%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU664^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n106.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 13:32:45 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU664^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n106.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 11:05:41 CDT 2014
% % CPUTime  : 300.01 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x140d908>, <kernel.DependentProduct object at 0x140d710>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x17ca290>, <kernel.DependentProduct object at 0x140d710>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x140dd40>, <kernel.DependentProduct object at 0x140dea8>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x140d950>, <kernel.Sort object at 0x12d77e8>) of role type named cartprodmempair1_type
% Using role type
% Declaring cartprodmempair1:Prop
% FOF formula (((eq Prop) cartprodmempair1) (forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))) of role definition named cartprodmempair1
% A new definition: (((eq Prop) cartprodmempair1) (forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))))
% Defined: cartprodmempair1:=(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))
% FOF formula (<kernel.Constant object at 0x17c7cf8>, <kernel.DependentProduct object at 0x140de60>) of role type named kfst_type
% Using role type
% Declaring kfst:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x140db48>, <kernel.DependentProduct object at 0x140d638>) of role type named ksnd_type
% Using role type
% Declaring ksnd:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x140dea8>, <kernel.Sort object at 0x12d77e8>) of role type named cartprodfstpairEq_type
% Using role type
% Declaring cartprodfstpairEq:Prop
% FOF formula (((eq Prop) cartprodfstpairEq) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((eq fofType) (kfst ((kpair Xx) Xy))) Xx)))))) of role definition named cartprodfstpairEq
% A new definition: (((eq Prop) cartprodfstpairEq) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((eq fofType) (kfst ((kpair Xx) Xy))) Xx))))))
% Defined: cartprodfstpairEq:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((eq fofType) (kfst ((kpair Xx) Xy))) Xx)))))
% FOF formula (<kernel.Constant object at 0x140d878>, <kernel.Sort object at 0x12d77e8>) of role type named cartprodsndpairEq_type
% Using role type
% Declaring cartprodsndpairEq:Prop
% FOF formula (((eq Prop) cartprodsndpairEq) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((eq fofType) (ksnd ((kpair Xx) Xy))) Xy)))))) of role definition named cartprodsndpairEq
% A new definition: (((eq Prop) cartprodsndpairEq) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((eq fofType) (ksnd ((kpair Xx) Xy))) Xy))))))
% Defined: cartprodsndpairEq:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((eq fofType) (ksnd ((kpair Xx) Xy))) Xy)))))
% FOF formula (cartprodmempair1->(cartprodfstpairEq->(cartprodsndpairEq->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) Xu)))))) of role conjecture named cartprodpairsurjEq
% Conjecture to prove = (cartprodmempair1->(cartprodfstpairEq->(cartprodsndpairEq->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) Xu)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(cartprodmempair1->(cartprodfstpairEq->(cartprodsndpairEq->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) Xu))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter cartprod:(fofType->(fofType->fofType)).
% Definition cartprodmempair1:=(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))):Prop.
% Parameter kfst:(fofType->fofType).
% Parameter ksnd:(fofType->fofType).
% Definition cartprodfstpairEq:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((eq fofType) (kfst ((kpair Xx) Xy))) Xx))))):Prop.
% Definition cartprodsndpairEq:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((eq fofType) (ksnd ((kpair Xx) Xy))) Xy))))):Prop.
% Trying to prove (cartprodmempair1->(cartprodfstpairEq->(cartprodsndpairEq->(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) Xu))))))
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x3:(P ((kpair (kfst Xu)) (ksnd Xu)))
% Instantiate: b:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x3:(P Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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 x3:(P ((kpair (kfst Xu)) (ksnd Xu)))
% Instantiate: b:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x3:(P Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x3:(P ((kpair (kfst Xu)) (ksnd Xu)))
% Instantiate: a:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found x3 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x3:(P1 Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x40:(P1 Xu)
% Found (fun (x40:(P1 Xu))=> x40) as proof of (P1 Xu)
% Found (fun (x40:(P1 Xu))=> x40) as proof of (P2 Xu)
% Found x3:(P Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found x3:(P Xu)
% Instantiate: a:=Xu:fofType
% Found x3 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x30:(P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P0 b0))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P0 b0))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of (P b0)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x3:(P Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P0 b0)
% 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) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P0 b0)
% 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 x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found x3:(P b)
% Found x3 as proof of (P0 ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found x30:(P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P1 b)
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P2 b)
% Found x30:(P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% 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 x3:(P0 b0)
% Instantiate: b0:=Xu:fofType
% Found (fun (x3:(P0 b0))=> x3) as proof of (P0 Xu)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of ((P0 b0)->(P0 Xu))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:(P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P0 b0)
% Found x3:(P Xu)
% Found x3 as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x3:(P0 ((kpair (kfst Xu)) (ksnd Xu)))
% Found (fun (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of ((P0 ((kpair (kfst Xu)) (ksnd Xu)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of (P ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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 x30:(P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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 x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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 x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 Xu)
% Found (fun (x3:(P0 Xu))=> x3) as proof of (P0 Xu)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 Xu))=> x3) as proof of ((P0 Xu)->(P0 Xu))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 Xu))=> x3) as proof of (P Xu)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) Xu)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xu)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xu)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found x3:(P ((kpair (kfst Xu)) (ksnd Xu)))
% Instantiate: a:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found x3 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xu)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x3:(P1 Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x40:(P1 Xu)
% Found (fun (x40:(P1 Xu))=> x40) as proof of (P1 Xu)
% Found (fun (x40:(P1 Xu))=> x40) as proof of (P2 Xu)
% Found x3:(P Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found x3:(P Xu)
% Instantiate: a:=Xu:fofType
% Found x3 as proof of (P0 a)
% Found x3:(P Xu)
% Instantiate: a:=Xu:fofType
% Found x3 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found x30:(P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P2 b)
% Found x30:(P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P2 b)
% Found x3:(P1 Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P0 b0))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P0 b0))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found x3:(P Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P0 b0)
% 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 x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x3:(P Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P0 b0)
% 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 x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found x3:(P b)
% Found x3 as proof of (P0 Xu)
% Found x3:(P b)
% Found x3 as proof of (P0 Xu)
% Found x3:(P b)
% Found x3 as proof of (P0 ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found x40:(P1 Xu)
% Found (fun (x40:(P1 Xu))=> x40) as proof of (P1 Xu)
% Found (fun (x40:(P1 Xu))=> x40) as proof of (P2 Xu)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found x30:(P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P1 b)
% Found x2:((in Xu) ((cartprod A) B))
% Instantiate: A0:=((cartprod A) B):fofType
% Found x2 as proof of ((in Xu) A0)
% Found x2:((in Xu) ((cartprod A) B))
% Instantiate: Xy:=Xu:fofType;B0:=((cartprod A) B):fofType
% Found x2 as proof of ((in Xy) B0)
% Found x2:((in Xu) ((cartprod A) B))
% Instantiate: A0:=((cartprod A) B):fofType;Xx:=Xu:fofType
% Found x2 as proof of ((in Xx) A0)
% Found x2:((in Xu) ((cartprod A) B))
% Instantiate: B0:=((cartprod A) B):fofType
% Found x2 as proof of ((in Xu) B0)
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P2 b)
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x3:(P ((kpair (kfst Xu)) (ksnd Xu)))
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P ((kpair (kfst Xu)) (ksnd Xu)))
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x30:(P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x3:(P0 b0)
% Instantiate: b0:=Xu:fofType
% Found (fun (x3:(P0 b0))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x3:(P0 b0)
% Instantiate: b0:=Xu:fofType
% Found (fun (x3:(P0 b0))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x30:(P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P0 b)
% Found (fun (x30:(P0 b))=> x30) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found x3:(P Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P0 b0)
% 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 x3:(P Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P0 b0)
% 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) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:(P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P0 b0)
% Found x30:(P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P0 b0)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 Xu)
% Found (fun (x3:(P0 Xu))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 Xu))=> x3) as proof of ((P0 Xu)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 Xu))=> x3) as proof of (P Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 Xu)
% Found (fun (x3:(P0 Xu))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 Xu))=> x3) as proof of ((P0 Xu)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 Xu))=> x3) as proof of (P Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x3:(P0 ((kpair (kfst Xu)) (ksnd Xu)))
% Found (fun (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of ((P0 ((kpair (kfst Xu)) (ksnd Xu)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of (P ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x3:(P0 ((kpair (kfst Xu)) (ksnd Xu)))
% Found (fun (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of ((P0 ((kpair (kfst Xu)) (ksnd Xu)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 ((kpair (kfst Xu)) (ksnd Xu))))=> x3) as proof of (P ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x4:(P2 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x4:(P2 b0))=> x4) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x4:(P2 b0))=> x4) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x4:(P2 b0))=> x4) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x4:(P1 Xu)
% Instantiate: b0:=Xu:fofType
% Found x4 as proof of (P2 b0)
% 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found x2:((in Xu) ((cartprod A) B))
% Instantiate: Xy:=Xu:fofType;B0:=((cartprod A) B):fofType
% Found x2 as proof of ((in Xy) B0)
% Found x2:((in Xu) ((cartprod A) B))
% Instantiate: A0:=((cartprod A) B):fofType;Xx:=Xu:fofType
% Found x2 as proof of ((in Xx) A0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (ksnd Xu))
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P1 Xu)
% Found (fun (x30:(P1 Xu))=> x30) as proof of (P2 Xu)
% Found x30:(P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P1 b)
% Found (fun (x30:(P1 b))=> x30) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x30:(P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:(P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% 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 x3:(P0 b0)
% Instantiate: b0:=Xu:fofType
% Found (fun (x3:(P0 b0))=> x3) as proof of (P0 Xu)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of ((P0 b0)->(P0 Xu))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b0))=> x3) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b0)
% Found x3:(P b)
% Found x3 as proof of (P0 ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x3:(P1 b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found x30:(P ((kpair (kfst Xu)) (ksnd Xu)))
% Found (fun (x30:(P ((kpair (kfst Xu)) (ksnd Xu))))=> x30) as proof of (P ((kpair (kfst Xu)) (ksnd Xu)))
% Found (fun (x30:(P ((kpair (kfst Xu)) (ksnd Xu))))=> x30) as proof of (P0 ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x30:(P ((kpair (kfst Xu)) (ksnd Xu)))
% Found (fun (x30:(P ((kpair (kfst Xu)) (ksnd Xu))))=> x30) as proof of (P ((kpair (kfst Xu)) (ksnd Xu)))
% Found (fun (x30:(P ((kpair (kfst Xu)) (ksnd Xu))))=> x30) as proof of (P0 ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x4:(P1 b)
% Instantiate: b0:=b:fofType
% Found x4 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x4:(P1 ((kpair (kfst Xu)) (ksnd Xu)))
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found x4 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x3:(P1 Xu)
% Instantiate: a:=Xu:fofType
% Found x3 as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b00)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b00)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b00)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b00)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b00)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b00)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b00)
% Found x3:(P b)
% Instantiate: a:=b:fofType
% Found x3 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x4:(P2 b)
% Instantiate: b0:=b:fofType
% Found (fun (x4:(P2 b))=> x4) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x4:(P2 b))=> x4) as proof of ((P2 b)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x4:(P2 b))=> x4) as proof of (P1 b0)
% 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 x4:(P2 b0)
% Instantiate: b0:=Xu:fofType
% Found (fun (x4:(P2 b0))=> x4) as proof of (P2 Xu)
% Found (fun (P2:(fofType->Prop)) (x4:(P2 b0))=> x4) as proof of ((P2 b0)->(P2 Xu))
% Found (fun (P2:(fofType->Prop)) (x4:(P2 b0))=> x4) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x4:(P2 b0)
% Instantiate: b0:=Xu:fofType
% Found (fun (x4:(P2 b0))=> x4) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x4:(P2 b0))=> x4) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x4:(P2 b0))=> x4) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x40:(P1 a)
% Found (fun (x40:(P1 a))=> x40) as proof of (P1 a)
% Found (fun (x40:(P1 a))=> x40) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b1)
% Found x40:(P1 Xu)
% Found (fun (x40:(P1 Xu))=> x40) as proof of (P1 Xu)
% Found (fun (x40:(P1 Xu))=> x40) as proof of (P2 Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P2 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P2 b0))=> x3) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P2 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P2 b0))=> x3) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P2 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P2 b0))=> x3) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P2 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P2 b0))=> x3) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x3:(P2 b0)
% Instantiate: b0:=((kpair (kfst Xu)) (ksnd Xu)):fofType
% Found (fun (x3:(P2 b0))=> x3) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x3:(P2 b0))=> x3) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x30:(P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P0 b0)
% Found x30:(P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P b0)
% Found (fun (x30:(P b0))=> x30) as proof of (P0 b0)
% Found x3:(P0 b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found x3:(P1 Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P2 b0)
% 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 x3:(P1 Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P2 b0)
% 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 x3:(P1 b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found x3:(P1 Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P2 b0)
% 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 x3:(P1 Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P2 b0)
% 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 x3:(P Xu)
% Found x3 as proof of (P0 Xu)
% Found x3:(P1 Xu)
% Instantiate: b0:=Xu:fofType
% Found x3 as proof of (P2 b0)
% 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 x3:(P0 b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst b)) (ksnd b))):(((eq fofType) ((kpair (kfst b)) (ksnd b))) ((kpair (kfst b)) (ksnd b)))
% Found (eq_ref0 ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found ((eq_ref fofType) ((kpair (kfst b)) (ksnd b))) as proof of (((eq fofType) ((kpair (kfst b)) (ksnd b))) b0)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b00)
% Found x3:(P1 b)
% Found x3 as proof of (P2 ((kpair (kfst Xu)) (ksnd Xu)))
% Found x3:(P1 b)
% Found x3 as proof of (P2 Xu)
% Found eq_ref00:=(eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))):(((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) ((kpair (kfst Xu)) (ksnd Xu)))
% Found (eq_ref0 ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found ((eq_ref fofType) ((kpair (kfst Xu)) (ksnd Xu))) as proof of (((eq fofType) ((kpair (kfst Xu)) (ksnd Xu))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((kpair (kfst Xu)) (ksnd Xu)))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xu)
% 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 x30:(P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P Xu)
% Found (fun (x30:(P Xu))=> x30) as proof of (P0 Xu)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found
% EOF
%------------------------------------------------------------------------------