TSTP Solution File: SEU704^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU704^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n187.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 13:32:52 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU704^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n187.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 11:15:21 CDT 2014
% % CPUTime : 300.02
% 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 0x1cea680>, <kernel.DependentProduct object at 0x1cea050>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1f3a128>, <kernel.Single object at 0x1ceab90>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x1cea050>, <kernel.DependentProduct object at 0x1ceacb0>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1cea200>, <kernel.DependentProduct object at 0x1cea4d0>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x1cea830>, <kernel.DependentProduct object at 0x1ceab90>) 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 0x1ceac20>, <kernel.Sort object at 0x1d9cb90>) of role type named iffalseProp1_type
% Using role type
% Declaring iffalseProp1:Prop
% FOF formula (((eq Prop) iffalseProp1) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->((in Xy) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))) of role definition named iffalseProp1
% A new definition: (((eq Prop) iffalseProp1) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->((in Xy) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))))
% Defined: iffalseProp1:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->((in Xy) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))
% FOF formula (<kernel.Constant object at 0x1cea200>, <kernel.Sort object at 0x1d9cb90>) of role type named iffalseProp2_type
% Using role type
% Declaring iffalseProp2:Prop
% FOF formula (((eq Prop) iffalseProp2) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xy) emptyset)))))))) of role definition named iffalseProp2
% A new definition: (((eq Prop) iffalseProp2) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xy) emptyset))))))))
% Defined: iffalseProp2:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xy) emptyset)))))))
% FOF formula (<kernel.Constant object at 0x1ceae60>, <kernel.Sort object at 0x1d9cb90>) of role type named iftrueProp1_type
% Using role type
% Declaring iftrueProp1:Prop
% FOF formula (((eq Prop) iftrueProp1) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))) of role definition named iftrueProp1
% A new definition: (((eq Prop) iftrueProp1) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))))
% Defined: iftrueProp1:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))
% FOF formula (<kernel.Constant object at 0x1ceae60>, <kernel.Sort object at 0x1d9cb90>) of role type named iftrueProp2_type
% Using role type
% Declaring iftrueProp2:Prop
% FOF formula (((eq Prop) iftrueProp2) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx) emptyset)))))))) of role definition named iftrueProp2
% A new definition: (((eq Prop) iftrueProp2) (forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx) emptyset))))))))
% Defined: iftrueProp2:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx) emptyset)))))))
% FOF formula (iffalseProp1->(iffalseProp2->(iftrueProp1->(iftrueProp2->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))))) of role conjecture named ifSingleton
% Conjecture to prove = (iffalseProp1->(iffalseProp2->(iftrueProp1->(iftrueProp2->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))))))))):Prop
% We need to prove ['(iffalseProp1->(iffalseProp2->(iftrueProp1->(iftrueProp2->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop).
% Definition iffalseProp1:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->((in Xy) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))):Prop.
% Definition iffalseProp2:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi->False)->(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xy) emptyset))))))):Prop.
% Definition iftrueProp1:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->((in Xx) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))):Prop.
% Definition iftrueProp2:=(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(Xphi->(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx) emptyset))))))):Prop.
% Trying to prove (iffalseProp1->(iffalseProp2->(iftrueProp1->(iftrueProp2->(forall (A:fofType) (Xphi:Prop) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->(singleton ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))))))))))
% Found eq_ref00:=(eq_ref0 (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))):(((eq (fofType->Prop)) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found (eq_ref0 (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset))))) b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) ((and ((in x5) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((and ((in x5) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((and ((in x5) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) ((and ((in x5) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((in x) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x) emptyset)))))
% Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) ((and ((in x5) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((and ((in x5) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))))
% Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((and ((in x5) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) ((and ((in x5) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((in x) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x) emptyset)))))
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) 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) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x6: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 (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx0:fofType)=> ((and ((in Xx0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin Xx0) emptyset)))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))):(((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset)))
% Found (eq_ref0 (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) as proof of (((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) b)
% Found ((eq_ref Prop) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) as proof of (((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) b)
% Found ((eq_ref Prop) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) as proof of (((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) b)
% Found ((eq_ref Prop) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) as proof of (((eq Prop) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset))) b)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Instantiate: b:=A:fofType;x5:=Xy:fofType
% Found x4 as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x6:(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Instantiate: b:=((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))):fofType
% Found x6 as proof of (P0 b)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found x6:(P0 b)
% Instantiate: b:=((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))):fofType
% Found (fun (x6:(P0 b))=> x6) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (fun (P0:(fofType->Prop)) (x6:(P0 b))=> x6) as proof of ((P0 b)->(P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (fun (P0:(fofType->Prop)) (x6:(P0 b))=> x6) as proof of (P b)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b0)
% Found x6:(P ((setadjoin x5) emptyset))
% Instantiate: b:=((setadjoin x5) emptyset):fofType
% Found x6 as proof of (P0 b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) 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 (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% 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 x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) 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 (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) 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 (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x60:(P ((setadjoin x5) emptyset))
% Found (fun (x60:(P ((setadjoin x5) emptyset)))=> x60) as proof of (P ((setadjoin x5) emptyset))
% Found (fun (x60:(P ((setadjoin x5) emptyset)))=> x60) as proof of (P0 ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) x5))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) x5))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x60:(P ((setadjoin x5) emptyset))
% Found (fun (x60:(P ((setadjoin x5) emptyset)))=> x60) as proof of (P ((setadjoin x5) emptyset))
% Found (fun (x60:(P ((setadjoin x5) emptyset)))=> x60) as proof of (P0 ((setadjoin x5) emptyset))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x6:(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Instantiate: b:=((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))):fofType
% Found x6 as proof of (P0 b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((setadjoin x5) emptyset)))
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found functional_extensionality_double:=(fun (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))) (x:(forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y))))=> (((((functional_extensionality_dep A) (fun (x2:A)=> (B->C))) f) g) (fun (x0:A)=> (((((functional_extensionality_dep B) (fun (x3:B)=> C)) (f x0)) (g x0)) (x x0))))):(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g)))
% Instantiate: b:=(forall (A:Type) (B:Type) (C:Type) (f:(A->(B->C))) (g:(A->(B->C))), ((forall (x:A) (y:B), (((eq C) ((f x) y)) ((g x) y)))->(((eq (A->(B->C))) f) g))):Prop
% Found functional_extensionality_double as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found x6:(P0 b)
% Instantiate: b:=((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))):fofType
% Found (fun (x6:(P0 b))=> x6) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (fun (P0:(fofType->Prop)) (x6:(P0 b))=> x6) as proof of ((P0 b)->(P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (fun (P0:(fofType->Prop)) (x6:(P0 b))=> x6) as proof of (P b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 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) b0)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin x5) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b0)
% Found x6:(P ((setadjoin x5) emptyset))
% Instantiate: b:=((setadjoin x5) emptyset):fofType
% Found x6 as proof of (P0 b)
% Found x6:(P ((setadjoin x5) emptyset))
% Instantiate: b:=((setadjoin x5) emptyset):fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f0 x5)):(((eq Prop) (f0 x5)) (f0 x5))
% Found (eq_ref0 (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found ((eq_ref Prop) (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found ((eq_ref Prop) (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f0 x5))) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f0 x5))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x5)):(((eq Prop) (f0 x5)) (f0 x5))
% Found (eq_ref0 (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found ((eq_ref Prop) (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found ((eq_ref Prop) (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f0 x5))) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f0 x5))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))):(((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) b)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found eq_ref00:=(eq_ref0 (f0 x5)):(((eq Prop) (f0 x5)) (f0 x5))
% Found (eq_ref0 (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found ((eq_ref Prop) (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found ((eq_ref Prop) (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f0 x5))) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f0 x5))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x5)):(((eq Prop) (f0 x5)) (f0 x5))
% Found (eq_ref0 (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found ((eq_ref Prop) (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found ((eq_ref Prop) (f0 x5)) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f0 x5))) as proof of (((eq Prop) (f0 x5)) (f x5))
% Found (fun (x5:fofType)=> ((eq_ref Prop) (f0 x5))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x5) emptyset)):(((eq fofType) ((setadjoin x5) emptyset)) ((setadjoin x5) emptyset))
% Found (eq_ref0 ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x5) emptyset)) as proof of (((eq fofType) ((setadjoin x5) emptyset)) b)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) 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 x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A0)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))->(P ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy)))))) P) as proof of (P0 ((dsetconstr A) (fun (Xz:fofType)=> ((or ((and Xphi) (((eq fofType) Xz) Xx))) ((and (Xphi->False)) (((eq fofType) Xz) Xy))))))
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in x5) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x3:((in Xx) A)
% Found x3 as proof of ((in Xx) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy) A)
% Found x4:((in Xy) A)
% Found x4 as proof of ((in Xy)
% EOF
%------------------------------------------------------------------------------