1rt) X1)) X0)) ((rt_ov X0) X1))))))
% 4.78/5.35 satz141c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ov X0) X1)) ((rt_ts ((rt_ov d_1rt) X1)) X0))))))
% 4.78/5.35 satz142:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) ((rp_ts X1) X0))))))
% 4.78/5.35 satz143:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts ((rp_ts X0) X1)) X2)) ((rp_ts X0) ((rp_ts X1) X2)))))))))
% 4.78/5.35 satz144:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts X0) ((rp_pl X1) X2))) ((rp_pl ((rp_ts X0) X1)) ((rp_ts X0) X2)))))))))
% 4.78/5.35 satz145a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.78/5.35 satz145b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.78/5.35 satz145c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.78/5.35 satz145d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.78/5.35 satz145e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.78/5.35 satz145f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.78/5.35 satz145g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz145h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 4.78/5.35 satz145j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz145k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 4.78/5.35 satz146a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_more X0) X1))))))))
% 4.78/5.35 satz146b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_is X0) X1))))))))
% 4.78/5.35 satz146c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_less X0) X1))))))))
% 4.78/5.35 satz146d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_more X0) X1))))))))
% 4.78/5.35 satz146e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_is X0) X1))))))))
% 4.78/5.35 satz146f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_less X0) X1))))))))
% 4.78/5.35 satz147:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz147a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz148a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz148b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz148c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz148d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz149:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz149a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.78/5.35 satz14:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0))))))
% 4.78/5.35 satz150:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (cutprop (ratset X0))))
% 4.78/5.35 satz151:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) d_1rp)) X0)))
% 4.78/5.35 satz151a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts X0) d_1rp))))
% 4.78/5.35 satz151b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts d_1rp) X0)) X0)))
% 4.78/5.35 satz151c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts d_1rp) X0))))
% 4.78/5.35 satz152:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_some (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) d_1rp)))))
% 4.78/5.35 satz153:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_one (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 4.78/5.35 satz153a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 4.78/5.35 satz153b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->(((rp_is ((rp_ts X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 4.78/5.35 satz153c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) ((rp_ov X0) X1))) X0)))))
% 4.78/5.35 satz153d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts X1) ((rp_ov X0) X1)))))))
% 4.78/5.35 satz153e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts ((rp_ov X0) X1)) X1)) X0)))))
% 4.78/5.35 satz153f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts ((rp_ov X0) X1)) X1))))))
% 4.78/5.35 satz153g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->((rp_is X2) ((rp_ov X0) X1)))))))))
% 4.78/5.35 satz154a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_more (rpofrt X0)) (rpofrt X1)))))))
% 4.78/5.35 satz154b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rp_is (rpofrt X0)) (rpofrt X1)))))))
% 4.78/5.35 satz154c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rp_less (rpofrt X0)) (rpofrt X1)))))))
% 4.78/5.35 satz154d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_more (rpofrt X0)) (rpofrt X1))->((rt_more X0) X1))))))
% 4.78/5.35 satz154e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_is (rpofrt X0)) (rpofrt X1))->((rt_is X0) X1))))))
% 4.78/5.35 satz154f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X0)) (rpofrt X1))->((rt_less X0) X1))))))
% 4.78/5.35 satz155a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_pl X0) X1))) ((rp_pl (rpofrt X0)) (rpofrt X1)))))))
% 4.78/5.35 satz155b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_is (rpofrt ((rt_mn X0) X1))) ((rp_mn (rpofrt X0)) (rpofrt X1))))))))
% 4.78/5.35 satz155c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ts X0) X1))) ((rp_ts (rpofrt X0)) (rpofrt X1)))))))
% 4.78/5.35 satz155d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ov X0) X1))) ((rp_ov (rpofrt X0)) (rpofrt X1)))))))
% 4.78/5.35 satz155e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_pl X0) X1))) ((rp_pl (rpofnt X0)) (rpofnt X1)))))))
% 4.78/5.35 satz155f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_ts X0) X1))) ((rp_ts (rpofnt X0)) (rpofnt X1)))))))
% 4.78/5.35 satz156a:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((rp_nt_nis ((ap nt_suct) X0)) rp_nt_1t)))
% 4.78/5.35 satz156b:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> (((rp_nt_is ((ap nt_suct) X0)) ((ap nt_suct) X1))->((rp_nt_is X0) X1))))))
% 4.78/5.35 satz156c:((all_of (fun (X0:fofType)=> ((in X0) (power nt_natt)))) (fun (X0:fofType)=> ((rp_nt_cond1 X0)->((rp_nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> ((rp_nt_in X1) X0)))))))
% 4.78/5.35 satz157a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->((rt_min ((d_Sep rat) (urt X0))) (rtofrp X0)))))
% 4.78/5.35 satz157b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->(rt_some (rt_min ((d_Sep rat) (urt X0)))))))
% 4.78/5.35 satz157c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_min ((d_Sep rat) (urt X0))) X1)->((rp_is X0) (rpofrt X1)))))))
% 4.78/5.35 satz157d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rt_some (rt_min ((d_Sep rat) (urt X0))))->(ratrp X0))))
% 4.78/5.35 satz158a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((rp_less (rpofrt X1)) X0))))))
% 4.78/5.35 satz158b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((rp_moreis (rpofrt X1)) X0))))))
% 4.78/5.35 satz158c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X1)) X0)->((lrt X0) X1))))))
% 4.78/5.35 satz158d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_moreis (rpofrt X1)) X0)->((urt X0) X1))))))
% 4.78/5.35 satz159:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rp_less X0) (rpofrt X2))) ((rp_less (rpofrt X2)) X1)))))))))
% 4.78/5.35 satz159a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rp_some (fun (X2:fofType)=> (((and3 (ratrp X2)) ((rp_less X0) X2)) ((rp_less X2) X1)))))))))
% 4.78/5.35 satz159app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(forall (X2:Prop), (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rp_less X0) (rpofrt X3))->(((rp_less (rpofrt X3)) X1)->X2))))->X2)))))))
% 4.78/5.35 satz15:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 4.78/5.35 satz160:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(rt_some (fun (X3:fofType)=> (rt_some (fun (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2)))))))))))))
% 4.78/5.35 satz160app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(forall (X3:Prop), (((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((rp_more (rpofrt X4)) X0)->((all_of (fun (X5:fofType)=> ((in X5) rat))) (fun (X5:fofType)=> (((rp_more (rpofrt X5)) X1)->(((rt_is ((rt_ts X4) X5)) X2)->X3)))))))->X3)))))))))
% 4.78/5.35 satz161:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_one (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))))
% 4.78/5.35 satz162:(rp_some irratrp)
% 4.78/5.35 satz163:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) X0)))
% 4.78/5.35 satz164:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is X1) X0))))))
% 4.78/5.35 satz165:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->(((r_is X1) X2)->((r_is X0) X2)))))))))
% 4.78/5.35 satz166a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(pos (abs X0)))))
% 4.78/5.35 satz166b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (abs X0)))))
% 4.78/5.35 satz166c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 4.78/5.35 satz166d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 4.78/5.35 satz166e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_nis X0) r_0)->(pos (abs X0)))))
% 4.78/5.35 satz166f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (abs X0)) r_0))))
% 4.78/5.35 satz167:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((orec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.78/5.35 satz167a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((or3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.78/5.35 satz167b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((ec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.78/5.35 satz167c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->(d_not ((r_less X0) X1)))))))
% 4.78/5.35 satz167d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->(d_not ((r_more X0) X1)))))))
% 4.78/5.35 satz167e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_more X0) X1))->((r_lessis X0) X1))))))
% 4.78/5.35 satz167f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_less X0) X1))->((r_moreis X0) X1))))))
% 4.78/5.35 satz167g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(d_not ((r_lessis X0) X1)))))))
% 4.78/5.35 satz167h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(d_not ((r_moreis X0) X1)))))))
% 4.78/5.35 satz167j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_moreis X0) X1))->((r_less X0) X1))))))
% 4.78/5.35 satz167k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_lessis X0) X1))->((r_more X0) X1))))))
% 4.78/5.35 satz168a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->((r_lessis X1) X0))))))
% 4.78/5.35 satz168b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->((r_moreis X1) X0))))))
% 4.78/5.35 satz169a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->((r_more X0) r_0))))
% 4.78/5.35 satz169b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_more X0) r_0)->(pos X0))))
% 4.78/5.35 satz169c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->((r_less X0) r_0))))
% 4.78/5.35 satz169d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_less X0) r_0)->(neg X0))))
% 4.78/5.35 satz16a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 4.78/5.35 satz16b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2)))))))))
% 4.78/5.35 satz16c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2)))))))))
% 4.78/5.35 satz16d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2)))))))))
% 4.78/5.35 satz170:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_moreis (abs X0)) r_0)))
% 4.78/5.35 satz170a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (d_not (neg (abs X0)))))
% 4.78/5.35 satz171:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_less X1) X2)->((r_less X0) X2)))))))))
% 4.78/5.35 satz172a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_less X1) X2)->((r_less X0) X2)))))))))
% 4.78/5.35 satz172b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_lessis X1) X2)->((r_less X0) X2)))))))))
% 4.78/5.35 satz172c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_moreis X0) X1)->(((r_more X1) X2)->((r_more X0) X2)))))))))
% 4.78/5.35 satz172d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->(((r_moreis X1) X2)->((r_more X0) X2)))))))))
% 4.78/5.35 satz173:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_lessis X0) X1)->(((r_lessis X1) X2)->((r_lessis X0) X2)))))))))
% 4.78/5.35 satz174:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((intrl X0)->(ratrl X0))))
% 4.78/5.35 satz175:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X0) X1)) ((r_pl X1) X0))))))
% 4.78/5.35 satz176a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(neg (r_m0 X0)))))
% 4.78/5.35 satz176b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (r_m0 X0)) r_0))))
% 4.78/5.35 satz176c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (r_m0 X0)))))
% 4.78/5.35 satz176d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg (r_m0 X0))->(pos X0))))
% 4.78/5.35 satz176e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is (r_m0 X0)) r_0)->((r_is X0) r_0))))
% 4.78/5.35 satz176f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos (r_m0 X0))->(neg X0))))
% 4.78/5.35 satz177:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (r_m0 (r_m0 X0))) X0)))
% 4.78/5.35 satz177a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) (r_m0 (r_m0 X0)))))
% 4.78/5.35 satz177b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is (r_m0 X0)) X1))))))
% 4.78/5.35 satz177c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is X1) (r_m0 X0)))))))
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% 4.78/5.35 satz178:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs (r_m0 X0))) (abs X0))))
% 4.78/5.35 satz178a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs X0)) (abs (r_m0 X0)))))
% 4.78/5.35 satz179:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl X0) (r_m0 X0))) r_0)))
% 4.78/5.35 satz179a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl (r_m0 X0)) X0)) r_0)))
% 4.78/5.35 satz17:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((lessis X1) X2)->((lessis X0) X2)))))))))
% 4.78/5.35 satz180:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_pl X0) X1))) ((r_pl (r_m0 X0)) (r_m0 X1)))))))
% 4.78/5.35 satz180a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl (r_m0 X0)) (r_m0 X1))) (r_m0 ((r_pl X0) X1)))))))
% 4.78/5.35 satz181:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_mn X0) X1))) ((r_mn X1) X0))))))
% 4.78/5.35 satz181a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_mn X0) X1)) (r_m0 ((r_mn X1) X0)))))))
% 4.78/5.35 satz182a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_mn X0) X1))->((r_more X0) X1))))))
% 4.78/5.35 satz182b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_mn X0) X1)) r_0)->((r_is X0) X1))))))
% 4.78/5.35 satz182c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_mn X0) X1))->((r_less X0) X1))))))
% 4.78/5.35 satz182d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(pos ((r_mn X0) X1)))))))
% 4.78/5.35 satz182e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is ((r_mn X0) X1)) r_0))))))
% 4.78/5.35 satz182f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(neg ((r_mn X0) X1)))))))
% 4.78/5.35 satz183a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->((r_less (r_m0 X0)) (r_m0 X1)))))))
% 4.78/5.35 satz183b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is (r_m0 X0)) (r_m0 X1)))))))
% 4.78/5.35 satz183c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->((r_more (r_m0 X0)) (r_m0 X1)))))))
% 4.78/5.35 satz183d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less (r_m0 X0)) (r_m0 X1))->((r_more X0) X1))))))
% 4.78/5.35 satz183e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is (r_m0 X0)) (r_m0 X1))->((r_is X0) X1))))))
% 4.78/5.35 satz183f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more (r_m0 X0)) (r_m0 X1))->((r_less X0) X1))))))
% 4.78/5.35 satz184:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (r_some (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))))))))
% 4.78/5.35 satz185:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((r_is ((r_pl ((r_mn X0) X1)) ((r_mn X2) X3))) ((r_mn ((r_pl X0) X2)) ((r_pl X1) X3)))))))))))
% 4.78/5.35 satz186:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_pl ((r_pl X0) X1)) X2)) ((r_pl X0) ((r_pl X1) X2)))))))))
% 4.78/5.35 satz187:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_one (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0)))))))
% 4.78/5.35 satz187a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X1) ((r_mn X0) X1))) X0)))))
% 4.78/5.35 satz187b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (r_some (fun (X2:fofType)=> ((r_is ((r_pl X1) X2)) X0)))))))
% 4.78/5.35 satz187c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is ((r_mn X0) X1)) X2))))))))
% 4.78/5.35 satz187d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X1) X2)) X0)->((r_is X2) ((r_mn X0) X1)))))))))
% 4.78/5.35 satz187e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is ((r_mn X0) X1)) X2))))))))
% 4.78/5.35 satz187f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X1)) X0)->((r_is X2) ((r_mn X0) X1)))))))))
% 4.78/5.35 satz188a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X0) X2)) ((r_pl X1) X2))->((r_more X0) X1))))))))
% 4.78/5.35 satz188b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X0) X2)) ((r_pl X1) X2))->((r_is X0) X1))))))))
% 4.78/5.35 satz188c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X0) X2)) ((r_pl X1) X2))->((r_less X0) X1))))))))
% 4.78/5.35 satz188d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 4.78/5.35 satz188e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 4.78/5.35 satz188f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X0) X2)) ((r_pl X1) X2)))))))))
% 4.78/5.35 satz188g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more ((r_pl X2) X0)) ((r_pl X2) X1))->((r_more X0) X1))))))))
% 4.78/5.35 satz188h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is ((r_pl X2) X0)) ((r_pl X2) X1))->((r_is X0) X1))))))))
% 4.78/5.35 satz188j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less ((r_pl X2) X0)) ((r_pl X2) X1))->((r_less X0) X1))))))))
% 4.78/5.35 satz188k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((r_more ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 4.78/5.35 satz188l:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X0) X1)->((r_is ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 4.78/5.35 satz188m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((r_less ((r_pl X2) X0)) ((r_pl X2) X1)))))))))
% 4.78/5.35 satz188n:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz188o:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X2) X0)) ((r_pl X3) X1))))))))))))
% 4.78/5.35 satz188p:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz188q:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X2) X0)) ((r_pl X3) X1))))))))))))
% 4.78/5.35 satz189:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz189a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz18:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0)))))
% 4.78/5.35 satz18a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1))))))
% 4.78/5.35 satz18b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0)))
% 4.78/5.35 satz18c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0))))
% 4.78/5.35 satz190a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_more X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz190b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_more X0) X1)->(((r_moreis X2) X3)->((r_more ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz190c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_less X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz190d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_less X0) X1)->(((r_lessis X2) X3)->((r_less ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz191:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_moreis X0) X1)->(((r_moreis X2) X3)->((r_moreis ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz191a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_lessis X0) X1)->(((r_lessis X2) X3)->((r_lessis ((r_pl X0) X2)) ((r_pl X1) X3))))))))))))
% 4.78/5.35 satz192a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) r_0)->((r_is ((r_ts X0) X1)) r_0))))))
% 4.78/5.35 satz192b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X1) r_0)->((r_is ((r_ts X0) X1)) r_0))))))
% 4.78/5.35 satz192c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is ((r_ts X0) X1)) r_0)->((l_or ((r_is X0) r_0)) ((r_is X1) r_0)))))))
% 4.78/5.35 satz192d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X0) r_0)->(((r_nis X1) r_0)->((r_nis ((r_ts X0) X1)) r_0)))))))
% 4.78/5.35 satz193:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (abs ((r_ts X0) X1))) ((r_ts (abs X0)) (abs X1)))))))
% 4.78/5.35 satz193a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (abs X0)) (abs X1))) (abs ((r_ts X0) X1)))))))
% 4.78/5.35 satz194:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts X1) X0))))))
% 4.78/5.35 satz195:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts X0) d_1rl)) X0)))
% 4.78/5.35 satz195a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts X0) d_1rl))))
% 4.78/5.35 satz195b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_ts d_1rl) X0)) X0)))
% 4.78/5.35 satz195c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) ((r_ts d_1rl) X0))))
% 4.78/5.35 satz196a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))))))))
% 4.78/5.35 satz196b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))))))))
% 4.78/5.35 satz196c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((neg X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))))))))
% 4.78/5.35 satz196d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((pos X1)->((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))))))))
% 4.78/5.35 satz196e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) ((r_ts (abs X0)) (abs X1)))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1))))))))))
% 4.78/5.35 satz196f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_is X0) r_0))->((d_not ((r_is X1) r_0))->(((r_is ((r_ts X0) X1)) (r_m0 ((r_ts (abs X0)) (abs X1))))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))))
% 4.78/5.35 satz196g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (pos X1))) ((d_and (neg X0)) (neg X1))))))))
% 4.78/5.35 satz196h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))
% 4.78/5.35 satz197a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) (r_m0 ((r_ts X0) X1)))))))
% 4.78/5.35 satz197b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) (r_m0 ((r_ts X0) X1)))))))
% 4.78/5.35 satz197c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) ((r_ts X0) (r_m0 X1)))))))
% 4.78/5.35 satz197d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) ((r_ts (r_m0 X0)) X1))))))
% 4.78/5.35 satz197e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts (r_m0 X0)) X1))))))
% 4.78/5.35 satz197f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts X0) (r_m0 X1)))))))
% 4.78/5.35 satz198:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) (r_m0 X1))) ((r_ts X0) X1))))))
% 4.78/5.35 satz198a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts (r_m0 X0)) (r_m0 X1)))))))
% 4.78/5.35 satz199:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts ((r_ts X0) X1)) X2)) ((r_ts X0) ((r_ts X1) X2)))))))))
% 4.78/5.35 satz19a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.78/5.35 satz19b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.78/5.35 satz19c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.78/5.35 satz19d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.78/5.35 satz19e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.78/5.35 satz19f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.78/5.35 satz19g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz19h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 4.78/5.35 satz19j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz19k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 4.78/5.35 satz19l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.78/5.35 satz19m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.78/5.35 satz19n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.78/5.35 satz19o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.78/5.35 satz1:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1)))))))
% 4.78/5.35 satz201:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_pl X1) X2))) ((r_pl ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 4.78/5.35 satz202:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_mn X1) X2))) ((r_mn ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 4.78/5.35 satz203a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.78/5.35 satz203b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X0) X2)) ((r_ts X1) X2)))))))))
% 4.78/5.35 satz203c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.78/5.35 satz203d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.78/5.35 satz203e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X2) X0)) ((r_ts X2) X1)))))))))
% 4.78/5.35 satz203f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.78/5.35 satz203g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.78/5.35 satz203j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.78/5.35 satz203k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.78/5.35 satz203m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.78/5.35 satz204:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_one (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 4.78/5.35 satz204a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_some (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 4.78/5.35 satz204b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is ((r_ts X1) X2)) X0)->(((r_is ((r_ts X1) X3)) X0)->((r_is X2) X3))))))))))))
% 4.78/5.35 satz204c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts X1) ((r_ov X0) X1))) X0))))))
% 4.78/5.35 satz204d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts X1) ((r_ov X0) X1))))))))
% 4.78/5.35 satz204e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts ((r_ov X0) X1)) X1)) X0))))))
% 4.78/5.35 satz204f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts ((r_ov X0) X1)) X1)))))))
% 4.78/5.35 satz204g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_nis X1) r_0)->(((r_is ((r_ts X1) X2)) X0)->((r_is X2) ((r_ov X0) X1))))))))))
% 4.78/5.35 satz205:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->(r_one (fun (X2:fofType)=> ((d_and (r_all (fun (X3:fofType)=> (((r_less X3) X2)->((r_in X3) X0))))) (r_all (fun (X3:fofType)=> (((r_more X3) X2)->((r_in X3) X1)))))))))))))))
% 4.78/5.35 satz205a:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X2) ((r_schnitt X0) X1))->((r_in X2) X0))))))))))))
% 4.78/5.35 satz205b:((all_of (fun (X0:fofType)=> ((in X0) (power real)))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) (power real)))) (fun (X1:fofType)=> ((r_all (fun (X2:fofType)=> ((l_or ((r_in X2) X0)) ((r_in X2) X1))))->(((nonempty real) X0)->(((nonempty real) X1)->((r_all (fun (X2:fofType)=> (((r_in X2) X0)->(r_all (fun (X3:fofType)=> (((r_in X3) X1)->((r_less X2) X3)))))))->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X2) ((r_schnitt X0) X1))->((r_in X2) X1))))))))))))
% 4.78/5.35 satz20a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1))))))))
% 4.78/5.35 satz20b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1))))))))
% 4.78/5.35 satz20c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1))))))))
% 4.78/5.35 satz20d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1))))))))
% 4.78/5.35 satz20e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1))))))))
% 4.78/5.35 satz20f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1))))))))
% 4.78/5.35 satz21:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz21a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz22a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz22b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz22c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz22d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz23:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz23a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.78/5.35 satz24:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1)))
% 4.78/5.35 satz24a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1))
% 4.78/5.35 satz24b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1)))
% 4.78/5.35 satz24c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0))))
% 4.78/5.35 satz25:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1)))))))
% 4.78/5.35 satz25a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0)))))))
% 4.78/5.35 satz25b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0))))))
% 4.78/5.35 satz25c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0))))))
% 4.78/5.35 satz26:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0))))))
% 4.78/5.35 satz26a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0))))))
% 4.78/5.35 satz26b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0))))))
% 4.78/5.35 satz26c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0))))))
% 4.78/5.35 satz27:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0))))
% 4.78/5.35 satz27a:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0))))
% 4.78/5.35 satz28:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))))))
% 4.78/5.35 satz28a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0)))
% 4.78/5.35 satz28b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0))))))
% 4.78/5.35 satz28c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0)))
% 4.78/5.35 satz28d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1))))))
% 4.78/5.35 satz28e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1))))
% 4.78/5.35 satz28f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1)))))))
% 4.78/5.35 satz28g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0))))
% 4.78/5.35 satz28h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1))))))
% 4.78/5.35 satz29:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))))))
% 4.78/5.35 satz2:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 4.78/5.35 satz30:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))))))))
% 4.78/5.35 satz31:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))))))))
% 4.78/5.35 satz32a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.78/5.35 satz32b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.78/5.35 satz32c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.78/5.35 satz32d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.78/5.35 satz32e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.78/5.35 satz32f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.78/5.35 satz32g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz32h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 4.78/5.35 satz32j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz32k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 4.78/5.35 satz32l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.78/5.35 satz32m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.78/5.35 satz32n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.78/5.35 satz32o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.78/5.35 satz33a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1))))))))
% 4.78/5.35 satz33b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1))))))))
% 4.78/5.35 satz33c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1))))))))
% 4.78/5.35 satz34:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz34a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz35a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz35b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz35c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz35d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz36:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz36a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.78/5.35 satz37:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0)))
% 4.78/5.35 satz38:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0))))))
% 4.78/5.35 satz39:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2)))))))))
% 4.78/5.35 satz3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 4.78/5.35 satz3a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 4.78/5.35 satz40:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1)))))))
% 4.78/5.35 satz40a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0)))))
% 4.78/5.35 satz40b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.78/5.35 satz40c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1))))))))
% 4.78/5.35 satz41:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.78/5.35 satz41a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.78/5.35 satz41b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.78/5.35 satz41c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1)))))))
% 4.78/5.35 satz41d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1)))))))
% 4.78/5.35 satz41e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1))))))
% 4.78/5.35 satz41f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1))))))
% 4.78/5.35 satz41g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1)))))))
% 4.78/5.35 satz41h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1)))))))
% 4.78/5.35 satz41j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1))))))
% 4.78/5.35 satz41k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1))))))
% 4.78/5.35 satz42:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0))))))
% 4.78/5.35 satz43:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0))))))
% 4.78/5.35 satz44:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3))))))))))))
% 4.78/5.35 satz45:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3))))))))))))
% 4.78/5.35 satz46:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3))))))))))))
% 4.78/5.35 satz47:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3))))))))))))
% 4.78/5.35 satz48:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0))))))
% 4.78/5.35 satz49:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0))))))
% 4.78/5.35 satz4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2))))))))))
% 4.78/5.35 satz4a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0))))
% 4.78/5.35 satz4b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1)))))))
% 4.78/5.36 satz4c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0))))
% 4.78/5.36 satz4d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1)))))))
% 4.78/5.36 satz4e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1))))
% 4.78/5.36 satz4f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1)))))))
% 4.78/5.36 satz4g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0))))
% 4.78/5.36 satz4h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1))))))
% 4.78/5.36 satz50:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 4.78/5.36 satz51a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 4.78/5.36 satz51b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2)))))))))
% 4.78/5.36 satz51c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2)))))))))
% 4.78/5.36 satz51d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2)))))))))
% 4.78/5.36 satz52:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lesseq X1) X2)->((lesseq X0) X2)))))))))
% 4.78/5.36 satz53:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0)))))
% 4.78/5.36 satz54:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0)))))
% 4.78/5.36 satz55:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1)))))))))
% 4.78/5.36 satz56:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz57:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2))))))))
% 4.78/5.36 satz57a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2)))))))))
% 4.78/5.36 satz58:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_pf X0) X1)) ((n_pf X1) X0))))))
% 4.78/5.36 satz59:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2)))))))))
% 4.78/5.36 satz5:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))))))))
% 4.78/5.36 satz60:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((moref ((n_pf X0) X1)) X0)))))
% 4.78/5.36 satz60a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((lessf X0) ((n_pf X0) X1))))))
% 4.78/5.36 satz61:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.78/5.36 satz62b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.78/5.36 satz62c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.78/5.36 satz62d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.78/5.36 satz62e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.78/5.36 satz62f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.78/5.36 satz62g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz62h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 4.78/5.36 satz62j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz62k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 4.78/5.36 satz63a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1))))))))
% 4.78/5.36 satz63b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1))))))))
% 4.78/5.36 satz63c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1))))))))
% 4.78/5.36 satz63d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1))))))))
% 4.78/5.36 satz63e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1))))))))
% 4.78/5.36 satz63f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1))))))))
% 4.78/5.36 satz64:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz64a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz65a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz65b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz65c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz65d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz66:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz66a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.78/5.36 satz67a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0))))))))
% 4.78/5.36 satz67b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 4.78/5.36 satz67d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1))))))))
% 4.78/5.36 satz67e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1))))))))))
% 4.78/5.36 satz68:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz69:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_tf X0) X1)) ((n_tf X1) X0))))))
% 4.78/5.36 satz6:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))))))
% 4.78/5.36 satz70:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2)))))))))
% 4.78/5.36 satz71:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2)))))))))
% 4.78/5.36 satz72a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.78/5.36 satz72b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.78/5.36 satz72c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.78/5.36 satz72d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.78/5.36 satz72e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.78/5.36 satz72f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.78/5.36 satz72g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz72h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 4.78/5.36 satz72j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz72k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 4.78/5.36 satz73a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1))))))))
% 4.78/5.36 satz73b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1))))))))
% 4.78/5.36 satz73c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1))))))))
% 4.78/5.36 satz73d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1))))))))
% 4.78/5.36 satz73e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1))))))))
% 4.78/5.36 satz73f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1))))))))
% 4.78/5.36 satz74:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz74a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz75a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz75b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz75c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz75d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz76:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz76a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.78/5.36 satz77a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0)))))))
% 4.78/5.36 satz77b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 4.78/5.36 satz78:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0)))
% 4.78/5.36 satz79:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0))))))
% 4.78/5.36 satz7:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))))
% 4.78/5.36 satz80:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2)))))))))
% 4.78/5.36 satz81:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.78/5.36 satz81a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.78/5.36 satz81b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.78/5.36 satz81c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1)))))))
% 4.78/5.36 satz81d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1)))))))
% 4.78/5.36 satz81e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1))))))
% 4.78/5.36 satz81f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1))))))
% 4.78/5.36 satz81g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1)))))))
% 4.78/5.36 satz81h:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(d_not ((rt_moreis X0) X1)))))))
% 4.78/5.36 satz81j:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_moreis X0) X1))->((rt_less X0) X1))))))
% 4.78/5.36 satz81k:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_lessis X0) X1))->((rt_more X0) X1))))))
% 4.78/5.36 satz82:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0))))))
% 4.78/5.36 satz83:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0))))))
% 4.78/5.36 satz84:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->((rt_lessis X1) X0))))))
% 4.78/5.36 satz85:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->((rt_moreis X1) X0))))))
% 4.78/5.36 satz86:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 4.78/5.36 satz87a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 4.78/5.36 satz87b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_lessis X1) X2)->((rt_less X0) X2)))))))))
% 4.78/5.36 satz87c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_moreis X0) X1)->(((rt_more X1) X2)->((rt_more X0) X2)))))))))
% 4.78/5.36 satz87d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_moreis X1) X2)->((rt_more X0) X2)))))))))
% 4.78/5.36 satz88:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X1) X2)->((rt_lessis X0) X2)))))))))
% 4.78/5.36 satz89:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_more X1) X0)))))
% 4.78/5.36 satz8:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2)))))))))
% 4.78/5.36 satz8a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2))))))))
% 4.78/5.36 satz8b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))))))
% 4.78/5.36 satz90:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_less X1) X0)))))
% 4.78/5.36 satz91:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rt_less X0) X2)) ((rt_less X2) X1)))))))))
% 4.78/5.36 satz92:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_pl X0) X1)) ((rt_pl X1) X0))))))
% 4.78/5.36 satz93:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_pl ((rt_pl X0) X1)) X2)) ((rt_pl X0) ((rt_pl X1) X2)))))))))
% 4.78/5.36 satz94:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_more ((rt_pl X0) X1)) X0)))))
% 4.78/5.36 satz94a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_less X0) ((rt_pl X0) X1))))))
% 4.78/5.36 satz95:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.78/5.36 satz96b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.78/5.36 satz96c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.78/5.36 satz96d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.78/5.36 satz96e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.78/5.36 satz96f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.78/5.36 satz97a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_more X0) X1))))))))
% 4.78/5.36 satz97b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_is X0) X1))))))))
% 4.78/5.36 satz97c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_less X0) X1))))))))
% 4.78/5.36 satz98:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.78/5.36 satz98a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.78/5.36 satz99a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.78/5.36 satz99b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.78/5.36 satz99c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.78/5.36 satz99d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.78/5.36 satz9:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2)))))))))
% 4.78/5.36 satz9a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 4.78/5.36 satz9b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 4.78/5.36 sc1:=(fun (X0:fofType)=> ((d_Sep cut) (fun (X1:fofType)=> ((r_in (pofrp X1)) X0)))):(fofType->fofType)
% 4.78/5.36 schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) ((d_5p205_prop3 X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.36 schnittprop:=(fun (X0:fofType) (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((d_and ((rp_in X2) X0)) ((lrt X2) X1))))):(fofType->(fofType->Prop))
% 4.78/5.36 schnittset:=(fun (X0:fofType)=> ((d_Sep rat) (schnittprop X0))):(fofType->fofType)
% 4.78/5.36 second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)):(fofType->(fofType->fofType))
% 4.78/5.36 second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 second_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1))))))
% 4.78/5.36 secondis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3))))))
% 4.78/5.36 seq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Pi real) (fun (X3:fofType)=> (((if (intrl X3)) (((if ((r_lessis X1) X3)) (((if ((r_lessis X3) X0)) X2) (ordsucc emptyset))) (ordsucc emptyset))) (ordsucc emptyset))))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 set_ext:(forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1))))
% 4.78/5.36 setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))):(fofType->(fofType->fofType))
% 4.78/5.36 setof_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0)))))
% 4.78/5.36 setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))):(fofType->(fofType->fofType))
% 4.78/5.36 shift_n1:=(fun (X0:fofType) (X1:fofType)=> (inn ((shiftl X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 shift_n2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rlofnt (((shift_n1 X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 shift_ns:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ap X2) (((shiftr X0) X1) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.36 shift_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((r_is X3) ((ap X2) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.78/5.36 shift_ul:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((shiftl X2) X1)):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 shiftf:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X4:fofType)=> ((ap X3) (((shiftr X0) X1) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.36 shiftl1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((shiftl X0) X1)) (((shift_ul X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 shiftl:=(fun (X0:fofType) (X1:fofType)=> (ntofrl ((r_mn ((r_pl X0) d_1rl)) X1))):(fofType->(fofType->fofType))
% 4.78/5.36 shiftr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((r_mn ((r_pl (((shift_n2 X0) X1) X2)) X1)) d_1rl)):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 shiftseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X3:fofType)=> (((shiftl1 X0) X1) ((((shift_ns X0) X1) X2) X3))))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 singlet_u0:=(inn n_1):(fofType->fofType)
% 4.78/5.36 snt:=(fun (X0:fofType) (X1:fofType)=> (cutof (schnittset X0))):(fofType->(fofType->fofType))
% 4.78/5.36 soft:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.36 sq1:=(fun (X0:fofType)=> ((rp_ts X0) X0)):(fofType->fofType)
% 4.78/5.36 sqrt:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))):(fofType->fofType)
% 4.78/5.36 sqrtset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rp_less ((rp_ts (rpofrt X1)) (rpofrt X1))) X0)))):(fofType->fofType)
% 4.78/5.36 srp:=(fun (X0:fofType)=> (sqrt (rpofpd X0))):(fofType->fofType)
% 4.78/5.36 st_disj:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.36 stc:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((schnitt (sc1 X0)) (sc1 X1))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 std:=(second1 cut):(fofType->fofType)
% 4.78/5.36 stm:=(first1 cut):(fofType->fofType)
% 4.78/5.36 stp:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (pofrp (((stc X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 subrelation:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (R':(A->(B->Prop)))=> (forall (x:A) (y:B), (((R x) y)->((R' x) y)))):(forall (A:Type) (B:Type), ((A->(B->Prop))->((A->(B->Prop))->Prop)))
% 4.78/5.36 suc_p:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat)))))
% 4.78/5.36 suct:=((d_Sigma natt) (fun (X0:fofType)=> (ntofn (ordsucc (nofnt X0))))):fofType
% 4.78/5.36 sum:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((sumprop X0) X1))):(fofType->(fofType->fofType))
% 4.78/5.36 sumprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_pl X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.78/5.36 sumprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((sumprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.36 surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.36 surjseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((((imseq X0) X1) X2) X3))))))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.36 times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->fofType)
% 4.78/5.36 timesdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_td X0) X1)))))):fofType
% 4.78/5.36 timesfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_tf X0) X1)))))):fofType
% 4.78/5.36 tofs:=(fun (X0:fofType) (X1:fofType)=> ap):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.78/5.36 u01:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X2) ((rt_pl X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.78/5.36 ubprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_moreis X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.78/5.36 ul1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((shiftl1 X0) X1)):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.78/5.36 um10:=(fun (X0:fofType)=> ((rt_mn (rtofn X0)) d_1rt)):(fofType->fofType)
% 4.78/5.36 um1:=(fun (X0:fofType)=> (nofrt (um10 X0))):(fofType->fofType)
% 4.78/5.36 union:(fofType->fofType)
% 4.78/5.36 unique:=(fun (A:Type) (P:(A->Prop)) (x:A)=> ((and (P x)) (forall (x':A), ((P x')->(((eq A) x) x'))))):(forall (A:Type), ((A->Prop)->(A->Prop)))
% 4.78/5.36 unique_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R x) y))))))=> ((((dependent_unique_choice A) (fun (x2:A)=> B)) R) x)):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R x) y)))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% 4.78/5.36 univof:(fofType->fofType)
% 4.78/5.36 unmore:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4))))))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 urt:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_in X1) (lcl X0)))):(fofType->(fofType->Prop))
% 4.86/5.44 wel:=(fun (X0:Prop)=> (d_not (d_not X0))):(Prop->Prop)
% 4.86/5.44 wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.44 wissel_wb:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.44 xi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2))))
% 4.86/5.44 xmy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_mn (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.86/5.44 xout:=(fun (X0:fofType)=> ((outn X0) X0)):(fofType->fofType)
% 4.86/5.44 xpy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_pl (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.86/5.44 xrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_xm X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.44 xty:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_ts (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.86/5.44 yrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_ym X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.44 zero:=(fun (X0:fofType)=> ((rp_is (stm X0)) (std X0))):(fofType->Prop)
% 4.86/5.44 zeta:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((((ite ((rp_less (((d_5160_fr X0) X1) X2)) d_1rp)) cut) (((d_5160_fr X0) X1) X2)) d_1rp)):(fofType->(fofType->(fofType->fofType)))]
% 4.86/5.44 ---termsubcontext
% 4.86/5.44 [[[[False:Prop
% 4.86/5.44 False_rect:(forall (P:Type), (False->P))
% 4.86/5.44 I:True
% 4.86/5.44 NNPP:=(fun (P:Prop) (H:(not (not P)))=> ((fun (C:((or P) (not P)))=> ((((((or_ind P) (not P)) P) (fun (H0:P)=> H0)) (fun (N:(not P))=> ((False_rect P) (H N)))) C)) (classic P))):(forall (P:Prop), ((not (not P))->P))
% 4.86/5.44 True:Prop
% 4.86/5.44 _TPTP_proj1:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj)):(fofType->fofType)
% 4.86/5.44 abs:=((indreal real) absdr):(fofType->fofType)
% 4.86/5.44 absd:=(fun (X0:fofType)=> ((((ite (negd X0)) dif) ((rp_df (std X0)) (stm X0))) X0)):(fofType->fofType)
% 4.86/5.44 absdr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (absd X0)))):fofType
% 4.86/5.44 all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))):(fofType->((fofType->Prop)->Prop))
% 4.86/5.44 all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))):((fofType->Prop)->((fofType->Prop)->Prop))
% 4.86/5.44 amone:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3)))))))):(fofType->((fofType->Prop)->Prop))
% 4.86/5.44 and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.86/5.44 and:(Prop->(Prop->Prop))
% 4.86/5.44 and_comm_i:=(fun (A:Prop) (B:Prop) (H:((and A) B))=> ((((conj B) A) (((proj2 A) B) H)) (((proj1 A) B) H))):(forall (A:Prop) (B:Prop), (((and A) B)->((and B) A)))
% 4.86/5.44 and_rect:=(fun (A:Prop) (B:Prop) (P:Type) (X:(A->(B->P))) (H:((and A) B))=> ((X (((proj1 A) B) H)) (((proj2 A) B) H))):(forall (A:Prop) (B:Prop) (P:Type), ((A->(B->P))->(((and A) B)->P)))
% 4.86/5.44 anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->Prop)))
% 4.86/5.44 ap:=(fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1)):(fofType->(fofType->fofType))
% 4.86/5.44 ap_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))
% 4.86/5.44 apb1:=(fun (X0:fofType) (X1:fofType)=> (rpofpd ((rp_pd X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.44 arpi:=(fun (X0:fofType)=> ((rp_ov d_1rp) (rpofpd X0))):(fofType->fofType)
% 4.86/5.44 atb3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd ((rp_td X0) X1)))):(fofType->(fofType->fofType))
% 4.86/5.44 beta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2))))
% 4.86/5.44 bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.44 changef:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.86/5.44 chi:=(fun (X0:fofType) (X1:fofType)=> (cutof ((diff X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.44 choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) (fun (y:B)=> ((R x) y)))))=> (((fun (P:Prop) (x0:(forall (x0:(A->(B->Prop))), (((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))->P)))=> (((((ex_ind (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x0:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x0) y)))))))) P) x0) ((((relational_choice A) B) R) x))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x0:(A->(B->Prop))) (x1:((and ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))))=> (((fun (P:Type) (x2:(((((subrelation A) B) x0) R)->((forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))->P)))=> (((((and_rect ((((subrelation A) B) x0) R)) (forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y)))))) P) x2) x1)) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x2:((((subrelation A) B) x0) R)) (x3:(forall (x00:A), ((ex B) ((unique B) (fun (y:B)=> ((x0 x00) y))))))=> (((fun (P:Prop) (x4:(forall (x1:(A->B)), ((forall (x10:A), ((x0 x10) (x1 x10)))->P)))=> (((((ex_ind (A->B)) (fun (f:(A->B))=> (forall (x1:A), ((x0 x1) (f x1))))) P) x4) ((((unique_choice A) B) x0) x3))) ((ex (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0)))))) (fun (x4:(A->B)) (x5:(forall (x10:A), ((x0 x10) (x4 x10))))=> ((((ex_intro (A->B)) (fun (f:(A->B))=> (forall (x0:A), ((R x0) (f x0))))) x4) (fun (x00:A)=> (((x2 x00) (x4 x00)) (x5 x00))))))))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% 4.86/5.44 choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% 4.86/5.44 class:=((ecect frac) n_eq):(fofType->fofType)
% 4.86/5.44 classic:(forall (P:Prop), ((or P) (not P)))
% 4.86/5.44 classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 4.86/5.44 cond1:=(n_in n_1):(fofType->Prop)
% 4.86/5.44 cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))):(fofType->Prop)
% 4.86/5.44 conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 4.86/5.44 cut:=((d_Sep (power rat)) cutprop):fofType
% 4.86/5.44 cutof:=((out (power rat)) cutprop):(fofType->fofType)
% 4.86/5.44 cutprop1:=(fun (X0:fofType)=> ((d_and (cutprop1a X0)) (cutprop1b X0))):(fofType->Prop)
% 4.86/5.44 cutprop1a:=(nonempty rat):(fofType->Prop)
% 4.86/5.44 cutprop1b:=(fun (X0:fofType)=> (d_not (rt_all (fun (X1:fofType)=> ((rt_in X1) X0))))):(fofType->Prop)
% 4.86/5.44 cutprop2:=(fun (X0:fofType)=> (rt_all (fun (X1:fofType)=> ((imp ((rt_in X1) X0)) ((cutprop2a X0) X1))))):(fofType->Prop)
% 4.86/5.44 cutprop2a:=(fun (X0:fofType) (X1:fofType)=> (rt_all (fun (X2:fofType)=> ((imp (d_not ((rt_in X2) X0))) ((rt_less X1) X2))))):(fofType->(fofType->Prop))
% 4.86/5.44 cutprop3:=(fun (X0:fofType)=> (d_not (rt_some (max X0)))):(fofType->Prop)
% 4.86/5.44 cutprop:=(fun (X0:fofType)=> (((and3 (cutprop1 X0)) (cutprop2 X0)) (cutprop3 X0))):(fofType->Prop)
% 4.86/5.44 d161_s:=(fun (X0:fofType)=> (pdofrp (srp X0))):(fofType->fofType)
% 4.86/5.44 d_10_prop1:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))
% 4.86/5.44 d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2)))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 4.86/5.44 d_1df:=(pdofrp d_1rp):fofType
% 4.86/5.44 d_1out:=(fun (X0:fofType)=> ((outn X0) n_1)):(fofType->fofType)
% 4.86/5.44 d_1rl:=(realof d_1df):fofType
% 4.86/5.44 d_1rp:=(rpofrt d_1rt):fofType
% 4.86/5.44 d_1rt:=(rtofn n_1):fofType
% 4.86/5.44 d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->fofType)
% 4.86/5.44 d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0)):(fofType->Prop)
% 4.86/5.44 d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))):(fofType->Prop)
% 4.86/5.44 d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))):(fofType->fofType)
% 4.86/5.44 d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))):(fofType->Prop)
% 4.86/5.44 d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_25_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))):(fofType->(fofType->Prop))
% 4.86/5.44 d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_29_prop1:=(fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_2rl:=((r_pl d_1rl) d_1rl):fofType
% 4.86/5.44 d_2x0:=(fun (X0:fofType)=> ((rt_pl X0) X0)):(fofType->fofType)
% 4.86/5.44 d_3129_z1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X0) ((rt_pl X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 d_3132_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((lrt X0) X1)) ((urt X0) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_3132_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((rt_is ((rt_mn X3) X2)) X1)):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.44 d_3132_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((d_3132_prop1 X0) X2) X3)) ((((d_3132_prop1 X0) X2) X3)->((((d_3132_prop2 X0) X1) X2) X3)))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.44 d_3132_prop4:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (((d_3132_prop3 X0) X1) X2))))):(fofType->(fofType->Prop))
% 4.86/5.44 d_3132_u0:=(fun (X0:fofType) (X1:fofType)=> ((rt_pl X1) X0)):(fofType->(fofType->fofType))
% 4.86/5.44 d_3132_v0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (um10 X2)) X0))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 d_3132_w0:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_pl X1) ((rt_ts (rtofn X2)) X0))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 d_367_vo:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))):(fofType->(fofType->fofType))
% 4.86/5.44 d_367_w:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.86/5.44 d_3r184_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (pos X1)) (pos X2)) ((r_is X0) ((r_mn X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_3r184_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_some ((d_3r184_prop1 X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_3r184_prop3:=(fun (X0:fofType)=> (r_some (d_3r184_prop2 X0))):(fofType->Prop)
% 4.86/5.44 d_4141_v0:=(fun (X0:fofType) (X1:fofType)=> ((rt_ts ((rt_ov d_1rt) X1)) X0)):(fofType->(fofType->fofType))
% 4.86/5.44 d_4144_x2:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_moreis X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.86/5.44 d_4152_chi:=(fun (X0:fofType)=> (cutof (inv X0))):(fofType->fofType)
% 4.86/5.44 d_4153_chi:=(fun (X0:fofType) (X1:fofType)=> ((rp_ts X1) X0)):(fofType->(fofType->fofType))
% 4.86/5.44 d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))):(fofType->fofType)
% 4.86/5.44 d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0)):fofType
% 4.86/5.44 d_428_prop1:=(fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))):(fofType->(fofType->Prop))
% 4.86/5.44 d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->Prop)
% 4.86/5.44 d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))):(fofType->(fofType->Prop))
% 4.86/5.44 d_430_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_431_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_477_v:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1)))):(fofType->(fofType->fofType))
% 4.86/5.44 d_5113_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nt_in (ntofn X1)) X0)):(fofType->(fofType->Prop))
% 4.86/5.44 d_5156_prop1:=(fun (X0:fofType) (X1:fofType)=> ((rp_nt_in (nttofnt X1)) X0)):(fofType->(fofType->Prop))
% 4.86/5.44 d_5157_s1:=(fun (X0:fofType)=> ((d_Sep rat) (urt X0))):(fofType->fofType)
% 4.86/5.44 d_5160_dn:=(fun (X0:fofType) (X1:fofType)=> ((rp_pl ((rp_pl X0) X1)) d_1rp)):(fofType->(fofType->fofType))
% 4.86/5.44 d_5160_fr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_ov (((d_5160_nm X0) X1) X2)) ((d_5160_dn X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 d_5160_nm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rp_mn (rpofrt X2)) ((rp_ts X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 d_5160_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.86/5.44 d_5160_prop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((d_5160_prop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_5160_xr:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((rt_ov X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.44 d_5160_y0:=(fun (X0:fofType)=> X0):(fofType->fofType)
% 4.86/5.44 d_5160_yr:=(fun (X0:fofType)=> (rpofrt (d_5160_y0 X0))):(fofType->fofType)
% 4.86/5.44 d_5161_dn:=(fun (X0:fofType)=> ((rp_pl (rpofrt X0)) ((rp_pl (rpofrt X0)) d_1rp))):(fofType->fofType)
% 4.86/5.44 d_5161_fr:=(fun (X0:fofType) (X1:fofType)=> ((rp_ov ((d_5161_nm X0) X1)) (d_5161_dn X1))):(fofType->(fofType->fofType))
% 4.86/5.44 d_5161_max:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_more X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType))
% 4.86/5.44 d_5161_min:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rp_less X0) X1)) cut) X0) X1)):(fofType->(fofType->fofType))
% 4.86/5.44 d_5161_nm:=(fun (X0:fofType) (X1:fofType)=> ((rp_mn X0) ((rp_ts (rpofrt X1)) (rpofrt X1)))):(fofType->(fofType->fofType))
% 4.86/5.44 d_5161_xm:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_more X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.86/5.44 d_5161_ym:=(fun (X0:fofType) (X1:fofType)=> ((((ite ((rt_less X0) X1)) rat) X0) X1)):(fofType->(fofType->fofType))
% 4.86/5.44 d_5162_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_eq ((n_tf ((n_fr X1) X0)) ((n_fr X1) X0))) ((n_fr (ordsucc n_1)) n_1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_5162_prop2:=(fun (X0:fofType)=> (n_some (d_5162_prop1 X0))):(fofType->Prop)
% 4.86/5.44 d_5162_prop3:=(n_some d_5162_prop2):Prop
% 4.86/5.44 d_5162_x0:=(rtofrp ksi):fofType
% 4.86/5.44 d_5162_y:=((ind nat) (min d_5162_prop2)):fofType
% 4.86/5.44 d_527_q:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (X0 (ntofn X1))):((fofType->Prop)->(fofType->Prop))
% 4.86/5.44 d_54_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (nofnt ((ap X0) (ntofn X1)))))):(fofType->fofType)
% 4.86/5.44 d_54_gt:=(fun (X0:fofType)=> ((d_Sigma natt) (fun (X1:fofType)=> (ntofn ((ap X0) (nofnt X1)))))):(fofType->fofType)
% 4.86/5.44 d_54_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc (nofnt X0)))) (d_24_prop1 X1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_59_i:=(fun (X0:fofType) (X1:fofType)=> ((n_is (nofnt X0)) (nofnt X1))):(fofType->(fofType->Prop))
% 4.86/5.44 d_59_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X0)) (nofnt X1)))):(fofType->(fofType->Prop))
% 4.86/5.44 d_59_iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop (nofnt X1)) (nofnt X0)))):(fofType->(fofType->Prop))
% 4.86/5.44 d_5p205_prop1:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_less X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop))
% 4.86/5.44 d_5p205_prop2:=(fun (X0:fofType) (X1:fofType)=> (rp_all (fun (X2:fofType)=> (((rp_more X2) X1)->((rp_in X2) X0))))):(fofType->(fofType->Prop))
% 4.86/5.44 d_5p205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5p205_prop1 X0) X2)) ((d_5p205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_5r205_prop1:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_less X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop))
% 4.86/5.44 d_5r205_prop2:=(fun (X0:fofType) (X1:fofType)=> (r_all (fun (X2:fofType)=> (((r_more X2) X1)->((r_in X2) X0))))):(fofType->(fofType->Prop))
% 4.86/5.44 d_5r205_prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((d_5r205_prop1 X0) X2)) ((d_5r205_prop2 X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 d_5r205_sp1:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_in (r_m0 X1)) X0)))):(fofType->fofType)
% 4.86/5.44 d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1))):((fofType->((fofType->fofType)->fofType))->(fofType->fofType))
% 4.86/5.44 d_In_rec_G:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))):((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))
% 4.86/5.44 d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1)):(fofType->fofType)
% 4.86/5.44 d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))):(fofType->fofType)
% 4.86/5.44 d_Pi:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))))):(fofType->((fofType->fofType)->fofType))
% 4.86/5.44 d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))):(fofType->Prop)
% 4.86/5.44 d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))):(fofType->((fofType->Prop)->((fofType->fofType)->fofType)))
% 4.86/5.44 d_Repl_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0)))))):(fofType->Prop)
% 4.86/5.44 d_Sep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset)):(fofType->((fofType->Prop)->fofType))
% 4.86/5.44 d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))):(fofType->((fofType->fofType)->fofType))
% 4.86/5.44 d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0)):(fofType->fofType)
% 4.86/5.44 d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))):(fofType->(fofType->Prop))
% 4.86/5.44 d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))):(fofType->(fofType->fofType))
% 4.86/5.44 d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))):(fofType->Prop)
% 4.86/5.44 d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))):(fofType->fofType)
% 4.86/5.44 d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))):(fofType->Prop)
% 4.86/5.44 d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))):(Prop->(Prop->Prop))
% 4.86/5.44 d_not:=(fun (X0:Prop)=> ((imp X0) False)):(Prop->Prop)
% 4.86/5.44 d_pair:=(fun (X0:fofType) (X1:fofType)=> pair):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.44 den:=(second1 nat):(fofType->fofType)
% 4.86/5.44 dependent_unique_choice:(forall (A:Type) (B:(A->Type)) (R:(forall (x:A), ((B x)->Prop))), ((forall (x:A), ((ex (B x)) ((unique (B x)) (fun (y:(B x))=> ((R x) y)))))->((ex (forall (x:A), (B x))) (fun (f:(forall (x:A), (B x)))=> (forall (x:A), ((R x) (f x)))))))
% 4.86/5.44 dif:=(pair1type cut):fofType
% 4.86/5.44 diff:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((rp_diffprop X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.44 diffprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((rt_more X1) X2)) (((rt_more X1) X2)->((rt_is X0) ((rt_mn X1) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 diffprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((urt X1) X4)) (((diffprop1 X2) X3) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.86/5.44 diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 e_fisi:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3)))))))
% 4.86/5.44 e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2):(fofType->((fofType->Prop)->(fofType->fofType)))
% 4.86/5.44 e_in_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 4.86/5.44 e_inp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2)))))
% 4.86/5.44 e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 e_isp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3))))))))
% 4.86/5.44 e_pair_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1)))))))))
% 4.86/5.44 ec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0))):(Prop->(Prop->(Prop->Prop)))
% 4.86/5.44 ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.86/5.44 ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.86/5.44 ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.86/5.44 ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->fofType))
% 4.86/5.44 ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.86/5.44 ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 4.86/5.44 empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))):(fofType->(fofType->Prop))
% 4.86/5.44 emptyset:fofType
% 4.86/5.44 eps:((fofType->Prop)->fofType)
% 4.86/5.44 eq:=(fun (T:Type) (a:T) (b:T)=> (forall (P:(T->Prop)), ((P a)->(P b)))):(forall (T:Type), (T->(T->Prop)))
% 4.86/5.44 eq_ref:=(fun (T:Type) (a:T) (P:(T->Prop)) (x:(P a))=> x):(forall (T:Type) (a:T), (((eq T) a) a))
% 4.86/5.44 eq_stepl:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) a) c))=> ((((((eq_trans T) c) a) b) ((((eq_sym T) a) c) Y)) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) a) c)->(((eq T) c) b))))
% 4.86/5.44 eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% 4.86/5.44 eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 4.86/5.44 eq_trans:=(fun (T:Type) (a:T) (b:T) (c:T) (X:(((eq T) a) b)) (Y:(((eq T) b) c))=> ((Y (fun (t:T)=> (((eq T) a) t))) X)):(forall (T:Type) (a:T) (b:T) (c:T), ((((eq T) a) b)->((((eq T) b) c)->(((eq T) a) c))))
% 4.86/5.44 esti:=(fun (X0:fofType)=> in):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 estie:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2)))))
% 4.86/5.44 estii:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1))))))
% 4.86/5.44 eta_expansion:=(fun (A:Type) (B:Type)=> ((eta_expansion_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)), (((eq (A->B)) f) (fun (x:A)=> (f x))))
% 4.86/5.44 eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fun (x:A) (P:((B x)->Prop)) (x0:(P (f x)))=> x0))):(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))), (((eq (forall (x:A), (B x))) f) (fun (x:A)=> (f x))))
% 4.86/5.44 ex:(forall (A:Type), ((A->Prop)->Prop))
% 4.86/5.44 ex_ind:(forall (A:Type) (F:(A->Prop)) (P:Prop), ((forall (x:A), ((F x)->P))->(((ex A) F)->P)))
% 4.86/5.44 ex_intro:(forall (A:Type) (P:(A->Prop)) (x:A), ((P x)->((ex A) P)))
% 4.86/5.44 famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))):(fofType->((fofType->fofType)->fofType))
% 4.86/5.44 first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)):(fofType->(fofType->fofType))
% 4.86/5.44 first:=(fun (X0:fofType) (X1:fofType)=> proj0):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 first_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 4.86/5.44 firstis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2))))))
% 4.86/5.44 fixf2:=((fixfu2 dif) rp_eq):(fofType->(fofType->Prop))
% 4.86/5.44 fixf:=((fixfu2 frac) n_eq):(fofType->(fofType->Prop))
% 4.86/5.44 fixfu2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7))))))))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.86/5.44 fixfu:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 4.86/5.44 fofType:Type
% 4.86/5.44 frac:=(pair1type nat):fofType
% 4.86/5.44 functional_extensionality:=(fun (A:Type) (B:Type)=> ((functional_extensionality_dep A) (fun (x1:A)=> B))):(forall (A:Type) (B:Type) (f:(A->B)) (g:(A->B)), ((forall (x:A), (((eq B) (f x)) (g x)))->(((eq (A->B)) f) g)))
% 4.86/5.44 functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% 4.86/5.44 functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% 4.86/5.44 half:=((r_ov d_1rl) d_2rl):fofType
% 4.86/5.44 i1_s:=(d_Sep nat):((fofType->Prop)->fofType)
% 4.86/5.44 if:=(fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2)))))):(Prop->(fofType->(fofType->fofType)))
% 4.86/5.44 if_i_0:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2)))
% 4.86/5.44 if_i_1:(forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1)))
% 4.86/5.44 if_i_correct:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2))))
% 4.86/5.44 if_i_or:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2)))
% 4.86/5.44 iff:=(fun (A:Prop) (B:Prop)=> ((and (A->B)) (B->A))):(Prop->(Prop->Prop))
% 4.86/5.44 iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 4.86/5.44 iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 4.86/5.44 iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 4.86/5.44 iii1_lbprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_lessis X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))):(fofType->(fofType->Prop))
% 4.86/5.44 iiia_x0:=(fun (X0:fofType)=> (rtofn (ntofrp X0))):(fofType->fofType)
% 4.86/5.44 iiit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X1) X0))):(fofType->(fofType->Prop))
% 4.86/5.44 iit:=(fun (X0:fofType) (X1:fofType)=> (nt_some ((nt_diffprop X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.44 image:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.44 imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1)):(Prop->(Prop->Prop))
% 4.86/5.44 improp:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and (((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))) ((((and3 (intrl X4)) ((r_lessis X1) X4)) ((r_lessis X4) X0))->(((((shift_prop1 X0) X1) X2) X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.86/5.44 imseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (r_some ((((improp X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.44 in:(fofType->(fofType->Prop))
% 4.86/5.44 incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))):(fofType->((fofType->Prop)->fofType))
% 4.86/5.44 ind_p:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0)))))
% 4.86/5.44 indeq2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))
% 4.86/5.44 indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 4.86/5.44 indrat:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.44 indreal2:=((indeq2 dif) rp_eq):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.44 indreal:=((indeq dif) rp_eq):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 inf:=(esti frac):(fofType->(fofType->Prop))
% 4.86/5.44 inj_h:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.86/5.44 injective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4))))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 injseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->(((r_is ((ap X2) X3)) ((ap X2) X4))->((r_is X3) X4))))))))))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType))
% 4.86/5.44 inseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->(((and3 (intrl ((ap X2) X3))) ((r_lessis X1) ((ap X2) X3))) ((r_lessis ((ap X2) X3)) X0)))))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 intd:=(fun (X0:fofType)=> ((l_or (zero X0)) (natd (absd X0)))):(fofType->Prop)
% 4.86/5.44 intd_a3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X0))):(fofType->(fofType->fofType))
% 4.86/5.44 intd_b2:=(fun (X0:fofType)=> (rpofpd (m0d X0))):(fofType->fofType)
% 4.86/5.44 intd_b3:=(fun (X0:fofType) (X1:fofType)=> (rpofpd (absd X1))):(fofType->(fofType->fofType))
% 4.86/5.44 intrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (intd X1))))):(fofType->Prop)
% 4.86/5.44 inv:=(fun (X0:fofType)=> ((d_Sep rat) (invprop X0))):(fofType->fofType)
% 4.86/5.44 inverse:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset)))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.44 invprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and ((urt X0) X2)) ((rt_less X2) X1))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.44 invprop2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 ((urt X0) X2)) (rt_some ((invprop1 X0) X2))) ((rt_is X1) ((rt_ov d_1rt) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 invprop:=(fun (X0:fofType) (X1:fofType)=> (rt_some ((invprop2 X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 irratd:=(fun (X0:fofType)=> (d_not (ratd X0))):(fofType->Prop)
% 4.86/5.45 irratrl:=(fun (X0:fofType)=> (d_not (ratrl X0))):(fofType->Prop)
% 4.86/5.45 irratrp:=(fun (X0:fofType)=> (d_not (ratrp X0))):(fofType->Prop)
% 4.86/5.45 is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)):(fofType->((fofType->Prop)->Prop))
% 4.86/5.45 isseti:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2))))))))
% 4.86/5.45 ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))):(Prop->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 iv4d_ai:=(fun (X0:fofType)=> (pdofrp (arpi X0))):(fofType->fofType)
% 4.86/5.45 iv5d_2:=((rp_pl d_1rp) d_1rp):fofType
% 4.86/5.45 ivr1_nr:=(fun (X0:fofType)=> rpofnd):(fofType->(fofType->fofType))
% 4.86/5.45 ivr1_pr:=(fun (X0:fofType)=> rpofpd):(fofType->(fofType->fofType))
% 4.86/5.45 ivr2_propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.45 ivr2_propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.45 ivr2_x0:=(fun (X0:fofType) (X1:fofType)=> (ntofrp ((ivr1_pr X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 ivr2_xn:=(fun (X0:fofType)=> ((((soft nat) real) ((d_Sigma nat) rlofnt)) (rlofnt X0))):(fofType->fofType)
% 4.86/5.45 k_EmptyAx:(((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False)
% 4.86/5.45 k_If_In_01:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset)))))
% 4.86/5.45 k_If_In_then_E:(forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2))))
% 4.86/5.45 k_In_0_1:((in emptyset) (ordsucc emptyset))
% 4.86/5.45 k_In_ind:(forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1))))
% 4.86/5.45 k_Pi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3))))))
% 4.86/5.45 k_PowerE:(forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0)))
% 4.86/5.45 k_PowerEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0)))
% 4.86/5.45 k_PowerI:(forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0))))
% 4.86/5.45 k_ReplEq:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3)))))))
% 4.86/5.45 k_Self_In_Power:(forall (X0:fofType), ((in X0) (power X0)))
% 4.86/5.45 k_SepE1:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0)))
% 4.86/5.45 k_SepE2:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2)))
% 4.86/5.45 k_SepI:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1)))))
% 4.86/5.45 k_Sigma_eta_proj0_proj1:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))))
% 4.86/5.45 k_UnionEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0))))))
% 4.86/5.45 k_UnivOf_In:(forall (X0:fofType), ((in X0) (univof X0)))
% 4.86/5.45 k_UnivOf_ZF_closed:(forall (X0:fofType), (d_ZF_closed (univof X0)))
% 4.86/5.45 k_satz123a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((or3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.86/5.45 k_satz123b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((ec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.86/5.45 k_satz67c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0))))))
% 4.86/5.45 ksi:=((ind cut) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) X0)) (rpofnt (ordsucc n_1))))):fofType
% 4.86/5.45 l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))):(Prop->(Prop->Prop))
% 4.86/5.45 l_et:(forall (X0:Prop), ((wel X0)->X0))
% 4.86/5.45 l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))):(Prop->(Prop->Prop))
% 4.86/5.45 l_or:=(fun (X0:Prop)=> (imp (d_not X0))):(Prop->(Prop->Prop))
% 4.86/5.45 l_some:=(fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1)))):(fofType->((fofType->Prop)->Prop))
% 4.86/5.45 lam_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1))))
% 4.86/5.45 lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))):((fofType->Prop)->(fofType->(fofType->Prop)))
% 4.86/5.45 lcl:=((e_in (power rat)) cutprop):(fofType->fofType)
% 4.86/5.45 left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 left:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 lessd:=(fun (X0:fofType) (X1:fofType)=> ((rp_less ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.86/5.45 lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.86/5.45 lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 lrt:=(fun (X0:fofType) (X1:fofType)=> ((rt_in X1) (lcl X0))):(fofType->(fofType->Prop))
% 4.86/5.45 m0d:=(fun (X0:fofType)=> ((rp_df (std X0)) (stm X0))):(fofType->fofType)
% 4.86/5.45 m0dr:=((d_Sigma dif) (fun (X0:fofType)=> (realof (m0d X0)))):fofType
% 4.86/5.45 max:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_ub X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop))
% 4.86/5.45 min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop))
% 4.86/5.45 mored:=(fun (X0:fofType) (X1:fofType)=> ((rp_more ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.86/5.45 moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.86/5.45 moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 mxy:=(fun (X0:fofType) (X1:fofType)=> ((r_ts half) ((r_pl X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 n1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (negd X1))):(fofType->(fofType->Prop))
% 4.86/5.45 n1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (negd X0)) (posd X1))):(fofType->(fofType->Prop))
% 4.86/5.45 nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)):(fofType->(fofType->Prop))
% 4.86/5.45 n_1:=(ordsucc emptyset):fofType
% 4.86/5.45 n_1_p:((is_of n_1) (fun (X0:fofType)=> ((in X0) nat)))
% 4.86/5.45 n_1o:=((outn n_1) n_1):fofType
% 4.86/5.45 n_1t:=((outn n_2) n_1):fofType
% 4.86/5.45 n_2:=((n_pl n_1) n_1):fofType
% 4.86/5.45 n_2t:=((outn n_2) n_2):fofType
% 4.86/5.45 n_all:=(all nat):((fofType->Prop)->Prop)
% 4.86/5.45 n_ax3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1)))
% 4.86/5.45 n_ax4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1))))))
% 4.86/5.45 n_ax5:((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0)))))))
% 4.86/5.45 n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop))
% 4.86/5.45 n_fr:=(pair1 nat):(fofType->(fofType->fofType))
% 4.86/5.45 n_in:=(esti nat):(fofType->(fofType->Prop))
% 4.86/5.45 n_is:=(e_is nat):(fofType->(fofType->Prop))
% 4.86/5.45 n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))):((fofType->Prop)->(fofType->Prop))
% 4.86/5.45 n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 n_one:=(one nat):((fofType->Prop)->Prop)
% 4.86/5.45 n_pf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.86/5.45 n_pl:=(fun (X0:fofType)=> (ap (plus X0))):(fofType->(fofType->fofType))
% 4.86/5.45 n_some:=(l_some nat):((fofType->Prop)->Prop)
% 4.86/5.45 n_tf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType))
% 4.86/5.45 n_ts:=(fun (X0:fofType)=> (ap (times X0))):(fofType->(fofType->fofType))
% 4.86/5.45 nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))):fofType
% 4.86/5.45 nat_1:(nat_p (ordsucc emptyset))
% 4.86/5.45 nat_ind:(forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1))))))
% 4.86/5.45 nat_inv:(forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1))))))))
% 4.86/5.45 nat_ordsucc:(forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0))))
% 4.86/5.45 nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))):(fofType->Prop)
% 4.86/5.45 nat_p_omega:(forall (X0:fofType), ((nat_p X0)->((in X0) omega)))
% 4.86/5.45 natd:=(fun (X0:fofType)=> ((d_and (posd X0)) ((posd X0)->(natrp (rpofpd X0))))):(fofType->Prop)
% 4.86/5.45 natprop:=(fun (X0:fofType) (X1:fofType)=> ((inf ((n_fr X1) n_1)) (class X0))):(fofType->(fofType->Prop))
% 4.86/5.45 natrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (natd X1))))):(fofType->Prop)
% 4.86/5.45 natrp:=(((image nat) cut) ((d_Sigma nat) rpofnt)):(fofType->Prop)
% 4.86/5.45 natrt:=(fun (X0:fofType)=> (n_some (natprop X0))):(fofType->Prop)
% 4.86/5.45 natt:=((d_Sep rat) natrt):fofType
% 4.86/5.45 ndofrp:=(fun (X0:fofType)=> ((rp_df d_1rp) ((rp_pl X0) d_1rp))):(fofType->fofType)
% 4.86/5.45 neg:=(fun (X0:fofType)=> ((l_some dif) (propn X0))):(fofType->Prop)
% 4.86/5.45 negd:=(fun (X0:fofType)=> ((rp_less (stm X0)) (std X0))):(fofType->Prop)
% 4.86/5.45 neq_ordsucc_0:(forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset)))
% 4.86/5.45 nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2)))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.45 nofnt:=(fun (X0:fofType)=> (nofrt (rtofnt X0))):(fofType->fofType)
% 4.86/5.45 nofrp:=(fun (X0:fofType)=> (realof (ndofrp X0))):(fofType->fofType)
% 4.86/5.45 nofrt:=(fun (X0:fofType)=> ((ind nat) (natprop X0))):(fofType->fofType)
% 4.86/5.45 non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))):(fofType->((fofType->Prop)->(fofType->Prop)))
% 4.86/5.45 nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))):(fofType->(fofType->Prop))
% 4.86/5.45 not:=(fun (P:Prop)=> (P->False)):(Prop->Prop)
% 4.86/5.45 nt_1t:=(ntofn n_1):fofType
% 4.86/5.45 nt_all:=(all natt):((fofType->Prop)->Prop)
% 4.86/5.45 nt_cond1:=(nt_in nt_1t):(fofType->Prop)
% 4.86/5.45 nt_cond2:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((imp ((nt_in X1) X0)) ((nt_in ((ap suct) X1)) X0))))):(fofType->Prop)
% 4.86/5.45 nt_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 nt_in:=(esti natt):(fofType->(fofType->Prop))
% 4.86/5.45 nt_is:=(e_is natt):(fofType->(fofType->Prop))
% 4.86/5.45 nt_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (nt_all (fun (X2:fofType)=> ((imp (X0 X2)) ((nt_lessis X1) X2))))):((fofType->Prop)->(fofType->Prop))
% 4.86/5.45 nt_less:=(fun (X0:fofType) (X1:fofType)=> ((rt_less (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.86/5.45 nt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((rt_lessis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.86/5.45 nt_min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((nt_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop))
% 4.86/5.45 nt_more:=(fun (X0:fofType) (X1:fofType)=> ((rt_more (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.86/5.45 nt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((rt_moreis (rtofnt X0)) (rtofnt X1))):(fofType->(fofType->Prop))
% 4.86/5.45 nt_natt:=((d_Sep cut) natrp):fofType
% 4.86/5.45 nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((nt_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 nt_one:=(one natt):((fofType->Prop)->Prop)
% 4.86/5.45 nt_pl:=(fun (X0:fofType) (X1:fofType)=> (ntofrt ((rt_pl (rtofnt X0)) (rtofnt X1)))):(fofType->(fofType->fofType))
% 4.86/5.45 nt_satz15:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> (((nt_less X0) X1)->(((nt_less X1) X2)->((nt_less X0) X2)))))))))
% 4.86/5.45 nt_satz1:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_nis X0) X1)->((nt_nis ((ap suct) X0)) ((ap suct) X1)))))))
% 4.86/5.45 nt_satz21:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) natt))) (fun (X3:fofType)=> (((nt_more X0) X1)->(((nt_more X2) X3)->((nt_more ((nt_pl X0) X2)) ((nt_pl X1) X3))))))))))))
% 4.86/5.45 nt_satz27:(forall (X0:(fofType->Prop)), ((nt_some X0)->(nt_some (nt_min X0))))
% 4.86/5.45 nt_satz4:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((one ((d_Pi natt) (fun (X1:fofType)=> natt))) (fun (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (nt_all (fun (X2:fofType)=> ((nt_is ((ap X1) ((ap suct) X2))) ((ap suct) ((ap X1) X2))))))))))
% 4.86/5.45 nt_satz5:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) natt))) (fun (X2:fofType)=> ((nt_is ((nt_pl ((nt_pl X0) X1)) X2)) ((nt_pl X0) ((nt_pl X1) X2)))))))))
% 4.86/5.45 nt_satz9:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((orec3 ((nt_is X0) X1)) (nt_some (fun (X2:fofType)=> ((nt_is X0) ((nt_pl X1) X2))))) (nt_some (fun (X2:fofType)=> ((nt_is X1) ((nt_pl X0) X2)))))))))
% 4.86/5.45 nt_some:=(l_some natt):((fofType->Prop)->Prop)
% 4.86/5.45 nt_suct:=((d_Sigma nt_natt) (fun (X0:fofType)=> (nttofnt (ordsucc (ntofntt X0))))):fofType
% 4.86/5.45 ntofn:=(fun (X0:fofType)=> (ntofrt (rtofn X0))):(fofType->fofType)
% 4.86/5.45 ntofntt:=(fun (X0:fofType)=> (ntofrp (rpofntt X0))):(fofType->fofType)
% 4.86/5.45 ntofrl:=(((soft nat) real) ((d_Sigma nat) rlofnt)):(fofType->fofType)
% 4.86/5.45 ntofrp:=(((soft nat) cut) ((d_Sigma nat) rpofnt)):(fofType->fofType)
% 4.86/5.45 ntofrt:=((out rat) natrt):(fofType->fofType)
% 4.86/5.45 nttofnt:=(fun (X0:fofType)=> (nttofrp (rpofnt X0))):(fofType->fofType)
% 4.86/5.45 nttofrp:=((out cut) natrp):(fofType->fofType)
% 4.86/5.45 num:=(first1 nat):(fofType->fofType)
% 4.86/5.45 obvious:=((imp False) False):Prop
% 4.86/5.45 omega:=((d_Sep (univof emptyset)) nat_p):fofType
% 4.86/5.45 omega_nat_p:(forall (X0:fofType), (((in X0) omega)->(nat_p X0)))
% 4.86/5.45 one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))):(fofType->((fofType->Prop)->Prop))
% 4.86/5.45 oneax:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1))))
% 4.86/5.45 or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.86/5.45 or:(Prop->(Prop->Prop))
% 4.86/5.45 or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% 4.86/5.45 or_first:=(fun (A:Prop) (B:Prop)=> (((((or_ind A) B) ((B->A)->A)) (fun (x:A) (x0:(B->A))=> x)) (fun (x:B) (x0:(B->A))=> (x0 x)))):(forall (A:Prop) (B:Prop), (((or A) B)->((B->A)->A)))
% 4.86/5.45 or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 4.86/5.45 or_introl:(forall (A:Prop) (B:Prop), (A->((or A) B)))
% 4.86/5.45 or_intror:(forall (A:Prop) (B:Prop), (B->((or A) B)))
% 4.86/5.45 or_second:=(fun (A:Prop) (B:Prop) (x:((or A) B))=> (((or_first B) A) (((or_comm_i A) B) x))):(forall (A:Prop) (B:Prop), (((or A) B)->((A->B)->B)))
% 4.86/5.45 ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0))):(fofType->fofType)
% 4.86/5.45 ordsucc_inj:(forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1)))
% 4.86/5.45 orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))):(Prop->(Prop->(Prop->Prop)))
% 4.86/5.45 orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))):(Prop->(Prop->Prop))
% 4.86/5.45 otax1:(forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 4.86/5.45 otax2:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2)))))
% 4.86/5.45 out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))):(fofType->((fofType->Prop)->(fofType->fofType)))
% 4.86/5.45 outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType))
% 4.86/5.45 p1n2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (negd X1))):(fofType->(fofType->Prop))
% 4.86/5.45 p1p2:=(fun (X0:fofType) (X1:fofType)=> ((d_and (posd X0)) (posd X1))):(fofType->(fofType->Prop))
% 4.86/5.45 pair1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2)))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))):(fofType->fofType)
% 4.86/5.45 pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))):(fofType->(fofType->fofType))
% 4.86/5.45 pair_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1))))))
% 4.86/5.45 pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)):(fofType->Prop)
% 4.86/5.45 pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 pair_u0:=(inn n_2):(fofType->fofType)
% 4.86/5.45 pairis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2))))
% 4.86/5.45 pdofnt:=(fun (X0:fofType)=> (pdofrp (rpofnt X0))):(fofType->fofType)
% 4.86/5.45 pdofrp:=(fun (X0:fofType)=> ((rp_df ((rp_pl X0) d_1rp)) d_1rp)):(fofType->fofType)
% 4.86/5.45 perm:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injseq X0) X1) X2)) (((surjseq X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->fofType)
% 4.86/5.45 plusdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_pd X0) X1)))))):fofType
% 4.86/5.45 plusfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_pf X0) X1)))))):fofType
% 4.86/5.45 pofrp:=(fun (X0:fofType)=> (realof (pdofrp X0))):(fofType->fofType)
% 4.86/5.45 pos:=(fun (X0:fofType)=> ((l_some dif) (propp X0))):(fofType->Prop)
% 4.86/5.45 posd:=(fun (X0:fofType)=> ((rp_more (stm X0)) (std X0))):(fofType->Prop)
% 4.86/5.45 power:(fofType->fofType)
% 4.86/5.45 pr1:=(fun (X0:fofType)=> rpofp):(fofType->(fofType->fofType))
% 4.86/5.45 prod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((prodprop X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 prodprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_ts X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.86/5.45 prodprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((prodprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj)):(fofType->fofType)
% 4.86/5.45 proj0_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0)))
% 4.86/5.45 proj0_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0))
% 4.86/5.45 proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 4.86/5.45 proj1_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))
% 4.86/5.45 proj1_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1))
% 4.86/5.45 proj2:(forall (A:Prop) (B:Prop), (((and A) B)->B))
% 4.86/5.45 proj_Sigma_eta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)))
% 4.86/5.45 proofsirrelevant:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) real))) (fun (X4:fofType)=> ((intrl X4)->(((r_lessis X1) X4)->(((r_lessis X4) X0)->((all_of (fun (X5:fofType)=> ((in X5) real))) (fun (X5:fofType)=> ((intrl X5)->(((r_lessis X1) X5)->(((r_lessis X5) X0)->(((r_is X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))))))))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.45 prop1:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3)))):(Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.86/5.45 prop1d:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((and3 (posd X1)) (posd X2)) ((rp_eq X0) ((rp_md X1) X2)))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 prop1t:=(fun (X0:fofType)=> (nt_all (fun (X1:fofType)=> ((nt_is ((ap X0) ((ap suct) X1))) ((ap suct) ((ap X0) X1)))))):(fofType->Prop)
% 4.86/5.45 prop2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))
% 4.86/5.45 prop2d:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) ((prop1d X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 prop2t:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((nt_is ((ap X1) nt_1t)) ((ap suct) X0))) (prop1t X1))):(fofType->(fofType->Prop))
% 4.86/5.45 prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->Prop)
% 4.86/5.45 propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.45 propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))):(fofType->(fofType->(fofType->(fofType->Prop))))
% 4.86/5.45 propn:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (negd X1))):(fofType->(fofType->Prop))
% 4.86/5.45 propp:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (posd X1))):(fofType->(fofType->Prop))
% 4.86/5.45 ps1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> rpofp):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 r_0:=(realof ((rp_df d_1rp) d_1rp)):fofType
% 4.86/5.45 r_all:=(all real):((fofType->Prop)->Prop)
% 4.86/5.45 r_class:=((ecect dif) rp_eq):(fofType->fofType)
% 4.86/5.45 r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))):(Prop->(Prop->Prop))
% 4.86/5.45 r_fixf:=((fixfu dif) rp_eq):(fofType->(fofType->Prop))
% 4.86/5.45 r_in:=(esti real):(fofType->(fofType->Prop))
% 4.86/5.45 r_inn:=(esti dif):(fofType->(fofType->Prop))
% 4.86/5.45 r_is:=(e_is real):(fofType->(fofType->Prop))
% 4.86/5.45 r_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((lessd X2) X3))))))):(fofType->(fofType->Prop))
% 4.86/5.45 r_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_less X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 r_m0:=((indreal real) m0dr):(fofType->fofType)
% 4.86/5.45 r_mn:=(fun (X0:fofType) (X1:fofType)=> ((r_pl X0) (r_m0 X1))):(fofType->(fofType->fofType))
% 4.86/5.45 r_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some dif) (fun (X2:fofType)=> ((l_some dif) (fun (X3:fofType)=> (((and3 ((r_inn X2) (r_class X0))) ((r_inn X3) (r_class X1))) ((mored X2) X3))))))):(fofType->(fofType->Prop))
% 4.86/5.45 r_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((r_more X0) X1)) ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 r_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((r_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 r_one:=(one real):((fofType->Prop)->Prop)
% 4.86/5.45 r_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind real) (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.86/5.45 r_pl:=((indreal2 real) plusdr):(fofType->(fofType->fofType))
% 4.86/5.45 r_schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind real) ((d_5r205_prop3 X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 r_some:=(l_some real):((fofType->Prop)->Prop)
% 4.86/5.45 r_sqrt:=(fun (X0:fofType)=> ((ind real) (fun (X1:fofType)=> ((d_and (d_not (neg X1))) ((r_is ((r_ts X1) X1)) X0))))):(fofType->fofType)
% 4.86/5.45 r_ts:=((indreal2 real) timesdr):(fofType->(fofType->fofType))
% 4.86/5.45 rat:=((ect frac) n_eq):fofType
% 4.86/5.45 ratd:=(fun (X0:fofType)=> ((d_not (zero X0))->(ratrp (rpofpd (absd X0))))):(fofType->Prop)
% 4.86/5.45 ratof:=((ectelt frac) n_eq):(fofType->fofType)
% 4.86/5.45 ratrl:=(fun (X0:fofType)=> ((l_some dif) (fun (X1:fofType)=> ((d_and ((r_inn X1) (r_class X0))) (ratd X1))))):(fofType->Prop)
% 4.86/5.45 ratrp:=(((image rat) cut) ((d_Sigma rat) rpofrt)):(fofType->Prop)
% 4.86/5.45 ratset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rt_less X1) X0)))):(fofType->fofType)
% 4.86/5.45 ratt:=((d_Sep cut) ratrp):fofType
% 4.86/5.45 real:=((ect dif) rp_eq):fofType
% 4.86/5.45 realof:=((ectelt dif) rp_eq):(fofType->fofType)
% 4.86/5.45 refis:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1))))
% 4.86/5.45 relational_choice:(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) (fun (y:B)=> ((R x) y))))->((ex (A->(B->Prop))) (fun (R':(A->(B->Prop)))=> ((and ((((subrelation A) B) R') R)) (forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R' x) y))))))))))
% 4.86/5.45 repl:(fofType->((fofType->fofType)->fofType))
% 4.86/5.45 right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 right:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 rlofnt:=(fun (X0:fofType)=> (realof (pdofnt X0))):(fofType->fofType)
% 4.86/5.45 rp1:=(fun (X0:fofType)=> ((rp_pl X0) d_1rp)):(fofType->fofType)
% 4.86/5.45 rp_all:=(all cut):((fofType->Prop)->Prop)
% 4.86/5.45 rp_df:=(pair1 cut):(fofType->(fofType->fofType))
% 4.86/5.45 rp_diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((diffprop2 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 rp_eq:=(fun (X0:fofType) (X1:fofType)=> ((rp_is ((rp_pl (stm X0)) (std X1))) ((rp_pl (stm X1)) (std X0)))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_in:=(esti cut):(fofType->(fofType->Prop))
% 4.86/5.45 rp_is:=(e_is cut):(fofType->(fofType->Prop))
% 4.86/5.45 rp_less:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((urt X0) X2)) ((lrt X1) X2))))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessd X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_less X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_md:=(fun (X0:fofType) (X1:fofType)=> ((rp_pd X0) (m0d X1))):(fofType->(fofType->fofType))
% 4.86/5.45 rp_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.86/5.45 rp_more:=(fun (X0:fofType) (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and ((lrt X0) X2)) ((urt X1) X2))))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rp_more X0) X1)) ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((mored X0) X1)) ((rp_eq X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_nt_1t:=(nttofnt n_1):fofType
% 4.86/5.45 rp_nt_all:=(all nt_natt):((fofType->Prop)->Prop)
% 4.86/5.45 rp_nt_cond1:=(rp_nt_in rp_nt_1t):(fofType->Prop)
% 4.86/5.45 rp_nt_cond2:=(fun (X0:fofType)=> (rp_nt_all (fun (X1:fofType)=> ((imp ((rp_nt_in X1) X0)) ((rp_nt_in ((ap nt_suct) X1)) X0))))):(fofType->Prop)
% 4.86/5.45 rp_nt_in:=(esti nt_natt):(fofType->(fofType->Prop))
% 4.86/5.45 rp_nt_is:=(e_is nt_natt):(fofType->(fofType->Prop))
% 4.86/5.45 rp_nt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rp_nt_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rp_nt_one:=(one nt_natt):((fofType->Prop)->Prop)
% 4.86/5.45 rp_nt_some:=(l_some nt_natt):((fofType->Prop)->Prop)
% 4.86/5.45 rp_one:=(one cut):((fofType->Prop)->Prop)
% 4.86/5.45 rp_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.86/5.45 rp_pd:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl (stm X0)) (stm X1))) ((rp_pl (std X0)) (std X1)))):(fofType->(fofType->fofType))
% 4.86/5.45 rp_pl:=(fun (X0:fofType) (X1:fofType)=> (cutof ((sum X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 rp_some:=(l_some cut):((fofType->Prop)->Prop)
% 4.86/5.45 rp_td:=(fun (X0:fofType) (X1:fofType)=> ((rp_df ((rp_pl ((rp_ts (stm X0)) (stm X1))) ((rp_ts (std X0)) (std X1)))) ((rp_pl ((rp_ts (stm X0)) (std X1))) ((rp_ts (std X0)) (stm X1))))):(fofType->(fofType->fofType))
% 4.86/5.45 rp_ts:=(fun (X0:fofType) (X1:fofType)=> (cutof ((prod X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 rpofn:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (nofrp X1))))):(fofType->fofType)
% 4.86/5.45 rpofnd:=(fun (X0:fofType)=> ((rp_mn (std X0)) (stm X0))):(fofType->fofType)
% 4.86/5.45 rpofnt:=(fun (X0:fofType)=> (rpofrt (rtofn X0))):(fofType->fofType)
% 4.86/5.45 rpofntt:=((e_in cut) natrp):(fofType->fofType)
% 4.86/5.45 rpofp:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((r_is X0) (pofrp X1))))):(fofType->fofType)
% 4.86/5.45 rpofpd:=(fun (X0:fofType)=> ((rp_mn (stm X0)) (std X0))):(fofType->fofType)
% 4.86/5.45 rpofrt:=(fun (X0:fofType)=> (cutof (ratset X0))):(fofType->fofType)
% 4.86/5.45 rpofrtt:=((e_in cut) ratrp):(fofType->fofType)
% 4.86/5.45 rt_all:=(all rat):((fofType->Prop)->Prop)
% 4.86/5.45 rt_in:=(esti rat):(fofType->(fofType->Prop))
% 4.86/5.45 rt_is:=(e_is rat):(fofType->(fofType->Prop))
% 4.86/5.45 rt_lb:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((iii1_lbprop X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rt_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))))):(fofType->(fofType->Prop))
% 4.86/5.45 rt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rt_min:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((rt_lb X0) X1)) ((rt_in X1) X0))):(fofType->(fofType->Prop))
% 4.86/5.45 rt_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.86/5.45 rt_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))))):(fofType->(fofType->Prop))
% 4.86/5.45 rt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rt_one:=(one rat):((fofType->Prop)->Prop)
% 4.86/5.45 rt_ov:=(fun (X0:fofType) (X1:fofType)=> ((ind rat) (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))):(fofType->(fofType->fofType))
% 4.86/5.45 rt_pl:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) plusfrt)):(fofType->(fofType->fofType))
% 4.86/5.45 rt_some:=(l_some rat):((fofType->Prop)->Prop)
% 4.86/5.45 rt_ts:=(fun (X0:fofType) (X1:fofType)=> ((((indrat X0) X1) rat) timesfrt)):(fofType->(fofType->fofType))
% 4.86/5.45 rt_ub:=(fun (X0:fofType) (X1:fofType)=> (rt_all ((ubprop X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rtc:=(fun (X0:fofType)=> (cutof (sqrtset X0))):(fofType->fofType)
% 4.86/5.45 rtofn:=(fun (X0:fofType)=> (ratof ((n_fr X0) n_1))):(fofType->fofType)
% 4.86/5.45 rtofnt:=((e_in rat) natrt):(fofType->fofType)
% 4.86/5.45 rtofrp:=(((soft rat) cut) ((d_Sigma rat) rpofrt)):(fofType->fofType)
% 4.86/5.45 rtofrtt:=(fun (X0:fofType)=> (rtofrp (rpofrtt X0))):(fofType->fofType)
% 4.86/5.45 rtt_all:=(all ratt):((fofType->Prop)->Prop)
% 4.86/5.45 rtt_is:=(e_is ratt):(fofType->(fofType->Prop))
% 4.86/5.45 rtt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rtt_is X0) X1))):(fofType->(fofType->Prop))
% 4.86/5.45 rtt_one:=(one ratt):((fofType->Prop)->Prop)
% 4.86/5.45 rtt_some:=(l_some ratt):((fofType->Prop)->Prop)
% 4.86/5.45 rttofrp:=((out cut) ratrp):(fofType->fofType)
% 4.86/5.45 rttofrt:=(fun (X0:fofType)=> (rttofrp (rpofrt X0))):(fofType->fofType)
% 4.86/5.45 s01:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_lessis X1) X0)))):(fofType->fofType)
% 4.86/5.45 s02:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_more X1) X0)))):(fofType->fofType)
% 4.86/5.45 s11:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_less X1) X0)))):(fofType->fofType)
% 4.86/5.45 s12:=(fun (X0:fofType)=> ((d_Sep real) (fun (X1:fofType)=> ((r_moreis X1) X0)))):(fofType->fofType)
% 4.86/5.45 satz100:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.86/5.45 satz100a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.86/5.45 satz101:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_one (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 4.86/5.45 satz101a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(rt_some (fun (X2:fofType)=> ((rt_is ((rt_pl X1) X2)) X0))))))))
% 4.86/5.45 satz101b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_pl X1) X2)) X0)->(((rt_is ((rt_pl X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 4.86/5.45 satz101c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl X1) ((rt_mn X0) X1))) X0))))))
% 4.86/5.45 satz101d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl X1) ((rt_mn X0) X1))))))))
% 4.86/5.45 satz101e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is ((rt_pl ((rt_mn X0) X1)) X1)) X0))))))
% 4.86/5.45 satz101f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_is X0) ((rt_pl ((rt_mn X0) X1)) X1)))))))
% 4.86/5.45 satz101g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_is ((rt_pl X1) X2)) X0)->((rt_is X2) ((rt_mn X0) X1))))))))))
% 4.86/5.45 satz102:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X0) X1)) ((rt_ts X1) X0))))))
% 4.86/5.45 satz103:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts ((rt_ts X0) X1)) X2)) ((rt_ts X0) ((rt_ts X1) X2)))))))))
% 4.86/5.45 satz104:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_ts X0) ((rt_pl X1) X2))) ((rt_pl ((rt_ts X0) X1)) ((rt_ts X0) X2)))))))))
% 4.86/5.45 satz105a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.86/5.45 satz105b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.86/5.45 satz105c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2)))))))))
% 4.86/5.45 satz105d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.86/5.45 satz105e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.86/5.45 satz105f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_ts X2) X0)) ((rt_ts X2) X1)))))))))
% 4.86/5.45 satz106a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_more X0) X1))))))))
% 4.86/5.45 satz106b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_is X0) X1))))))))
% 4.86/5.45 satz106c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X2))->((rt_less X0) X1))))))))
% 4.86/5.45 satz107:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.86/5.45 satz107a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.86/5.45 satz108a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.86/5.45 satz108b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.86/5.45 satz108c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.86/5.45 satz108d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.86/5.45 satz109:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_moreis X2) X3)->((rt_moreis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.86/5.45 satz109a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X2) X3)->((rt_lessis ((rt_ts X0) X2)) ((rt_ts X1) X3))))))))))))
% 4.86/5.45 satz10:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.86/5.45 satz10a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.86/5.45 satz10b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 4.86/5.45 satz10c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1)))))))
% 4.86/5.45 satz10d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1)))))))
% 4.86/5.45 satz10e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1))))))
% 4.86/5.45 satz10f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1))))))
% 4.86/5.45 satz10g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1)))))))
% 4.86/5.45 satz10h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1)))))))
% 4.86/5.45 satz10j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1))))))
% 4.86/5.45 satz10k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1))))))
% 4.86/5.45 satz110:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_one (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 4.86/5.45 satz110a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((rt_is ((rt_ts X1) X2)) X0)))))))
% 4.86/5.45 satz110b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->(((rt_is ((rt_ts X1) X3)) X0)->((rt_is X2) X3)))))))))))
% 4.86/5.45 satz110c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts X1) ((rt_ov X0) X1))) X0)))))
% 4.86/5.45 satz110d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts X1) ((rt_ov X0) X1)))))))
% 4.86/5.45 satz110e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov X0) X1)) X1)) X0)))))
% 4.86/5.45 satz110f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is X0) ((rt_ts ((rt_ov X0) X1)) X1))))))
% 4.86/5.45 satz110g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_ts X1) X2)) X0)->((rt_is X2) ((rt_ov X0) X1)))))))))
% 4.86/5.45 satz111a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moref ((n_fr X0) n_1)) ((n_fr X1) n_1))->((d_29_ii X0) X1))))))
% 4.86/5.45 satz111b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1))->((n_is X0) X1))))))
% 4.86/5.45 satz111c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1))->((iii X0) X1))))))
% 4.86/5.45 satz111d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((moref ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.86/5.45 satz111e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is X0) X1)->((n_eq ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.86/5.45 satz111f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((lessf ((n_fr X0) n_1)) ((n_fr X1) n_1)))))))
% 4.86/5.45 satz111g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->(n_one (natprop X0)))))
% 4.86/5.45 satz112a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_pf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_pl X0) X1)) n_1))))))
% 4.86/5.45 satz112b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_tf ((n_fr X0) n_1)) ((n_fr X1) n_1))) ((n_fr ((n_ts X0) X1)) n_1))))))
% 4.86/5.45 satz112c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_pl (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_pl X0) X1)))))))))
% 4.86/5.45 satz112d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_pl X0) X1))))))))
% 4.86/5.45 satz112e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->((inf ((n_fr ((n_ts (nofrt X0)) (nofrt X1))) n_1)) (class ((rt_ts X0) X1)))))))))
% 4.86/5.45 satz112f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(natrt ((rt_ts X0) X1))))))))
% 4.86/5.45 satz112g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((natrt X0)->((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((natrt X1)->(((rt_more X0) X1)->(natrt ((rt_mn X0) X1)))))))))
% 4.86/5.45 satz112h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_pl (rtofn X0)) (rtofn X1))) (rtofn ((n_pl X0) X1)))))))
% 4.86/5.45 satz112j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X0)) (rtofn X1))) (rtofn ((n_ts X0) X1)))))))
% 4.86/5.45 satz113a:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((nt_nis ((ap suct) X0)) nt_1t)))
% 4.86/5.45 satz113b:((all_of (fun (X0:fofType)=> ((in X0) natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> (((nt_is ((ap suct) X0)) ((ap suct) X1))->((nt_is X0) X1))))))
% 4.86/5.45 satz113c:((all_of (fun (X0:fofType)=> ((in X0) (power natt)))) (fun (X0:fofType)=> ((nt_cond1 X0)->((nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) natt))) (fun (X1:fofType)=> ((nt_in X1) X0)))))))
% 4.86/5.45 satz114:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((rt_is ((rt_ts (rtofn (den X0))) (ratof X0))) (rtofn (num X0)))))
% 4.86/5.45 satz114a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ts (rtofn X1)) (ratof ((n_fr X0) X1)))) (rtofn X0))))))
% 4.86/5.45 satz114b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is (ratof ((n_fr X0) X1))) ((rt_ov (rtofn X0)) (rtofn X1)))))))
% 4.86/5.45 satz114c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rt_is ((rt_ov (rtofn X0)) (rtofn X1))) (ratof ((n_fr X0) X1)))))))
% 4.86/5.45 satz115:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (n_some (fun (X2:fofType)=> ((rt_more ((rt_ts (rtofn X2)) X0)) X1)))))))
% 4.86/5.45 satz115a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> ((d_and (natrt X2)) ((rt_more ((rt_ts X2) X0)) X1))))))))
% 4.86/5.45 satz116:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) X0)))
% 4.86/5.45 satz117:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_is X0) X1)->((rp_is X1) X0))))))
% 4.86/5.45 satz118:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->(((rp_is X1) X2)->((rp_is X0) X2)))))))))
% 4.86/5.45 satz119:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X2) X1)->((urt X0) X2)))))))))
% 4.86/5.45 satz119a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X1) X2)->((urt X0) X2)))))))))
% 4.86/5.45 satz11:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0))))))
% 4.86/5.45 satz120:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X2) X1)->((lrt X0) X2)))))))))
% 4.86/5.45 satz120a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X1) X2)->((lrt X0) X2)))))))))
% 4.86/5.45 satz121:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_less X1) X0))))))
% 4.86/5.45 satz122:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->((rp_more X1) X0))))))
% 4.86/5.45 satz123:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((orec3 ((rp_is X0) X1)) ((rp_more X0) X1)) ((rp_less X0) X1))))))
% 4.86/5.45 satz123c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->(d_not ((rp_less X0) X1)))))))
% 4.86/5.45 satz123d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->(d_not ((rp_more X0) X1)))))))
% 4.86/5.45 satz123e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_more X0) X1))->((rp_lessis X0) X1))))))
% 4.86/5.45 satz123f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_less X0) X1))->((rp_moreis X0) X1))))))
% 4.86/5.45 satz123g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(d_not ((rp_lessis X0) X1)))))))
% 4.86/5.45 satz123h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(d_not ((rp_moreis X0) X1)))))))
% 4.86/5.45 satz123j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_moreis X0) X1))->((rp_less X0) X1))))))
% 4.86/5.45 satz123k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((d_not ((rp_lessis X0) X1))->((rp_more X0) X1))))))
% 4.86/5.45 satz124:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_moreis X0) X1)->((rp_lessis X1) X0))))))
% 4.86/5.45 satz125:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_lessis X0) X1)->((rp_moreis X1) X0))))))
% 4.86/5.45 satz126:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 4.86/5.45 satz127a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_less X1) X2)->((rp_less X0) X2)))))))))
% 4.86/5.45 satz127b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->(((rp_lessis X1) X2)->((rp_less X0) X2)))))))))
% 4.86/5.45 satz127c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_moreis X0) X1)->(((rp_more X1) X2)->((rp_more X0) X2)))))))))
% 4.86/5.45 satz127d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_moreis X1) X2)->((rp_more X0) X2)))))))))
% 4.86/5.45 satz128:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X1) X2)->((rp_lessis X0) X2)))))))))
% 4.86/5.45 satz129:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((sum X0) X1))))))
% 4.86/5.45 satz129a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_pl X2) X3)) ((sum X0) X1)))))))))))))
% 4.86/5.45 satz12:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0))))))
% 4.86/5.45 satz130:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_pl X0) X1)) ((rp_pl X1) X0))))))
% 4.86/5.45 satz131:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_pl ((rp_pl X0) X1)) X2)) ((rp_pl X0) ((rp_pl X1) X2)))))))))
% 4.86/5.45 satz132:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (rt_some (fun (X2:fofType)=> (rt_some (fun (X3:fofType)=> ((d_and ((d_and ((lrt X0) X2)) ((urt X0) X3))) (((d_and ((lrt X0) X2)) ((urt X0) X3))->((rt_is ((rt_mn X3) X2)) X1)))))))))))
% 4.86/5.45 satz132app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (forall (X1:Prop), ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((lrt X0) X3)->((all_of (fun (X4:fofType)=> ((in X4) rat))) (fun (X4:fofType)=> (((urt X0) X4)->(((rt_is ((rt_mn X4) X3)) X2)->X1)))))))->X1))))))
% 4.86/5.45 satz133:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_more ((rp_pl X0) X1)) X0)))))
% 4.86/5.45 satz133a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_less X0) ((rp_pl X0) X1))))))
% 4.86/5.45 satz134:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.86/5.45 satz135b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.86/5.45 satz135c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2)))))))))
% 4.86/5.45 satz135d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.86/5.45 satz135e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.86/5.45 satz135f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1)))))))))
% 4.86/5.45 satz135g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz135h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 4.86/5.45 satz135j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz135k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X2) X0)) ((rp_pl X3) X1))))))))))))
% 4.86/5.45 satz136a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_more X0) X1))))))))
% 4.86/5.45 satz136b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_is X0) X1))))))))
% 4.86/5.45 satz136c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X2))->((rp_less X0) X1))))))))
% 4.86/5.45 satz136d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_more X0) X1))))))))
% 4.86/5.45 satz136e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_is X0) X1))))))))
% 4.86/5.45 satz136f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_pl X2) X0)) ((rp_pl X2) X1))->((rp_less X0) X1))))))))
% 4.86/5.45 satz137:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz137a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz138a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz138b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz138c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz138d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz139:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz139a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_pl X0) X2)) ((rp_pl X1) X3))))))))))))
% 4.86/5.45 satz13:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0))))))
% 4.86/5.45 satz140:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_one (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 4.86/5.45 satz140a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(rp_some (fun (X2:fofType)=> ((rp_is ((rp_pl X1) X2)) X0))))))))
% 4.86/5.45 satz140b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_pl X1) X2)) X0)->(((rp_is ((rp_pl X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 4.86/5.45 satz140c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl X1) ((rp_mn X0) X1))) X0))))))
% 4.86/5.45 satz140d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl X1) ((rp_mn X0) X1))))))))
% 4.86/5.45 satz140e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is ((rp_pl ((rp_mn X0) X1)) X1)) X0))))))
% 4.86/5.45 satz140f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->((rp_is X0) ((rp_pl ((rp_mn X0) X1)) X1)))))))
% 4.86/5.45 satz140g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->(((rp_is ((rp_pl X1) X2)) X0)->((rp_is X2) ((rp_mn X0) X1))))))))))
% 4.86/5.45 satz140h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_more X0) X1)->(cutprop ((diff X0) X1)))))))
% 4.86/5.45 satz141:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (cutprop ((prod X0) X1))))))
% 4.86/5.45 satz141a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((urt X0) X2)->((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((urt X1) X3)->(d_not ((rt_in ((rt_ts X2) X3)) ((prod X0) X1)))))))))))))
% 4.86/5.45 satz141b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ts ((rt_ov d_1rt) X1)) X0)) ((rt_ov X0) X1))))))
% 4.86/5.45 satz141c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_ov X0) X1)) ((rt_ts ((rt_ov d_1rt) X1)) X0))))))
% 4.86/5.45 satz142:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) ((rp_ts X1) X0))))))
% 4.86/5.45 satz143:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts ((rp_ts X0) X1)) X2)) ((rp_ts X0) ((rp_ts X1) X2)))))))))
% 4.86/5.45 satz144:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((rp_is ((rp_ts X0) ((rp_pl X1) X2))) ((rp_pl ((rp_ts X0) X1)) ((rp_ts X0) X2)))))))))
% 4.86/5.45 satz145a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.86/5.45 satz145b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.86/5.45 satz145c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2)))))))))
% 4.86/5.45 satz145d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more X0) X1)->((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.86/5.45 satz145e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is X0) X1)->((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.86/5.45 satz145f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less X0) X1)->((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1)))))))))
% 4.86/5.45 satz145g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz145h:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 4.86/5.45 satz145j:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz145k:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X2) X0)) ((rp_ts X3) X1))))))))))))
% 4.86/5.45 satz146a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_more X0) X1))))))))
% 4.86/5.45 satz146b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_is X0) X1))))))))
% 4.86/5.45 satz146c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X2))->((rp_less X0) X1))))))))
% 4.86/5.45 satz146d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_more ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_more X0) X1))))))))
% 4.86/5.45 satz146e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_is X0) X1))))))))
% 4.86/5.45 satz146f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_less ((rp_ts X2) X0)) ((rp_ts X2) X1))->((rp_less X0) X1))))))))
% 4.86/5.45 satz147:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz147a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz148a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_more X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz148b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_more X0) X1)->(((rp_moreis X2) X3)->((rp_more ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz148c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_less X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz148d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_less X0) X1)->(((rp_lessis X2) X3)->((rp_less ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz149:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_moreis X0) X1)->(((rp_moreis X2) X3)->((rp_moreis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz149a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_lessis X0) X1)->(((rp_lessis X2) X3)->((rp_lessis ((rp_ts X0) X2)) ((rp_ts X1) X3))))))))))))
% 4.86/5.45 satz14:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0))))))
% 4.86/5.45 satz150:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (cutprop (ratset X0))))
% 4.86/5.45 satz151:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts X0) d_1rp)) X0)))
% 4.86/5.45 satz151a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts X0) d_1rp))))
% 4.86/5.45 satz151b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is ((rp_ts d_1rp) X0)) X0)))
% 4.86/5.45 satz151c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rp_is X0) ((rp_ts d_1rp) X0))))
% 4.86/5.45 satz152:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_some (fun (X1:fofType)=> ((rp_is ((rp_ts X0) X1)) d_1rp)))))
% 4.86/5.45 satz153:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_one (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 4.86/5.45 satz153a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((rp_is ((rp_ts X1) X2)) X0)))))))
% 4.86/5.45 satz153b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) cut))) (fun (X3:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->(((rp_is ((rp_ts X1) X3)) X0)->((rp_is X2) X3)))))))))))
% 4.86/5.45 satz153c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) ((rp_ov X0) X1))) X0)))))
% 4.86/5.45 satz153d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts X1) ((rp_ov X0) X1)))))))
% 4.86/5.45 satz153e:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is ((rp_ts ((rp_ov X0) X1)) X1)) X0)))))
% 4.86/5.45 satz153f:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((rp_is X0) ((rp_ts ((rp_ov X0) X1)) X1))))))
% 4.86/5.45 satz153g:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) cut))) (fun (X2:fofType)=> (((rp_is ((rp_ts X1) X2)) X0)->((rp_is X2) ((rp_ov X0) X1)))))))))
% 4.86/5.45 satz154a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_more (rpofrt X0)) (rpofrt X1)))))))
% 4.86/5.45 satz154b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rp_is (rpofrt X0)) (rpofrt X1)))))))
% 4.86/5.45 satz154c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rp_less (rpofrt X0)) (rpofrt X1)))))))
% 4.86/5.45 satz154d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_more (rpofrt X0)) (rpofrt X1))->((rt_more X0) X1))))))
% 4.86/5.45 satz154e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_is (rpofrt X0)) (rpofrt X1))->((rt_is X0) X1))))))
% 4.86/5.45 satz154f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X0)) (rpofrt X1))->((rt_less X0) X1))))))
% 4.86/5.45 satz155a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_pl X0) X1))) ((rp_pl (rpofrt X0)) (rpofrt X1)))))))
% 4.86/5.45 satz155b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rp_is (rpofrt ((rt_mn X0) X1))) ((rp_mn (rpofrt X0)) (rpofrt X1))))))))
% 4.86/5.45 satz155c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ts X0) X1))) ((rp_ts (rpofrt X0)) (rpofrt X1)))))))
% 4.86/5.45 satz155d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rp_is (rpofrt ((rt_ov X0) X1))) ((rp_ov (rpofrt X0)) (rpofrt X1)))))))
% 4.86/5.45 satz155e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_pl X0) X1))) ((rp_pl (rpofnt X0)) (rpofnt X1)))))))
% 4.86/5.45 satz155f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((rp_is (rpofnt ((n_ts X0) X1))) ((rp_ts (rpofnt X0)) (rpofnt X1)))))))
% 4.86/5.45 satz156a:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((rp_nt_nis ((ap nt_suct) X0)) rp_nt_1t)))
% 4.86/5.45 satz156b:((all_of (fun (X0:fofType)=> ((in X0) nt_natt))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> (((rp_nt_is ((ap nt_suct) X0)) ((ap nt_suct) X1))->((rp_nt_is X0) X1))))))
% 4.86/5.45 satz156c:((all_of (fun (X0:fofType)=> ((in X0) (power nt_natt)))) (fun (X0:fofType)=> ((rp_nt_cond1 X0)->((rp_nt_cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nt_natt))) (fun (X1:fofType)=> ((rp_nt_in X1) X0)))))))
% 4.86/5.45 satz157a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->((rt_min ((d_Sep rat) (urt X0))) (rtofrp X0)))))
% 4.86/5.45 satz157b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((ratrp X0)->(rt_some (rt_min ((d_Sep rat) (urt X0)))))))
% 4.86/5.45 satz157c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_min ((d_Sep rat) (urt X0))) X1)->((rp_is X0) (rpofrt X1)))))))
% 4.86/5.45 satz157d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((rt_some (rt_min ((d_Sep rat) (urt X0))))->(ratrp X0))))
% 4.86/5.45 satz158a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((lrt X0) X1)->((rp_less (rpofrt X1)) X0))))))
% 4.86/5.45 satz158b:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((urt X0) X1)->((rp_moreis (rpofrt X1)) X0))))))
% 4.86/5.45 satz158c:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_less (rpofrt X1)) X0)->((lrt X0) X1))))))
% 4.86/5.45 satz158d:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rp_moreis (rpofrt X1)) X0)->((urt X0) X1))))))
% 4.86/5.45 satz159:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rp_less X0) (rpofrt X2))) ((rp_less (rpofrt X2)) X1)))))))))
% 4.86/5.45 satz159a:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(rp_some (fun (X2:fofType)=> (((and3 (ratrp X2)) ((rp_less X0) X2)) ((rp_less X2) X1)))))))))
% 4.86/5.45 satz159app:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> (((rp_less X0) X1)->(forall (X2:Prop), (((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rp_less X0) (rpofrt X3))->(((rp_less (rpofrt X3)) X1)->X2))))->X2)))))))
% 4.86/5.45 satz15:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 4.86/5.45 satz160:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) cut))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rp_more (rpofrt X2)) ((rp_ts X0) X1))->(rt_some (fun (X3:fofType)=> (rt_some (fun (X4:fofType)=> (((and3 ((rp_more (rpofrt X3)) X0)) ((rp_more (rpofrt X4)) X1)) ((rt_is ((rt_ts X3) X4)) X2)))))))))))))
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% 4.86/5.45 satz161:((all_of (fun (X0:fofType)=> ((in X0) cut))) (fun (X0:fofType)=> (rp_one (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))))
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% 4.86/5.45 satz164:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) X1)->((r_is X1) X0))))))
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% 4.86/5.45 satz166a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(pos (abs X0)))))
% 4.86/5.45 satz166b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->(pos (abs X0)))))
% 4.86/5.45 satz166c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((pos X0)->((pos X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 4.86/5.45 satz166d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg X0)->((neg X1)->(((r_is (abs X0)) (abs X1))->((r_is X0) X1))))))))
% 4.86/5.45 satz166e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_nis X0) r_0)->(pos (abs X0)))))
% 4.86/5.45 satz166f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (abs X0)) r_0))))
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% 4.86/5.45 satz167a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((or3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.86/5.45 satz167b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((ec3 ((r_is X0) X1)) ((r_more X0) X1)) ((r_less X0) X1))))))
% 4.86/5.45 satz167c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->(d_not ((r_less X0) X1)))))))
% 4.86/5.45 satz167d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_lessis X0) X1)->(d_not ((r_more X0) X1)))))))
% 4.86/5.45 satz167e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_more X0) X1))->((r_lessis X0) X1))))))
% 4.86/5.45 satz167f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_less X0) X1))->((r_moreis X0) X1))))))
% 4.86/5.45 satz167g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_more X0) X1)->(d_not ((r_lessis X0) X1)))))))
% 4.86/5.45 satz167h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_less X0) X1)->(d_not ((r_moreis X0) X1)))))))
% 4.86/5.45 satz167j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_moreis X0) X1))->((r_less X0) X1))))))
% 4.86/5.45 satz167k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((d_not ((r_lessis X0) X1))->((r_more X0) X1))))))
% 4.86/5.45 satz168a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_moreis X0) X1)->((r_lessis X1) X0))))))
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% 4.86/5.45 satz169a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->((r_more X0) r_0))))
% 4.86/5.45 satz169b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_more X0) r_0)->(pos X0))))
% 4.86/5.45 satz169c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((neg X0)->((r_less X0) r_0))))
% 4.86/5.45 satz169d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_less X0) r_0)->(neg X0))))
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% 4.86/5.45 satz16b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2)))))))))
% 4.86/5.45 satz16c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2)))))))))
% 4.86/5.45 satz16d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2)))))))))
% 4.86/5.45 satz170:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_moreis (abs X0)) r_0)))
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% 4.86/5.45 satz172b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->(((r_lessis X1) X2)->((r_less X0) X2)))))))))
% 4.86/5.45 satz172c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_moreis X0) X1)->(((r_more X1) X2)->((r_more X0) X2)))))))))
% 4.86/5.45 satz172d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->(((r_moreis X1) X2)->((r_more X0) X2)))))))))
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% 4.86/5.45 satz174:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((intrl X0)->(ratrl X0))))
% 4.86/5.45 satz175:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_pl X0) X1)) ((r_pl X1) X0))))))
% 4.86/5.45 satz176a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((pos X0)->(neg (r_m0 X0)))))
% 4.86/5.45 satz176b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is X0) r_0)->((r_is (r_m0 X0)) r_0))))
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% 4.86/5.45 satz176e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> (((r_is (r_m0 X0)) r_0)->((r_is X0) r_0))))
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% 4.86/5.45 satz177a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is X0) (r_m0 (r_m0 X0)))))
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% 4.86/5.45 satz177c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_is X0) (r_m0 X1))->((r_is X1) (r_m0 X0)))))))
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% 4.86/5.45 satz178a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is (abs X0)) (abs (r_m0 X0)))))
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% 4.86/5.45 satz179a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((r_is ((r_pl (r_m0 X0)) X0)) r_0)))
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% 4.86/5.45 satz196h:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((neg ((r_ts X0) X1))->((l_or ((d_and (pos X0)) (neg X1))) ((d_and (neg X0)) (pos X1))))))))
% 4.86/5.45 satz197a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) (r_m0 ((r_ts X0) X1)))))))
% 4.86/5.45 satz197b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) (r_m0 ((r_ts X0) X1)))))))
% 4.86/5.45 satz197c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) X1)) ((r_ts X0) (r_m0 X1)))))))
% 4.86/5.45 satz197d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) (r_m0 X1))) ((r_ts (r_m0 X0)) X1))))))
% 4.86/5.45 satz197e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts (r_m0 X0)) X1))))))
% 4.86/5.45 satz197f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is (r_m0 ((r_ts X0) X1))) ((r_ts X0) (r_m0 X1)))))))
% 4.86/5.45 satz198:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts (r_m0 X0)) (r_m0 X1))) ((r_ts X0) X1))))))
% 4.86/5.45 satz198a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((r_is ((r_ts X0) X1)) ((r_ts (r_m0 X0)) (r_m0 X1)))))))
% 4.86/5.45 satz199:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts ((r_ts X0) X1)) X2)) ((r_ts X0) ((r_ts X1) X2)))))))))
% 4.86/5.45 satz19a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
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% 4.86/5.45 satz19c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.86/5.45 satz19d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
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% 4.86/5.45 satz19h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 4.86/5.45 satz19j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz19k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 4.86/5.45 satz19l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.86/5.45 satz19m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.86/5.45 satz19n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 4.86/5.45 satz19o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 4.86/5.45 satz1:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1)))))))
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% 4.86/5.45 satz202:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((r_is ((r_ts X0) ((r_mn X1) X2))) ((r_mn ((r_ts X0) X1)) ((r_ts X0) X2)))))))))
% 4.86/5.45 satz203a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.86/5.45 satz203b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_is X2) r_0)->((r_is ((r_ts X0) X2)) ((r_ts X1) X2)))))))))
% 4.86/5.45 satz203c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.86/5.45 satz203d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((pos X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
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% 4.86/5.45 satz203f:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_more X0) X1)->((neg X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.86/5.45 satz203g:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.86/5.45 satz203j:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X0) X2)) ((r_ts X1) X2))))))))))
% 4.86/5.45 satz203k:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((pos X2)->((r_less ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.86/5.45 satz203m:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> (((r_less X0) X1)->((neg X2)->((r_more ((r_ts X2) X0)) ((r_ts X2) X1))))))))))
% 4.86/5.45 satz204:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_one (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 4.86/5.45 satz204a:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->(r_some (fun (X2:fofType)=> ((r_is ((r_ts X1) X2)) X0))))))))
% 4.86/5.45 satz204b:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((all_of (fun (X2:fofType)=> ((in X2) real))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> (((r_is ((r_ts X1) X2)) X0)->(((r_is ((r_ts X1) X3)) X0)->((r_is X2) X3))))))))))))
% 4.86/5.45 satz204c:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts X1) ((r_ov X0) X1))) X0))))))
% 4.86/5.45 satz204d:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is X0) ((r_ts X1) ((r_ov X0) X1))))))))
% 4.86/5.45 satz204e:((all_of (fun (X0:fofType)=> ((in X0) real))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) real))) (fun (X1:fofType)=> (((r_nis X1) r_0)->((r_is ((r_ts ((r_ov X0) X1)) X1)) X0))))))
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% 4.86/5.45 satz20c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1))))))))
% 4.86/5.45 satz20d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1))))))))
% 4.86/5.45 satz20e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1))))))))
% 4.86/5.45 satz20f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1))))))))
% 4.86/5.45 satz21:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz21a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz22a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz22b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz22c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz22d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz23:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz23a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 4.86/5.45 satz24:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1)))
% 4.86/5.45 satz24a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1))
% 4.86/5.45 satz24b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1)))
% 4.86/5.45 satz24c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0))))
% 4.86/5.45 satz25:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1)))))))
% 4.86/5.45 satz25a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0)))))))
% 4.86/5.45 satz25b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0))))))
% 4.86/5.45 satz25c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0))))))
% 4.86/5.45 satz26:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0))))))
% 4.86/5.45 satz26a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0))))))
% 4.86/5.45 satz26b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0))))))
% 4.86/5.45 satz26c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0))))))
% 4.86/5.45 satz27:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0))))
% 4.86/5.45 satz27a:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0))))
% 4.86/5.45 satz28:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))))))
% 4.86/5.45 satz28a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0)))
% 4.86/5.45 satz28b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0))))))
% 4.86/5.45 satz28c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0)))
% 4.86/5.45 satz28d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1))))))
% 4.86/5.45 satz28e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1))))
% 4.86/5.45 satz28f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1)))))))
% 4.86/5.45 satz28g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0))))
% 4.86/5.45 satz28h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1))))))
% 4.86/5.45 satz29:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))))))
% 4.86/5.45 satz2:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 4.86/5.45 satz30:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))))))))
% 4.86/5.45 satz31:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))))))))
% 4.86/5.45 satz32a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.86/5.45 satz32b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.86/5.45 satz32c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.86/5.45 satz32d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.86/5.45 satz32e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.86/5.45 satz32f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.86/5.45 satz32g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz32h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 4.86/5.45 satz32j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz32k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 4.86/5.45 satz32l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.86/5.45 satz32m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.86/5.45 satz32n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.86/5.45 satz32o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 4.86/5.45 satz33a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1))))))))
% 4.86/5.45 satz33b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1))))))))
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% 4.86/5.45 satz34:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz34a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz35a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz35b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz35c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz35d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz36:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz36a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 4.86/5.45 satz37:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0)))
% 4.86/5.45 satz38:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0))))))
% 4.86/5.45 satz39:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2)))))))))
% 4.86/5.45 satz3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 4.86/5.45 satz3a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 4.86/5.45 satz40:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1)))))))
% 4.86/5.45 satz40a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0)))))
% 4.86/5.45 satz40b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 4.86/5.45 satz40c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1))))))))
% 4.86/5.45 satz41:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.86/5.45 satz41a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.86/5.45 satz41b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 4.86/5.45 satz41c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1)))))))
% 4.86/5.45 satz41d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1)))))))
% 4.86/5.45 satz41e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1))))))
% 4.86/5.45 satz41f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1))))))
% 4.86/5.45 satz41g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1)))))))
% 4.86/5.45 satz41h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1)))))))
% 4.86/5.45 satz41j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1))))))
% 4.86/5.45 satz41k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1))))))
% 4.86/5.45 satz42:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0))))))
% 4.86/5.45 satz43:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0))))))
% 4.86/5.45 satz44:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3))))))))))))
% 4.86/5.45 satz45:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3))))))))))))
% 4.86/5.45 satz46:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3))))))))))))
% 4.86/5.45 satz47:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3))))))))))))
% 4.86/5.45 satz48:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0))))))
% 4.86/5.45 satz49:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0))))))
% 4.86/5.45 satz4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2))))))))))
% 4.86/5.45 satz4a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0))))
% 4.86/5.45 satz4b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1)))))))
% 4.86/5.45 satz4c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0))))
% 4.86/5.45 satz4d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1)))))))
% 4.86/5.45 satz4e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1))))
% 4.86/5.45 satz4f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1)))))))
% 4.86/5.45 satz4g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0))))
% 4.86/5.45 satz4h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1))))))
% 4.86/5.45 satz50:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 4.86/5.45 satz51a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 4.86/5.45 satz51b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2)))))))))
% 4.86/5.45 satz51c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2)))))))))
% 4.86/5.45 satz51d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2)))))))))
% 4.86/5.45 satz52:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lesseq X1) X2)->((lesseq X0) X2)))))))))
% 4.86/5.45 satz53:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0)))))
% 4.86/5.45 satz54:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0)))))
% 4.86/5.45 satz55:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1)))))))))
% 4.86/5.45 satz56:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz57:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2))))))))
% 4.86/5.45 satz57a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2)))))))))
% 4.86/5.45 satz58:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_pf X0) X1)) ((n_pf X1) X0))))))
% 4.86/5.45 satz59:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2)))))))))
% 4.86/5.45 satz5:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))))))))
% 4.86/5.45 satz60:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((moref ((n_pf X0) X1)) X0)))))
% 4.86/5.45 satz60a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((lessf X0) ((n_pf X0) X1))))))
% 4.86/5.45 satz61:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.86/5.45 satz62b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.86/5.45 satz62c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 4.86/5.45 satz62d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.86/5.45 satz62e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.86/5.45 satz62f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 4.86/5.45 satz62g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz62h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 4.86/5.45 satz62j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz62k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 4.86/5.45 satz63a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1))))))))
% 4.86/5.45 satz63b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1))))))))
% 4.86/5.45 satz63c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1))))))))
% 4.86/5.45 satz63d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1))))))))
% 4.86/5.45 satz63e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1))))))))
% 4.86/5.45 satz63f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1))))))))
% 4.86/5.45 satz64:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz64a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz65a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz65b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz65c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz65d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz66:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz66a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 4.86/5.45 satz67a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0))))))))
% 4.86/5.45 satz67b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 4.86/5.45 satz67d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1))))))))
% 4.86/5.45 satz67e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1))))))))))
% 4.86/5.45 satz68:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz69:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_tf X0) X1)) ((n_tf X1) X0))))))
% 4.86/5.45 satz6:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))))))
% 4.86/5.45 satz70:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2)))))))))
% 4.86/5.45 satz71:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((n_eq ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2)))))))))
% 4.86/5.45 satz72a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.86/5.45 satz72b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.86/5.45 satz72c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 4.86/5.45 satz72d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.86/5.45 satz72e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->((n_eq ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.86/5.45 satz72f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->((lessf ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 4.86/5.45 satz72g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz72h:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 4.86/5.45 satz72j:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz72k:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 4.86/5.45 satz73a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1))))))))
% 4.86/5.45 satz73b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1))))))))
% 4.86/5.45 satz73c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1))))))))
% 4.86/5.45 satz73d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1))))))))
% 4.86/5.45 satz73e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1))))))))
% 4.86/5.45 satz73f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1))))))))
% 4.86/5.45 satz74:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz74a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz75a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz75b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz75c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz75d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz76:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz76a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 4.86/5.45 satz77a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0)))))))
% 4.86/5.45 satz77b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 4.86/5.45 satz78:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0)))
% 4.86/5.45 satz79:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0))))))
% 4.86/5.45 satz7:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))))
% 4.86/5.45 satz80:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2)))))))))
% 4.86/5.45 satz81:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.86/5.45 satz81a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.86/5.45 satz81b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 4.86/5.45 satz81c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1)))))))
% 4.86/5.45 satz81d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1)))))))
% 4.86/5.45 satz81e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1))))))
% 4.86/5.45 satz81f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1))))))
% 4.86/5.45 satz81g:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1)))))))
% 4.86/5.45 satz81h:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(d_not ((rt_moreis X0) X1)))))))
% 4.86/5.45 satz81j:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_moreis X0) X1))->((rt_less X0) X1))))))
% 4.86/5.45 satz81k:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_lessis X0) X1))->((rt_more X0) X1))))))
% 4.86/5.45 satz82:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0))))))
% 4.86/5.45 satz83:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0))))))
% 4.86/5.45 satz84:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->((rt_lessis X1) X0))))))
% 4.86/5.45 satz85:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->((rt_moreis X1) X0))))))
% 4.86/5.45 satz86:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 4.86/5.45 satz87a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_less X1) X2)->((rt_less X0) X2)))))))))
% 4.86/5.45 satz87b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->(((rt_lessis X1) X2)->((rt_less X0) X2)))))))))
% 4.86/5.45 satz87c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_moreis X0) X1)->(((rt_more X1) X2)->((rt_more X0) X2)))))))))
% 4.86/5.45 satz87d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->(((rt_moreis X1) X2)->((rt_more X0) X2)))))))))
% 4.86/5.45 satz88:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_lessis X0) X1)->(((rt_lessis X1) X2)->((rt_lessis X0) X2)))))))))
% 4.86/5.45 satz89:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_more X1) X0)))))
% 4.86/5.45 satz8:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2)))))))))
% 4.86/5.45 satz8a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2))))))))
% 4.86/5.45 satz8b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))))))
% 4.86/5.45 satz90:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> (rt_some (fun (X1:fofType)=> ((rt_less X1) X0)))))
% 4.86/5.45 satz91:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->(rt_some (fun (X2:fofType)=> ((d_and ((rt_less X0) X2)) ((rt_less X2) X1)))))))))
% 4.86/5.45 satz92:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_is ((rt_pl X0) X1)) ((rt_pl X1) X0))))))
% 4.86/5.45 satz93:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((rt_is ((rt_pl ((rt_pl X0) X1)) X2)) ((rt_pl X0) ((rt_pl X1) X2)))))))))
% 4.86/5.45 satz94:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_more ((rt_pl X0) X1)) X0)))))
% 4.86/5.45 satz94a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((rt_less X0) ((rt_pl X0) X1))))))
% 4.86/5.45 satz95:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.86/5.45 satz96b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.86/5.45 satz96c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2)))))))))
% 4.86/5.45 satz96d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more X0) X1)->((rt_more ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.86/5.45 satz96e:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->((rt_is ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.86/5.45 satz96f:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less X0) X1)->((rt_less ((rt_pl X2) X0)) ((rt_pl X2) X1)))))))))
% 4.86/5.45 satz97a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_more X0) X1))))))))
% 4.86/5.45 satz97b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_is X0) X1))))))))
% 4.86/5.45 satz97c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X2))->((rt_less X0) X1))))))))
% 4.86/5.45 satz98:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.86/5.45 satz98a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.86/5.45 satz99a:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_moreis X0) X1)->(((rt_more X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.86/5.45 satz99b:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_more X0) X1)->(((rt_moreis X2) X3)->((rt_more ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.86/5.45 satz99c:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_lessis X0) X1)->(((rt_less X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.86/5.45 satz99d:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) rat))) (fun (X3:fofType)=> (((rt_less X0) X1)->(((rt_lessis X2) X3)->((rt_less ((rt_pl X0) X2)) ((rt_pl X1) X3))))))))))))
% 4.86/5.45 satz9:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2)))))))))
% 4.86/5.45 satz9a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 4.86/5.45 satz9b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 4.86/5.45 sc1:=(fun (X0:fofType)=> ((d_Sep cut) (fun (X1:fofType)=> ((r_in (pofrp X1)) X0)))):(fofType->fofType)
% 4.86/5.45 schnitt:=(fun (X0:fofType) (X1:fofType)=> ((ind cut) ((d_5p205_prop3 X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 schnittprop:=(fun (X0:fofType) (X1:fofType)=> (rp_some (fun (X2:fofType)=> ((d_and ((rp_in X2) X0)) ((lrt X2) X1))))):(fofType->(fofType->Prop))
% 4.86/5.45 schnittset:=(fun (X0:fofType)=> ((d_Sep rat) (schnittprop X0))):(fofType->fofType)
% 4.86/5.45 second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)):(fofType->(fofType->fofType))
% 4.86/5.45 second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 second_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1))))))
% 4.86/5.45 secondis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3))))))
% 4.86/5.45 seq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Pi real) (fun (X3:fofType)=> (((if (intrl X3)) (((if ((r_lessis X1) X3)) (((if ((r_lessis X3) X0)) X2) (ordsucc emptyset))) (ordsucc emptyset))) (ordsucc emptyset))))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 set_ext:(forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1))))
% 4.86/5.45 setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))):(fofType->(fofType->fofType))
% 4.86/5.45 setof_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0)))))
% 4.86/5.45 setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))):(fofType->(fofType->fofType))
% 4.86/5.45 shift_n1:=(fun (X0:fofType) (X1:fofType)=> (inn ((shiftl X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 shift_n2:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rlofnt (((shift_n1 X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 shift_ns:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ap X2) (((shiftr X0) X1) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 shift_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((r_is X3) ((ap X2) X4))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.86/5.45 shift_ul:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((shiftl X2) X1)):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 shiftf:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X4:fofType)=> ((ap X3) (((shiftr X0) X1) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 shiftl1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((shiftl X0) X1)) (((shift_ul X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 shiftl:=(fun (X0:fofType) (X1:fofType)=> (ntofrl ((r_mn ((r_pl X0) d_1rl)) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 shiftr:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((r_mn ((r_pl (((shift_n2 X0) X1) X2)) X1)) d_1rl)):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 shiftseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to ((shiftl X0) X1))) (fun (X3:fofType)=> (((shiftl1 X0) X1) ((((shift_ns X0) X1) X2) X3))))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 singlet_u0:=(inn n_1):(fofType->fofType)
% 4.86/5.45 snt:=(fun (X0:fofType) (X1:fofType)=> (cutof (schnittset X0))):(fofType->(fofType->fofType))
% 4.86/5.45 soft:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.45 sq1:=(fun (X0:fofType)=> ((rp_ts X0) X0)):(fofType->fofType)
% 4.86/5.45 sqrt:=(fun (X0:fofType)=> ((ind cut) (fun (X1:fofType)=> ((rp_is ((rp_ts X1) X1)) X0)))):(fofType->fofType)
% 4.86/5.45 sqrtset:=(fun (X0:fofType)=> ((d_Sep rat) (fun (X1:fofType)=> ((rp_less ((rp_ts (rpofrt X1)) (rpofrt X1))) X0)))):(fofType->fofType)
% 4.86/5.45 srp:=(fun (X0:fofType)=> (sqrt (rpofpd X0))):(fofType->fofType)
% 4.86/5.45 st_disj:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 stc:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((schnitt (sc1 X0)) (sc1 X1))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 std:=(second1 cut):(fofType->fofType)
% 4.86/5.45 stm:=(first1 cut):(fofType->fofType)
% 4.86/5.45 stp:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (pofrp (((stc X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.45 subrelation:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (R':(A->(B->Prop)))=> (forall (x:A) (y:B), (((R x) y)->((R' x) y)))):(forall (A:Type) (B:Type), ((A->(B->Prop))->((A->(B->Prop))->Prop)))
% 4.86/5.45 suc_p:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat)))))
% 4.86/5.45 suct:=((d_Sigma natt) (fun (X0:fofType)=> (ntofn (ordsucc (nofnt X0))))):fofType
% 4.86/5.45 sum:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep rat) ((sumprop X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.45 sumprop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> (((and3 ((lrt X0) X3)) ((lrt X1) X4)) ((rt_is X2) ((rt_pl X3) X4)))):(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 4.86/5.45 sumprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (rt_some (fun (X3:fofType)=> (rt_some ((((sumprop1 X0) X1) X2) X3))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.45 surjseq:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) real))) (fun (X3:fofType)=> ((intrl X3)->(((r_lessis X1) X3)->(((r_lessis X3) X0)->((((imseq X0) X1) X2) X3))))))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.47 times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->fofType)
% 4.86/5.47 timesdr:=((d_Sigma dif) (fun (X0:fofType)=> ((d_Sigma dif) (fun (X1:fofType)=> (realof ((rp_td X0) X1)))))):fofType
% 4.86/5.47 timesfrt:=((d_Sigma frac) (fun (X0:fofType)=> ((d_Sigma frac) (fun (X1:fofType)=> (ratof ((n_tf X0) X1)))))):fofType
% 4.86/5.47 tofs:=(fun (X0:fofType) (X1:fofType)=> ap):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.47 u01:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((rt_ov X2) ((rt_pl X0) X1))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.47 ubprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((imp ((rt_in X2) X0)) ((rt_moreis X1) X2))):(fofType->(fofType->(fofType->Prop)))
% 4.86/5.47 ul1:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((shiftl1 X0) X1)):(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 4.86/5.47 um10:=(fun (X0:fofType)=> ((rt_mn (rtofn X0)) d_1rt)):(fofType->fofType)
% 4.86/5.47 um1:=(fun (X0:fofType)=> (nofrt (um10 X0))):(fofType->fofType)
% 4.86/5.47 union:(fofType->fofType)
% 4.86/5.47 unique:=(fun (A:Type) (P:(A->Prop)) (x:A)=> ((and (P x)) (forall (x':A), ((P x')->(((eq A) x) x'))))):(forall (A:Type), ((A->Prop)->(A->Prop)))
% 4.86/5.47 unique_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (x:(forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R x) y))))))=> ((((dependent_unique_choice A) (fun (x2:A)=> B)) R) x)):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), ((forall (x:A), ((ex B) ((unique B) (fun (y:B)=> ((R x) y)))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), ((R x) (f x)))))))
% 4.86/5.47 univof:(fofType->fofType)
% 4.86/5.47 unmore:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4))))))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.47 urt:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_in X1) (lcl X0)))):(fofType->(fofType->Prop))
% 4.86/5.47 wel:=(fun (X0:Prop)=> (d_not (d_not X0))):(Prop->Prop)
% 4.86/5.47 wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))):(fofType->(fofType->(fofType->fofType)))
% 4.86/5.47 wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3)):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.47 wissel_wb:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType))))
% 4.86/5.47 xi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2))))
% 4.86/5.47 xmy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_mn (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.86/5.47 xout:=(fun (X0:fofType)=> ((outn X0) X0)):(fofType->fofType)
% 4.86/5.47 xpy:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_pl (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.86/5.47 xrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_xm X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.47 xty:=(fun (X0:fofType) (X1:fofType)=> (nofrt ((rt_ts (iiia_x0 X0)) (iiia_x0 X1)))):(fofType->(fofType->fofType))
% 4.86/5.47 yrm:=(fun (X0:fofType) (X1:fofType)=> (rpofrt ((d_5161_ym X0) X1))):(fofType->(fofType->fofType))
% 4.86/5.47 zero:=(fun (X0:fofType)=> ((rp_is (stm X0)) (std X0))):(fofType->Prop)
% 4.86/5.47 zeta:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((((ite ((rp_less (((d_5160_fr X0) X1) X2)) d_1rp)) cut) (((d_5160_fr X0) X1) X2)) d_1rp)):(fofType->(fofType->(fofType->fofType)))]X0:fofType
% 4.86/5.47 X1:(fofType->Prop)
% 4.86/5.47 X2:fofType]x:((is_of X2) (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1))))]x0:fofType] (rdef{??}) X2:=((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset))):Prop
% 4.86/5.47 ---
% 4.86/5.47 self=((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset))):Prop
% 4.86/5.47 term=(((e_in X0) X1) X2):fofType
% 4.86/5.47 --- does not match type in application fofType vs Prop in (((e_in X0) X1) ((ex fofType) (fun X0:fofType=> ((in X0) emptyset))))
% 4.86/5.47 Unexpected exception Does not match type in application fofType vs Prop in (((e_in X0) X1) ((ex fofType) (fun X0:fofType=> ((in X0) emptyset))))
% 4.86/5.47
% 4.86/5.47 Traceback (most recent call last):
% 4.86/5.47 File "CASC.py", line 80, in <module>
% 4.86/5.47 proof=problem.solve()
% 4.86/5.47 File "/export/starexec/sandbox/solver/bin/TPTP.py", line 95, in solve
% 4.86/5.47 for x in self.solveyielding():
% 4.86/5.47 File "/export/starexec/sandbox/solver/bin/TPTP.py", line 83, in solveyielding
% 4.86/5.47 for proof in proofgen: yield proof
% 4.86/5.47 File "/export/starexec/sandbox/solver/bin/prover.py", line 422, in proveyielding
% 4.86/5.47 results=node.look() #Can add nodes
% 4.86/5.47 File "/export/starexec/sandbox/solver/bin/prover.py", line 1221, in look
% 4.86/5.47 matching=target.match(term.body,self.context,termbodycontext,instantiate=True)
% 4.86/5.47 File "/export/starexec/sandbox/solver/bin/kernel.py", line 576, in match
% 4.86/5.47 atermmatch=s.abstracttermmatch(params,context,termcontext,instantiate=instantiate)
% 4.86/5.47 File "/export/starexec/sandbox/solver/bin/kernel.py", line 1192, in abstracttermmatch
% 4.86/5.47 print "t=%s:%s" % (t,t.gettype(termsubcontext))
% 4.86/5.47 kernel.TypecheckError: Does not match type in application fofType vs Prop in (((e_in X0) X1) ((ex fofType) (fun X0:fofType=> ((in X0) emptyset))))
% 4.86/5.47
%------------------------------------------------------------------------------