TSTP Solution File: SEU639^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU639^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n096.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:32:41 EDT 2014
% Result : Timeout 300.01s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU639^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n096.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:59:31 CDT 2014
% % CPUTime : 300.01
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x805b90>, <kernel.DependentProduct object at 0x8058c0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xbfd3b0>, <kernel.Single object at 0x805638>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x8058c0>, <kernel.DependentProduct object at 0x805fc8>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x805ea8>, <kernel.DependentProduct object at 0x8056c8>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x805bd8>, <kernel.Sort object at 0x6ebab8>) of role type named dsetconstrI_type
% Using role type
% Declaring dsetconstrI:Prop
% FOF formula (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named dsetconstrI
% A new definition: (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0x805998>, <kernel.Sort object at 0x6ebab8>) of role type named dsetconstrEL_type
% Using role type
% Declaring dsetconstrEL:Prop
% FOF formula (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))) of role definition named dsetconstrEL
% A new definition: (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))))
% Defined: dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0x805cb0>, <kernel.Sort object at 0x6ebab8>) of role type named dsetconstrER_type
% Using role type
% Declaring dsetconstrER:Prop
% FOF formula (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))) of role definition named dsetconstrER
% A new definition: (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))))
% Defined: dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))
% FOF formula (<kernel.Constant object at 0x8055f0>, <kernel.Sort object at 0x6ebab8>) of role type named setext_type
% Using role type
% Declaring setext:Prop
% FOF formula (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))) of role definition named setext
% A new definition: (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))))
% Defined: setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))
% FOF formula (<kernel.Constant object at 0x805ea8>, <kernel.Sort object at 0x6ebab8>) of role type named uniqinunit_type
% Using role type
% Declaring uniqinunit:Prop
% FOF formula (((eq Prop) uniqinunit) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy)))) of role definition named uniqinunit
% A new definition: (((eq Prop) uniqinunit) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))))
% Defined: uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x8054d0>, <kernel.Sort object at 0x6ebab8>) of role type named eqinunit_type
% Using role type
% Declaring eqinunit:Prop
% FOF formula (((eq Prop) eqinunit) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset))))) of role definition named eqinunit
% A new definition: (((eq Prop) eqinunit) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset)))))
% Defined: eqinunit:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset))))
% FOF formula (<kernel.Constant object at 0x805440>, <kernel.DependentProduct object at 0x8057a0>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) of role definition named singleton
% A new definition: (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))))
% Defined: singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))
% FOF formula (<kernel.Constant object at 0x8054d0>, <kernel.DependentProduct object at 0x805638>) of role type named ex1_type
% Using role type
% Declaring ex1:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named ex1
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Defined: ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% FOF formula (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(uniqinunit->(eqinunit->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((forall (Xy:fofType), (((in Xy) A)->((Xphi Xy)->(((eq fofType) Xy) Xx))))->((ex1 A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))) of role conjecture named ex1I
% Conjecture to prove = (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(uniqinunit->(eqinunit->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((forall (Xy:fofType), (((in Xy) A)->((Xphi Xy)->(((eq fofType) Xy) Xx))))->((ex1 A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))):Prop
% We need to prove ['(dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(uniqinunit->(eqinunit->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((forall (Xy:fofType), (((in Xy) A)->((Xphi Xy)->(((eq fofType) Xy) Xx))))->((ex1 A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))):Prop.
% Definition dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))):Prop.
% Definition dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))):Prop.
% Definition setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))):Prop.
% Definition uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))):Prop.
% Definition eqinunit:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset)))):Prop.
% Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop).
% Definition ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))):(fofType->((fofType->Prop)->Prop)).
% Trying to prove (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(uniqinunit->(eqinunit->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((forall (Xy:fofType), (((in Xy) A)->((Xphi Xy)->(((eq fofType) Xy) Xx))))->((ex1 A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))
% Found x5:((in Xx) A)
% Instantiate: x8:=Xx:fofType
% Found x5 as proof of ((in x8) A)
% Found x6:(Xphi Xx)
% Instantiate: x8:=Xx:fofType
% Found x6 as proof of (Xphi x8)
% Found ((x900 x5) x6) as proof of ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((x90 x8) x5) x6) as proof of ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((((x9 Xphi) x8) x5) x6) as proof of ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x8) x5) x6) as proof of ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x8) x5) x6) as proof of ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) (fun (x:fofType)=> ((and ((in x) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x) emptyset)))))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found ((eta_expansion_dep0 (fun (x9:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((and ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((and ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((in x) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x) emptyset)))))
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((and ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((and ((in x8) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((in x) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x) emptyset)))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x00000:=(x0000 x9):((in Xx0) A)
% Found (x0000 x9) as proof of ((in Xx0) A)
% Found ((x000 Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> ((x00 Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) b)
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) b)
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) b)
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) b)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found (x400 ((eq_ref fofType) ((setadjoin x8) emptyset))) as proof of ((in ((setadjoin x8) emptyset)) ((setadjoin ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)) emptyset))
% Found ((x40 ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)) ((eq_ref fofType) ((setadjoin x8) emptyset))) as proof of ((in ((setadjoin x8) emptyset)) ((setadjoin ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)) emptyset))
% Found (((x4 ((setadjoin x8) emptyset)) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)) ((eq_ref fofType) ((setadjoin x8) emptyset))) as proof of ((in ((setadjoin x8) emptyset)) ((setadjoin ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)) emptyset))
% Found (((x4 ((setadjoin x8) emptyset)) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)) ((eq_ref fofType) ((setadjoin x8) emptyset))) as proof of ((in ((setadjoin x8) emptyset)) ((setadjoin ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)) emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x9:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eta_expansion_dep0 (fun (x9:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x9:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found eq_ref000:=(eq_ref00 P):((P Xx0)->(P Xx0))
% Found (eq_ref00 P) as proof of (P0 Xx0)
% Found ((eq_ref0 Xx0) P) as proof of (P0 Xx0)
% Found (((eq_ref fofType) Xx0) P) as proof of (P0 Xx0)
% Found (((eq_ref fofType) Xx0) P) as proof of (P0 Xx0)
% Found x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: A0:=A:fofType
% Found x9 as proof of ((in Xx0) ((dsetconstr A0) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (x1000 x9) as proof of (Xphi Xx0)
% Found ((x100 Xphi) x9) as proof of (Xphi Xx0)
% Found (((x10 A) Xphi) x9) as proof of (Xphi Xx0)
% Found ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9) as proof of (Xphi Xx0)
% Found ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9) as proof of (Xphi Xx0)
% Found ((x70 (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)) as proof of (((eq fofType) Xx0) x8)
% Found (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)) as proof of (((eq fofType) Xx0) x8)
% Found (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)) as proof of (((eq fofType) Xx0) x8)
% Found (x400 (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (Xx0:fofType) (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)))) as proof of (((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)))) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) ((setadjoin x8) emptyset))))
% Found eq_ref00:=(eq_ref0 (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))):(((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset)))
% Found (eq_ref0 (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) as proof of (((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) b)
% Found ((eq_ref Prop) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) as proof of (((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) b)
% Found ((eq_ref Prop) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) as proof of (((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) b)
% Found ((eq_ref Prop) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) as proof of (((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x8) emptyset))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x00000:=(x0000 x9):((in Xx0) A)
% Found (x0000 x9) as proof of ((in Xx0) A)
% Found ((x000 Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> ((x00 Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x6:(Xphi Xx)
% Instantiate: Xy:=Xx:fofType
% Found x6 as proof of (Xphi Xy)
% Found x5:((in Xx) A)
% Instantiate: Xy:=Xx:fofType
% Found x5 as proof of ((in Xy) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) b)
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) b)
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) b)
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) b)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) b))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x6:(Xphi Xx)
% Instantiate: Xy:=Xx:fofType
% Found x6 as proof of (Xphi Xy)
% Found x5:((in Xx) A)
% Instantiate: Xy:=Xx:fofType
% Found x5 as proof of ((in Xy) A)
% Found x9:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: Xx0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of (P0 Xx0)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found x9:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: Xx0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of (P0 Xx0)
% Found x9:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found x9:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found x6:(Xphi Xx)
% Instantiate: Xy:=Xx:fofType
% Found x6 as proof of (Xphi Xy)
% Found x5:((in Xx) A)
% Instantiate: Xy:=Xx:fofType
% Found x5 as proof of ((in Xy) A)
% Found x9:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: A0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of (P0 A0)
% Found x9:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: A0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of (P0 A0)
% Found eq_ref000:=(eq_ref00 P):((P Xx0)->(P Xx0))
% Found (eq_ref00 P) as proof of (P0 Xx0)
% Found ((eq_ref0 Xx0) P) as proof of (P0 Xx0)
% Found (((eq_ref fofType) Xx0) P) as proof of (P0 Xx0)
% Found (((eq_ref fofType) Xx0) P) as proof of (P0 Xx0)
% Found eq_ref000:=(eq_ref00 P):((P Xx0)->(P Xx0))
% Found (eq_ref00 P) as proof of (P0 Xx0)
% Found ((eq_ref0 Xx0) P) as proof of (P0 Xx0)
% Found (((eq_ref fofType) Xx0) P) as proof of (P0 Xx0)
% Found (((eq_ref fofType) Xx0) P) as proof of (P0 Xx0)
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: A0:=A:fofType
% Found x9 as proof of ((in Xx0) ((dsetconstr A0) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (x1000 x9) as proof of (Xphi Xx0)
% Found ((x100 Xphi) x9) as proof of (Xphi Xx0)
% Found (((x10 A) Xphi) x9) as proof of (Xphi Xx0)
% Found ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9) as proof of (Xphi Xx0)
% Found ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9) as proof of (Xphi Xx0)
% Found ((x70 (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)) as proof of (((eq fofType) Xx0) x8)
% Found (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)) as proof of (((eq fofType) Xx0) x8)
% Found (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)) as proof of (((eq fofType) Xx0) x8)
% Found (x400 (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (Xx0:fofType) (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)))) as proof of (((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) (((x7 Xx0) (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9)) ((((fun (A0:fofType) (Xphi0:(fofType->Prop))=> (((x1 A0) Xphi0) Xx0)) A) Xphi) x9)))) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) ((setadjoin x8) emptyset))))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) A0)->((in Xx0) A0))
% Found (eq_ref00 (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin x8) emptyset)))
% Found ((eq_ref0 A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin x8) emptyset)))
% Found (((eq_ref fofType) A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin x8) emptyset)))
% Found (((eq_ref fofType) A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin x8) emptyset)))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) A0) (in Xx0))) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin x8) emptyset)))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) A0) (in Xx0))) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((setadjoin x8) emptyset))))
% Found x10:((in Xx0) ((setadjoin x8) emptyset))
% Instantiate: A0:=((setadjoin x8) emptyset):fofType
% Found (fun (x10:((in Xx0) ((setadjoin x8) emptyset)))=> x10) as proof of ((in Xx0) A0)
% Found (fun (Xx0:fofType) (x10:((in Xx0) ((setadjoin x8) emptyset)))=> x10) as proof of (((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) A0))
% Found (fun (Xx0:fofType) (x10:((in Xx0) ((setadjoin x8) emptyset)))=> x10) as proof of (forall (Xx:fofType), (((in Xx) ((setadjoin x8) emptyset))->((in Xx) A0)))
% Found x10:((in Xx0) A0)
% Instantiate: A0:=((setadjoin x8) emptyset):fofType
% Found (fun (x10:((in Xx0) A0))=> x10) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (Xx0:fofType) (x10:((in Xx0) A0))=> x10) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin x8) emptyset)))
% Found (fun (Xx0:fofType) (x10:((in Xx0) A0))=> x10) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((setadjoin x8) emptyset))))
% Found x6:(Xphi Xx)
% Instantiate: Xy:=Xx:fofType
% Found x6 as proof of (Xphi Xy)
% Found x5:((in Xx) A)
% Instantiate: Xy:=Xx:fofType
% Found x5 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((setadjoin x8) emptyset))
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found ((x40 ((setadjoin x8) emptyset)) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found (((x4 Xx0) ((setadjoin x8) emptyset)) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found (((x4 Xx0) ((setadjoin x8) emptyset)) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) A0))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) A0))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) A0))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) A0))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0))) as proof of (((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) A0))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0))) as proof of (forall (Xx:fofType), (((in Xx) ((setadjoin x8) emptyset))->((in Xx) A0)))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((setadjoin x8) emptyset))
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found ((x40 ((setadjoin x8) emptyset)) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found (((x4 Xx0) ((setadjoin x8) emptyset)) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found (((x4 Xx0) ((setadjoin x8) emptyset)) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found x9:((in Xx0) ((setadjoin x8) emptyset))
% Instantiate: Xx1:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P Xx1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin ((setadjoin x8) emptyset)) emptyset)):(((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found (eq_ref0 ((setadjoin ((setadjoin x8) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found x9:((in Xx0) ((setadjoin x8) emptyset))
% Instantiate: b:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin ((setadjoin x8) emptyset)) emptyset)):(((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) ((setadjoin ((setadjoin x8) emptyset)) emptyset))
% Found (eq_ref0 ((setadjoin ((setadjoin x8) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) b))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found x000:=(x00 Xphi):(forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% Found (x00 Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A)))
% Found x00000:=(x0000 x9):((in Xx0) A)
% Found (x0000 x9) as proof of ((in Xx0) A)
% Found ((x000 Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> ((x00 Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found x00000:=(x0000 x9):((in Xx0) A)
% Found (x0000 x9) as proof of ((in Xx0) A)
% Found ((x000 Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> ((x00 Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found x9:(P ((setadjoin x8) emptyset))
% Instantiate: b:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x9:(P ((setadjoin x8) emptyset))
% Instantiate: Xx0:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P0 Xx0)
% Found x9:(P ((setadjoin x8) emptyset))
% Instantiate: b:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 ((setadjoin x8) emptyset))->(P1 ((setadjoin x8) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 ((setadjoin x8) emptyset))->(P1 ((setadjoin x8) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x9:(P ((setadjoin x8) emptyset))
% Instantiate: Xx0:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P0 Xx0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P1):((P1 ((setadjoin x8) emptyset))->(P1 ((setadjoin x8) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 ((setadjoin x8) emptyset))->(P1 ((setadjoin x8) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x6:(Xphi Xx)
% Instantiate: Xy:=Xx:fofType
% Found x6 as proof of (Xphi Xy)
% Found x5:((in Xx) A)
% Instantiate: Xy:=Xx:fofType
% Found x5 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found x9:(P ((setadjoin x8) emptyset))
% Instantiate: A0:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P0 A0)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) A0)->((in Xx0) A0))
% Found (eq_ref00 (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found ((eq_ref0 A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (((eq_ref fofType) A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (((eq_ref fofType) A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) A0) (in Xx0))) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) A0) (in Xx0))) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((setadjoin ((setadjoin x8) emptyset)) emptyset))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) A0))
% Found ((eq_ref0 ((setadjoin ((setadjoin x8) emptyset)) emptyset)) (in Xx0)) as proof of (((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) A0))
% Found (((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) (in Xx0)) as proof of (((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) A0))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) (in Xx0))) as proof of (((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) A0))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) (in Xx0))) as proof of (forall (Xx:fofType), (((in Xx) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx) A0)))
% Found x000:=(x00 Xphi):(forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% Found (x00 Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x9:(P ((setadjoin x8) emptyset))
% Instantiate: A0:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P0 A0)
% Found eq_ref00:=(eq_ref0 Xx1):(((eq fofType) Xx1) Xx1)
% Found (eq_ref0 Xx1) as proof of (((eq fofType) Xx1) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx1) as proof of (((eq fofType) Xx1) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (x400 ((eq_ref fofType) Xx1)) as proof of ((in Xx1) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found ((x40 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx1)) as proof of ((in Xx1) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found (((x4 Xx1) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx1)) as proof of ((in Xx1) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found (((x4 Xx1) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx1)) as proof of ((in Xx1) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 ((setadjoin x8) emptyset))->(P1 ((setadjoin x8) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 ((setadjoin x8) emptyset))->(P1 ((setadjoin x8) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) A0)->((in Xx0) A0))
% Found (eq_ref00 (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found ((eq_ref0 A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (((eq_ref fofType) A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (((eq_ref fofType) A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) A0) (in Xx0))) as proof of (((in Xx0) A0)->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) A0) (in Xx0))) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((setadjoin ((setadjoin x8) emptyset)) emptyset))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) A0))
% Found ((eq_ref0 ((setadjoin ((setadjoin x8) emptyset)) emptyset)) (in Xx0)) as proof of (((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) A0))
% Found (((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) (in Xx0)) as proof of (((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) A0))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) (in Xx0))) as proof of (((in Xx0) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx0) A0))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) ((setadjoin ((setadjoin x8) emptyset)) emptyset)) (in Xx0))) as proof of (forall (Xx:fofType), (((in Xx) ((setadjoin ((setadjoin x8) emptyset)) emptyset))->((in Xx) A0)))
% Found x000:=(x00 Xphi):(forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% Found (x00 Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P1):((P1 ((setadjoin x8) emptyset))->(P1 ((setadjoin x8) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 ((setadjoin x8) emptyset))->(P1 ((setadjoin x8) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P1) as proof of (P2 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->(P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x8) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found x10:((in Xx0) A0)
% Instantiate: A0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found (fun (x10:((in Xx0) A0))=> x10) as proof of ((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (Xx0:fofType) (x10:((in Xx0) A0))=> x10) as proof of (((in Xx0) A0)->((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (fun (Xx0:fofType) (x10:((in Xx0) A0))=> x10) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) A0)->((in Xx0) A0))
% Found (eq_ref00 (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found ((eq_ref0 A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (((eq_ref fofType) A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (((eq_ref fofType) A0) (in Xx0)) as proof of (((in Xx0) A0)->((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) A0) (in Xx0))) as proof of (((in Xx0) A0)->((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (fun (Xx0:fofType)=> (((eq_ref fofType) A0) (in Xx0))) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found ((x40 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found (((x4 Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found (((x4 Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: Xx1:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of (P Xx1)
% Found x9:((in Xx0) ((setadjoin x8) emptyset))
% Instantiate: Xx1:=Xx0:fofType;x8:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of ((in Xx1) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found x9:((in Xx0) ((setadjoin x8) emptyset))
% Instantiate: Xx1:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P Xx1)
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P1 ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found x9:((in Xx0) ((setadjoin x8) emptyset))
% Instantiate: Xx1:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P Xx1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found ((x40 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found (((x4 Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found (((x4 Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x8) emptyset))->(P ((setadjoin x8) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) P) as proof of (P0 ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) Xy)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) Xy)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) Xy)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) Xy)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x40 Xy) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found (((x4 Xx0) Xy) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found (fun (x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx0) Xy) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found x001:=(x00 Xphi0):(forall (Xx:fofType), (((in Xx) ((dsetconstr ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (Xy:fofType)=> (Xphi0 Xy))))->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (x00 Xphi0) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (Xy:fofType)=> (Xphi0 Xy))))->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (x00 Xphi0) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) (fun (Xy:fofType)=> (Xphi0 Xy))))->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found x9:((in Xx0) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x9 as proof of (P b)
% Found x9:((in Xx0) ((setadjoin x8) emptyset))
% Instantiate: b:=((setadjoin x8) emptyset):fofType
% Found x9 as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xx0):(((eq fofType) Xx0) Xx0)
% Found (eq_ref0 Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found ((eq_ref fofType) Xx0) as proof of (((eq fofType) Xx0) x8)
% Found (x400 ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found ((x40 x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (((x4 Xx0) x8) ((eq_ref fofType) Xx0)) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found (fun (x10:((in Xx0) A0))=> (((x4 Xx0) x8) ((eq_ref fofType) Xx0))) as proof of ((in Xx0) ((setadjoin x8) emptyset))
% Found eq_ref00:=(eq_ref0 ((setadjoin x8) emptyset)):(((eq fofType) ((setadjoin x8) emptyset)) ((setadjoin x8) emptyset))
% Found (eq_ref0 ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x8) emptyset)) as proof of (((eq fofType) ((setadjoin x8) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (x400 ((eq_ref fofType) b)) as proof of (P b)
% Found ((x40 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((eq_ref fofType) b)) as proof of (P b)
% Found (((x4 b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((eq_ref fofType) b)) as proof of (P b)
% Found (((x4 b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((eq_ref fofType) b)) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (x400 ((eq_ref fofType) b)) as proof of (P b)
% Found ((x40 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((eq_ref fofType) b)) as proof of (P b)
% Found (((x4 b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((eq_ref fofType) b)) as proof of (P b)
% Found (((x4 b) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((eq_ref fofType) b)) as proof of (P b)
% Found x00000:=(x0000 x9):((in Xx0) A)
% Found (x0000 x9) as proof of ((in Xx0) A)
% Found ((x000 Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> ((x00 Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eta_expansion_dep0 (fun (x11:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion_dep fofType) (fun (x11:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion_dep fofType) (fun (x11:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion_dep fofType) (fun (x11:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin x8) emptyset))->((in Xx0) ((setadjoin x8) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found ((eq_ref0 ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found (((eq_ref fofType) ((setadjoin x8) emptyset)) (in Xx0)) as proof of (P ((setadjoin x8) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1))))->((in Xx0) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))))
% Found (eq_ref00 (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx1:fofType)=> (Xphi Xx1)))) (in Xx0)) as proof of (P1 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x00000:=(x0000 x9):((in Xx0) A)
% Found (x0000 x9) as proof of ((in Xx0) A)
% Found ((x000 Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> ((x00 Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found x00000:=(x0000 x9):((in Xx0) A)
% Found (x0000 x9) as proof of ((in Xx0) A)
% Found ((x000 Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> ((x00 Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found x00000:=(x0000 x9):((in Xx0) A)
% Found (x0000 x9) as proof of ((in Xx0) A)
% Found ((x000 Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> ((x00 Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fofType->Prop))=> (((x0 A) Xphi0) Xx0)) Xphi) x9) as proof of ((in Xx0) A)
% Found (((fun (Xphi0:(fo
% EOF
%------------------------------------------------------------------------------