TSTP Solution File: SYO132^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO132^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:43 EDT 2022
% Result : Timeout 288.75s 289.06s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO132^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % RAMPerCPU : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Fri Mar 11 15:54:22 EST 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.34 Python 2.7.5
% 2.13/2.29 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 2.13/2.29 FOF formula (<kernel.Constant object at 0x2649998>, <kernel.Constant object at 0x2649bd8>) of role type named cX
% 2.13/2.29 Using role type
% 2.13/2.29 Declaring cX:fofType
% 2.13/2.29 FOF formula (<kernel.Constant object at 0x2649e18>, <kernel.DependentProduct object at 0x266b2d8>) of role type named cS
% 2.13/2.29 Using role type
% 2.13/2.29 Declaring cS:(fofType->Prop)
% 2.13/2.29 FOF formula (<kernel.Constant object at 0x2649bd8>, <kernel.DependentProduct object at 0x266b290>) of role type named cT
% 2.13/2.29 Using role type
% 2.13/2.29 Declaring cT:(fofType->Prop)
% 2.13/2.29 FOF formula (<kernel.Constant object at 0x2649e18>, <kernel.DependentProduct object at 0x266b2d8>) of role type named cP
% 2.13/2.29 Using role type
% 2.13/2.29 Declaring cP:((fofType->Prop)->Prop)
% 2.13/2.29 FOF formula (((and ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))->((and (cP cT)) (cS cX))) of role conjecture named cTHM503
% 2.13/2.29 Conjecture to prove = (((and ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))->((and (cP cT)) (cS cX))):Prop
% 2.13/2.29 We need to prove ['(((and ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))->((and (cP cT)) (cS cX)))']
% 2.13/2.29 Parameter fofType:Type.
% 2.13/2.29 Parameter cX:fofType.
% 2.13/2.29 Parameter cS:(fofType->Prop).
% 2.13/2.29 Parameter cT:(fofType->Prop).
% 2.13/2.29 Parameter cP:((fofType->Prop)->Prop).
% 2.13/2.29 Trying to prove (((and ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))->((and (cP cT)) (cS cX)))
% 2.13/2.29 Found x2:(cP cS)
% 2.13/2.29 Found x2 as proof of (cP cS)
% 2.13/2.29 Found x2:(cP cS)
% 2.13/2.29 Found x2 as proof of (cP cS)
% 2.13/2.29 Found x100:=(x10 x2):(cP cT)
% 2.13/2.29 Found (x10 x2) as proof of (cP cT)
% 2.13/2.29 Found ((x1 cP) x2) as proof of (cP cT)
% 2.13/2.29 Found ((x1 cP) x2) as proof of (cP cT)
% 2.13/2.29 Found x2:(cP cS)
% 2.13/2.29 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 2.13/2.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 2.13/2.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 2.13/2.29 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 2.13/2.29 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 2.13/2.29 Found (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 2.13/2.29 Found (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 2.13/2.29 Found x100:=(x10 x2):(cP cT)
% 2.13/2.29 Found (x10 x2) as proof of (cP cT)
% 2.13/2.29 Found ((x1 cP) x2) as proof of (cP cT)
% 2.13/2.29 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 2.13/2.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 2.13/2.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 2.13/2.29 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 2.13/2.29 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 2.13/2.29 Found (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 2.13/2.29 Found (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 2.13/2.29 Found x100:=(x10 x2):(cP cT)
% 2.13/2.29 Found (x10 x2) as proof of (cP cT)
% 2.13/2.29 Found ((x1 cP) x2) as proof of (cP cT)
% 2.13/2.29 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 2.13/2.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 2.13/2.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 2.13/2.29 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 2.13/2.29 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 2.13/2.29 Found (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 2.13/2.29 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 3.56/3.71 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 3.56/3.71 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 3.56/3.71 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 3.56/3.71 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 3.56/3.71 Found (((fun (P:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 3.56/3.71 Found (((fun (P:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P:Type) (x2:((cP cS)->((cT cX)->P)))=> (((((and_rect (cP cS)) (cT cX)) P) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 3.56/3.71 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 3.56/3.71 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 3.56/3.71 Instantiate: b:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% 3.56/3.71 Found conj as proof of b
% 3.56/3.71 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 3.56/3.71 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found x0:((and (cP cS)) (cT cX))
% 3.56/3.71 Instantiate: b:=(cT cX):Prop
% 3.56/3.71 Found x0 as proof of (P b)
% 3.56/3.71 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 3.56/3.71 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 3.56/3.71 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 3.56/3.71 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 3.56/3.71 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 3.56/3.71 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 3.56/3.71 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 3.56/3.71 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 3.56/3.71 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 3.56/3.71 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 3.56/3.71 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 3.56/3.71 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 3.56/3.71 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 3.56/3.71 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 3.56/3.71 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 3.56/3.71 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 3.56/3.71 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 3.56/3.71 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 8.53/8.74 Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% 8.53/8.74 Found iff_refl as proof of b
% 8.53/8.74 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 8.53/8.74 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 8.53/8.74 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 8.53/8.74 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 8.53/8.74 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found x0:((and (cP cS)) (cT cX))
% 8.53/8.74 Instantiate: b:=(cT cX):Prop
% 8.53/8.74 Found x0 as proof of (P b)
% 8.53/8.74 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 8.53/8.74 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 8.53/8.74 Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% 8.53/8.74 Found iff_refl as proof of b
% 8.53/8.74 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 8.53/8.74 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found x0:((and (cP cS)) (cT cX))
% 8.53/8.74 Instantiate: b:=(cT cX):Prop
% 8.53/8.74 Found x0 as proof of (P b)
% 8.53/8.74 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 8.53/8.74 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 8.53/8.74 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 8.53/8.74 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 8.53/8.74 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 8.53/8.74 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 8.53/8.74 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 8.53/8.74 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 8.53/8.74 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 8.53/8.74 Found or_ind as proof of b
% 8.53/8.74 Found x100:=(x10 x2):(cP cT)
% 8.53/8.74 Found (x10 x2) as proof of (cP cT)
% 8.53/8.74 Found ((x1 cP) x2) as proof of (cP cT)
% 8.53/8.74 Found ((x1 cP) x2) as proof of (cP cT)
% 8.53/8.74 Found ((conj00 ((x1 cP) x2)) or_ind) as proof of (P b)
% 8.53/8.74 Found (((conj0 b) ((x1 cP) x2)) or_ind) as proof of (P b)
% 8.53/8.74 Found ((((conj (cP cT)) b) ((x1 cP) x2)) or_ind) as proof of (P b)
% 8.53/8.74 Found ((((conj (cP cT)) b) ((x1 cP) x2)) or_ind) as proof of (P b)
% 10.94/11.16 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 10.94/11.16 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 10.94/11.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 10.94/11.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 10.94/11.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 10.94/11.16 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 10.94/11.16 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 10.94/11.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 10.94/11.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 10.94/11.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 10.94/11.16 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 10.94/11.16 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 10.94/11.16 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 10.94/11.16 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 10.94/11.16 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 10.94/11.16 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 10.94/11.16 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 10.94/11.16 Found or_ind as proof of b
% 10.94/11.16 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 10.94/11.16 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 10.94/11.16 Found or_ind as proof of b
% 10.94/11.16 Found x100:=(x10 x2):(cP cT)
% 10.94/11.16 Found (x10 x2) as proof of (cP cT)
% 10.94/11.16 Found ((x1 cP) x2) as proof of (cP cT)
% 10.94/11.16 Found ((x1 cP) x2) as proof of (cP cT)
% 10.94/11.16 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P b)))
% 10.94/11.16 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P b)
% 10.94/11.16 Found ((and_rect1 (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P b)
% 10.94/11.16 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P b)
% 10.94/11.16 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P b)
% 10.94/11.16 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 10.94/11.16 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 10.94/11.16 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 10.94/11.16 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 10.94/11.16 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 10.94/11.16 Found x100:=(x10 x2):(cP cT)
% 10.94/11.16 Found (x10 x2) as proof of (cP cT)
% 10.94/11.16 Found ((x1 cP) x2) as proof of (cP cT)
% 10.94/11.16 Found ((x1 cP) x2) as proof of (cP cT)
% 10.94/11.16 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P b))
% 10.94/11.16 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P b)))
% 10.94/11.16 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P b)
% 10.94/11.16 Found ((and_rect1 (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P b)
% 10.94/11.16 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P b)
% 10.94/11.16 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (P b)
% 10.94/11.16 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of ((((eq (fofType->Prop)) cS) cT)->(P b))
% 14.13/14.29 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(P b)))
% 14.13/14.29 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P b)
% 14.13/14.29 Found ((and_rect0 (P b)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P b)
% 14.13/14.29 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (P b)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P b)
% 14.13/14.29 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (P b)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P b)
% 14.13/14.29 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 14.13/14.29 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 14.13/14.29 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 14.13/14.29 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 14.13/14.29 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found x100:=(x10 x2):(cP cT)
% 14.13/14.29 Found (x10 x2) as proof of (cP cT)
% 14.13/14.29 Found ((x1 cP) x2) as proof of (cP cT)
% 14.13/14.29 Found ((x1 cP) x2) as proof of (cP cT)
% 14.13/14.29 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 14.13/14.29 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 14.13/14.29 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 14.13/14.29 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 14.13/14.29 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 14.13/14.29 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 21.18/21.40 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 21.18/21.40 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 21.18/21.40 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 21.18/21.40 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 21.18/21.40 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x2:(cP cS)
% 21.18/21.40 Found x2 as proof of (cP cS)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 21.18/21.40 Found x100:=(x10 x2):(cP cT)
% 21.18/21.40 Found (x10 x2) as proof of (cP cT)
% 21.18/21.40 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found x2:(cP cS)
% 24.31/24.48 Found x2 as proof of (cP cS)
% 24.31/24.48 Found x100:=(x10 x2):(cP cT)
% 24.31/24.48 Found (x10 x2) as proof of (cP cT)
% 24.31/24.48 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 24.31/24.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 24.31/24.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 24.31/24.48 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found x100:=(x10 x2):(cP cT)
% 24.31/24.48 Found (x10 x2) as proof of (cP cT)
% 24.31/24.48 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 24.31/24.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 24.31/24.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 24.31/24.48 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found x100:=(x10 x2):(cP cT)
% 24.31/24.48 Found (x10 x2) as proof of (cP cT)
% 24.31/24.48 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found x100:=(x10 x2):(cP cT)
% 24.31/24.48 Found (x10 x2) as proof of (cP cT)
% 24.31/24.48 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found x100:=(x10 x2):(cP cT)
% 24.31/24.48 Found (x10 x2) as proof of (cP cT)
% 24.31/24.48 Found ((x1 cP) x2) as proof of (cP cT)
% 24.31/24.48 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 24.31/24.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 24.31/24.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 24.31/24.48 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.31/24.48 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 24.31/24.48 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 24.31/24.48 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 24.31/24.48 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 24.31/24.48 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 24.71/24.88 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 24.71/24.88 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 24.71/24.88 Found x2:(cP cS)
% 24.71/24.88 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 24.71/24.88 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found x2:(cP cS)
% 24.71/24.88 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 24.71/24.88 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found x2:(cP cS)
% 24.71/24.88 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 24.71/24.88 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found x2:(cP cS)
% 24.71/24.88 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 24.71/24.88 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.71/24.88 Found x100:=(x10 x2):(cP cT)
% 24.71/24.88 Found (x10 x2) as proof of (cP cT)
% 24.71/24.88 Found ((x1 cP) x2) as proof of (cP cT)
% 24.71/24.88 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 24.71/24.88 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 24.87/25.06 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found x100:=(x10 x2):(cP cT)
% 24.87/25.06 Found (x10 x2) as proof of (cP cT)
% 24.87/25.06 Found ((x1 cP) x2) as proof of (cP cT)
% 24.87/25.06 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 24.87/25.06 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found x2:(cP cS)
% 24.87/25.06 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 24.87/25.06 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.87/25.06 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.87/25.06 Found x2:(cP cS)
% 24.87/25.06 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 24.87/25.06 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.87/25.06 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 24.87/25.06 Found x100:=(x10 x2):(cP cT)
% 24.87/25.06 Found (x10 x2) as proof of (cP cT)
% 24.87/25.06 Found ((x1 cP) x2) as proof of (cP cT)
% 24.87/25.06 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 24.87/25.06 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 24.87/25.06 Found x100:=(x10 x2):(cP cT)
% 24.87/25.06 Found (x10 x2) as proof of (cP cT)
% 24.87/25.06 Found ((x1 cP) x2) as proof of (cP cT)
% 24.87/25.06 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 24.87/25.06 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 25.07/25.29 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found x2:(cP cS)
% 25.07/25.29 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 25.07/25.29 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 25.07/25.29 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 25.07/25.29 Found x100:=(x10 x2):(cP cT)
% 25.07/25.29 Found (x10 x2) as proof of (cP cT)
% 25.07/25.29 Found ((x1 cP) x2) as proof of (cP cT)
% 25.07/25.29 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 25.07/25.29 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found x2:(cP cS)
% 25.07/25.29 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 25.07/25.29 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 25.07/25.29 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 25.07/25.29 Found x100:=(x10 x2):(cP cT)
% 25.07/25.29 Found (x10 x2) as proof of (cP cT)
% 25.07/25.29 Found ((x1 cP) x2) as proof of (cP cT)
% 25.07/25.29 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 25.07/25.29 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 25.07/25.29 Found x100:=(x10 x2):(cP cT)
% 25.07/25.29 Found (x10 x2) as proof of (cP cT)
% 25.07/25.29 Found ((x1 cP) x2) as proof of (cP cT)
% 25.07/25.29 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 25.07/25.29 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 27.29/27.45 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found x100:=(x10 x2):(cP cT)
% 27.29/27.45 Found (x10 x2) as proof of (cP cT)
% 27.29/27.45 Found ((x1 cP) x2) as proof of (cP cT)
% 27.29/27.45 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 27.29/27.45 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 27.29/27.45 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 27.29/27.45 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 27.29/27.45 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 27.29/27.45 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 27.29/27.45 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 27.29/27.45 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 27.29/27.45 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.29/27.45 Found (eq_ref0 b) as proof of (((eq Prop) b) (cS cX))
% 27.29/27.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 27.29/27.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 27.29/27.45 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 27.29/27.45 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 27.29/27.45 Instantiate: a:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 27.29/27.45 Found iff_sym as proof of a
% 27.29/27.45 Found x100:=(x10 x2):(cP cT)
% 27.29/27.45 Found (x10 x2) as proof of (cP cT)
% 27.29/27.45 Found ((x1 cP) x2) as proof of (cP cT)
% 27.29/27.45 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 27.29/27.45 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 27.29/27.45 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 27.29/27.45 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.29/27.45 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 27.29/27.45 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 27.29/27.45 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 27.29/27.45 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.29/27.45 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.68 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.68 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.68 Found x100:=(x10 x2):(cP cT)
% 27.51/27.68 Found (x10 x2) as proof of (cP cT)
% 27.51/27.68 Found ((x1 cP) x2) as proof of (cP cT)
% 27.51/27.68 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 27.51/27.68 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 27.51/27.68 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 27.51/27.68 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.68 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.68 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.68 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 27.51/27.68 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 27.51/27.68 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 27.51/27.68 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.68 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.68 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.68 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.68 Found x100:=(x10 x2):(cP cT)
% 27.51/27.68 Found (x10 x2) as proof of (cP cT)
% 27.51/27.71 Found ((x1 cP) x2) as proof of (cP cT)
% 27.51/27.71 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 27.51/27.71 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 27.51/27.71 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 27.51/27.71 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.71 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.71 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.71 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 27.51/27.71 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 27.51/27.71 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 27.51/27.71 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.71 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.71 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.71 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 27.51/27.71 Found x100:=(x10 x2):(cP cT)
% 27.51/27.71 Found (x10 x2) as proof of (cP cT)
% 27.51/27.71 Found ((x1 cP) x2) as proof of (cP cT)
% 27.51/27.71 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 27.51/27.71 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 27.51/27.71 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 27.51/27.71 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.71 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.71 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 27.51/27.71 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 27.51/27.71 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 27.51/27.71 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 33.94/34.11 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 33.94/34.11 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 33.94/34.11 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 33.94/34.11 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 33.94/34.11 Found x0:((and (cP cS)) (cT cX))
% 33.94/34.11 Instantiate: a:=(cT cX):Prop
% 33.94/34.11 Found x0 as proof of (P a)
% 33.94/34.11 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 33.94/34.11 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.94/34.11 Found (eq_ref0 b) as proof of (((eq Prop) b) (cS cX))
% 33.94/34.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 33.94/34.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 33.94/34.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 33.94/34.11 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 33.94/34.11 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 33.94/34.11 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 33.94/34.11 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 33.94/34.11 Found (eq_ref0 b) as proof of (((eq Prop) b) (cS cX))
% 33.94/34.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 33.94/34.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 33.94/34.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 33.94/34.11 Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 33.94/34.11 Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% 33.94/34.11 Found eq_sym as proof of a
% 33.94/34.11 Found x1:(((eq (fofType->Prop)) cS) cT)
% 33.94/34.11 Instantiate: b:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 33.94/34.11 Found x1 as proof of a
% 33.94/34.11 Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 33.94/34.11 Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% 33.94/34.11 Found eq_sym as proof of a
% 33.94/34.11 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 33.94/34.11 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 33.94/34.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 33.94/34.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 33.94/34.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 33.94/34.11 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 41.53/41.70 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 41.53/41.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 41.53/41.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 41.53/41.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 41.53/41.70 Found x1:(((eq (fofType->Prop)) cS) cT)
% 41.53/41.70 Instantiate: b:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 41.53/41.70 Found x1 as proof of a
% 41.53/41.70 Found x0:((and (cP cS)) (cT cX))
% 41.53/41.70 Instantiate: a:=(cT cX):Prop
% 41.53/41.70 Found x0 as proof of (P a)
% 41.53/41.70 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 41.53/41.70 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 41.53/41.70 Found (eq_ref0 b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 41.53/41.70 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 41.53/41.70 Found (eq_ref0 b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 41.53/41.70 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 41.53/41.70 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 41.53/41.70 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 41.53/41.70 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 41.53/41.70 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 41.53/41.70 Found x0:((and (cP cS)) (cT cX))
% 41.53/41.70 Instantiate: a:=(cT cX):Prop
% 41.53/41.70 Found x0 as proof of (P a)
% 41.53/41.70 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 41.53/41.70 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 41.53/41.70 Found (eq_ref0 b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (cS cX))
% 41.53/41.70 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 41.53/41.70 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 41.53/41.70 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 49.03/49.19 Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 49.03/49.19 Found classical_choice as proof of a
% 49.03/49.19 Found x1:(((eq (fofType->Prop)) cS) cT)
% 49.03/49.19 Instantiate: b:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 49.03/49.19 Found x1 as proof of a
% 49.03/49.19 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 49.03/49.19 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 49.03/49.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 49.03/49.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 49.03/49.19 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 49.03/49.19 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 49.03/49.19 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 49.03/49.19 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 49.03/49.19 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 49.03/49.19 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 49.03/49.19 Found x100:=(x10 x2):(cP cT)
% 49.03/49.19 Found (x10 x2) as proof of (cP cT)
% 49.03/49.19 Found ((x1 cP) x2) as proof of (cP cT)
% 49.03/49.19 Found ((x1 cP) x2) as proof of (cP cT)
% 49.03/49.19 Found ((conj00 ((x1 cP) x2)) classical_choice) as proof of (P a)
% 49.03/49.19 Found (((conj0 a) ((x1 cP) x2)) classical_choice) as proof of (P a)
% 49.03/49.19 Found ((((conj (cP cT)) a) ((x1 cP) x2)) classical_choice) as proof of (P a)
% 49.03/49.19 Found ((((conj (cP cT)) a) ((x1 cP) x2)) classical_choice) as proof of (P a)
% 49.03/49.19 Found x2:(cP cS)
% 49.03/49.19 Found x2 as proof of (cP cS)
% 49.03/49.19 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 49.03/49.19 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 49.03/49.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 49.03/49.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 49.03/49.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 49.03/49.19 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 49.03/49.19 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 49.03/49.19 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 49.03/49.19 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 49.03/49.19 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 49.03/49.19 Found x100:=(x10 x2):(cP cT)
% 49.03/49.19 Found (x10 x2) as proof of (cP cT)
% 49.03/49.19 Found ((x1 cP) x2) as proof of (cP cT)
% 49.03/49.19 Found ((x1 cP) x2) as proof of (cP cT)
% 49.03/49.19 Found ((conj00 ((x1 cP) x2)) x1) as proof of (P a)
% 49.03/49.19 Found (((conj0 a) ((x1 cP) x2)) x1) as proof of (P a)
% 49.03/49.19 Found ((((conj (cP cT)) a) ((x1 cP) x2)) x1) as proof of (P a)
% 49.03/49.19 Found ((((conj (cP cT)) a) ((x1 cP) x2)) x1) as proof of (P a)
% 49.03/49.19 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 49.03/49.19 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 49.03/49.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 49.03/49.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 49.03/49.19 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 49.03/49.19 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 49.03/49.19 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 49.03/49.19 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 49.03/49.19 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 49.03/49.19 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 49.03/49.19 Found x100:=(x10 x2):(cP cT)
% 49.03/49.19 Found (x10 x2) as proof of (cP cT)
% 49.03/49.19 Found ((x1 cP) x2) as proof of (cP cT)
% 49.03/49.19 Found ((x1 cP) x2) as proof of (cP cT)
% 49.03/49.19 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 51.82/52.00 Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 51.82/52.00 Found classical_choice as proof of a
% 51.82/52.00 Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% 51.82/52.00 Instantiate: a:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% 51.82/52.00 Found classical_choice as proof of a
% 51.82/52.00 Found conj10:=(conj1 (((eq (fofType->Prop)) cS) cT)):(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->((and ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))))
% 51.82/52.00 Found (conj1 (((eq (fofType->Prop)) cS) cT)) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->a))
% 51.82/52.00 Found ((conj ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->a))
% 51.82/52.00 Found ((conj ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->a))
% 51.82/52.00 Found ((conj ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->a))
% 51.82/52.00 Found (and_rect00 ((conj ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))) as proof of a
% 51.82/52.00 Found ((and_rect0 a) ((conj ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))) as proof of a
% 51.82/52.00 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) a) ((conj ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))) as proof of a
% 51.82/52.00 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) a) ((conj ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT))) as proof of a
% 51.82/52.00 Found x1:(((eq (fofType->Prop)) cS) cT)
% 51.82/52.00 Instantiate: b:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 51.82/52.00 Found x1 as proof of a
% 51.82/52.00 Found x100:=(x10 x2):(cP cT)
% 51.82/52.00 Found (x10 x2) as proof of (cP cT)
% 51.82/52.00 Found ((x1 cP) x2) as proof of (cP cT)
% 51.82/52.00 Found ((x1 cP) x2) as proof of (cP cT)
% 52.09/52.24 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P a)))
% 52.09/52.24 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 52.09/52.24 Found ((and_rect1 (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 52.09/52.24 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 52.09/52.24 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 52.09/52.24 Found x1:(((eq (fofType->Prop)) cS) cT)
% 52.09/52.24 Instantiate: b:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 52.09/52.24 Found x1 as proof of a
% 52.09/52.24 Found x100:=(x10 x2):(cP cT)
% 52.09/52.24 Found (x10 x2) as proof of (cP cT)
% 52.09/52.24 Found ((x1 cP) x2) as proof of (cP cT)
% 52.09/52.24 Found ((x1 cP) x2) as proof of (cP cT)
% 52.09/52.24 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P a))
% 52.09/52.24 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P a)))
% 52.09/52.24 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 52.09/52.24 Found ((and_rect1 (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 52.09/52.24 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 52.09/52.24 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (P a)
% 52.09/52.24 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of ((((eq (fofType->Prop)) cS) cT)->(P a))
% 52.09/52.24 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(P a)))
% 52.09/52.24 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P a)
% 52.09/52.24 Found ((and_rect0 (P a)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P a)
% 52.09/52.24 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (P a)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P a)
% 52.09/52.24 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (P a)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P a)
% 53.39/53.61 Found x2:(cP cS)
% 53.39/53.61 Found x2 as proof of (cP cS)
% 53.39/53.61 Found x2:(cP cS)
% 53.39/53.61 Found x2 as proof of (cP cS)
% 53.39/53.61 Found x2:(cP cS)
% 53.39/53.61 Found x2 as proof of (cP cS)
% 53.39/53.61 Found x2:(cP cS)
% 53.39/53.61 Found x2 as proof of (cP cS)
% 53.39/53.61 Found x2:(cP cS)
% 53.39/53.61 Found x2 as proof of (cP cS)
% 53.39/53.61 Found x100:=(x10 x2):(cP cT)
% 53.39/53.61 Found (x10 x2) as proof of (cP cT)
% 53.39/53.61 Found ((x1 cP) x2) as proof of (cP cT)
% 53.39/53.61 Found ((x1 cP) x2) as proof of (cP cT)
% 53.39/53.61 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P a)))
% 53.39/53.61 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 53.39/53.61 Found ((and_rect1 (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 53.39/53.61 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 53.39/53.61 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 53.39/53.61 Found x100:=(x10 x2):(cP cT)
% 53.39/53.61 Found (x10 x2) as proof of (cP cT)
% 53.39/53.61 Found ((x1 cP) x2) as proof of (cP cT)
% 53.39/53.61 Found ((x1 cP) x2) as proof of (cP cT)
% 53.39/53.61 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P a))
% 53.39/53.61 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P a)))
% 53.39/53.61 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 53.39/53.61 Found ((and_rect1 (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 53.39/53.61 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P a)
% 53.39/53.61 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (P a)
% 53.39/53.61 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of ((((eq (fofType->Prop)) cS) cT)->(P a))
% 53.39/53.61 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(P a)))
% 53.39/53.61 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P a)
% 53.39/53.61 Found ((and_rect0 (P a)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P a)
% 62.23/62.41 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (P a)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P a)
% 62.23/62.41 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (P a)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (P a)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P a)
% 62.23/62.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.23/62.41 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 62.23/62.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 62.23/62.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 62.23/62.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 62.23/62.41 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 62.23/62.41 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 62.23/62.41 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 62.23/62.41 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 62.23/62.41 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found x100:=(x10 x2):(cP cT)
% 62.23/62.41 Found (x10 x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found x100:=(x10 x2):(cP cT)
% 62.23/62.41 Found (x10 x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found x100:=(x10 x2):(cP cT)
% 62.23/62.41 Found (x10 x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found x100:=(x10 x2):(cP cT)
% 62.23/62.41 Found (x10 x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found x100:=(x10 x2):(cP cT)
% 62.23/62.41 Found (x10 x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found x100:=(x10 x2):(cP cT)
% 62.23/62.41 Found (x10 x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found ((x1 cP) x2) as proof of (cP cT)
% 62.23/62.41 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 62.23/62.41 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 62.23/62.41 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 62.23/62.41 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 62.23/62.41 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 62.23/62.41 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 62.23/62.41 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 62.23/62.41 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 62.23/62.41 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found x2:(cP cS)
% 62.23/62.41 Found x2 as proof of (cP cS)
% 62.23/62.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.23/62.41 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 62.23/62.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 62.23/62.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 62.23/62.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 62.23/62.41 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 62.23/62.41 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 62.23/62.41 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 62.23/62.41 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 62.23/62.41 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 62.23/62.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 62.23/62.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 62.23/62.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 67.52/67.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 67.52/67.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 67.52/67.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.52/67.69 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 67.52/67.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 67.52/67.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 67.52/67.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 67.52/67.69 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 67.52/67.69 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 67.52/67.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 67.52/67.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 67.52/67.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 67.52/67.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 67.52/67.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 67.52/67.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 67.52/67.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 67.52/67.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 67.52/67.69 Found x2:(cP cS)
% 67.52/67.69 Found x2 as proof of (cP cS)
% 67.52/67.69 Found x2:(cP cS)
% 67.52/67.69 Found x2 as proof of (cP cS)
% 67.52/67.69 Found x2:(cP cS)
% 67.52/67.69 Found x2 as proof of (cP cS)
% 67.52/67.69 Found x2:(cP cS)
% 67.52/67.69 Found x2 as proof of (cP cS)
% 67.52/67.69 Found x2:(cP cS)
% 67.52/67.69 Found x2 as proof of (cP cS)
% 67.52/67.69 Found x100:=(x10 x2):(cP cT)
% 67.52/67.69 Found (x10 x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found x100:=(x10 x2):(cP cT)
% 67.52/67.69 Found (x10 x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found x2:(cP cS)
% 67.52/67.69 Found x2 as proof of (cP cS)
% 67.52/67.69 Found x100:=(x10 x2):(cP cT)
% 67.52/67.69 Found (x10 x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found x2:(cP cS)
% 67.52/67.69 Found x2 as proof of (cP cS)
% 67.52/67.69 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 67.52/67.69 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 67.52/67.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 67.52/67.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 67.52/67.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 67.52/67.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 67.52/67.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 67.52/67.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 67.52/67.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 67.52/67.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 67.52/67.69 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 67.52/67.69 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 67.52/67.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 67.52/67.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 67.52/67.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 67.52/67.69 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 67.52/67.69 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 67.52/67.69 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 67.52/67.69 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 67.52/67.69 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 67.52/67.69 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 67.52/67.69 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 67.52/67.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 67.52/67.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 67.52/67.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 67.52/67.69 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 67.52/67.69 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 67.52/67.69 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 67.52/67.69 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 67.52/67.69 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 67.52/67.69 Found x100:=(x10 x2):(cP cT)
% 67.52/67.69 Found (x10 x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found x2:(cP cS)
% 67.52/67.69 Found x2 as proof of (cP cS)
% 67.52/67.69 Found x100:=(x10 x2):(cP cT)
% 67.52/67.69 Found (x10 x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found ((x1 cP) x2) as proof of (cP cT)
% 67.52/67.69 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 67.52/67.69 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 67.52/67.69 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 67.52/67.69 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 67.52/67.69 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 67.52/67.69 Found x100:=(x10 x2):(cP cT)
% 75.40/75.56 Found (x10 x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 75.40/75.56 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 75.40/75.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 75.40/75.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 75.40/75.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 75.40/75.56 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 75.40/75.56 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 75.40/75.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 75.40/75.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 75.40/75.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 75.40/75.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 75.40/75.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 75.40/75.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 75.40/75.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 75.40/75.56 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 75.40/75.56 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 75.40/75.56 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 75.40/75.56 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 75.40/75.56 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x100:=(x10 x2):(cP cT)
% 75.40/75.56 Found (x10 x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x100:=(x10 x2):(cP cT)
% 75.40/75.56 Found (x10 x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x100:=(x10 x2):(cP cT)
% 75.40/75.56 Found (x10 x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found x100:=(x10 x2):(cP cT)
% 75.40/75.56 Found (x10 x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found x2:(cP cS)
% 75.40/75.56 Found x2 as proof of (cP cS)
% 75.40/75.56 Found x100:=(x10 x2):(cP cT)
% 75.40/75.56 Found (x10 x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found x100:=(x10 x2):(cP cT)
% 75.40/75.56 Found (x10 x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found ((x1 cP) x2) as proof of (cP cT)
% 75.40/75.56 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 75.40/75.56 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 75.40/75.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 75.40/75.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 76.74/76.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 76.74/76.92 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 76.74/76.92 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 76.74/76.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 76.74/76.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 76.74/76.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x100:=(x10 x2):(cP cT)
% 76.74/76.92 Found (x10 x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found x100:=(x10 x2):(cP cT)
% 76.74/76.92 Found (x10 x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x100:=(x10 x2):(cP cT)
% 76.74/76.92 Found (x10 x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 76.74/76.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 76.74/76.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 76.74/76.92 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 76.74/76.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 76.74/76.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 76.74/76.92 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 76.74/76.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 76.74/76.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 76.74/76.92 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x100:=(x10 x2):(cP cT)
% 76.74/76.92 Found (x10 x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found x100:=(x10 x2):(cP cT)
% 76.74/76.92 Found (x10 x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found x100:=(x10 x2):(cP cT)
% 76.74/76.92 Found (x10 x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found x100:=(x10 x2):(cP cT)
% 76.74/76.92 Found (x10 x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found ((x1 cP) x2) as proof of (cP cT)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found x2:(cP cS)
% 76.74/76.92 Found x2 as proof of (cP cS)
% 76.74/76.92 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 76.74/76.92 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 77.89/78.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 77.89/78.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 77.89/78.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 77.89/78.05 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 77.89/78.05 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 77.89/78.05 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 77.89/78.05 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 77.89/78.05 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 77.89/78.05 Found x100:=(x10 x2):(cP cT)
% 77.89/78.05 Found (x10 x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found x100:=(x10 x2):(cP cT)
% 77.89/78.05 Found (x10 x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 77.89/78.05 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 77.89/78.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 77.89/78.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 77.89/78.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 77.89/78.05 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 77.89/78.05 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 77.89/78.05 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 77.89/78.05 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 77.89/78.05 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 77.89/78.05 Found x2:(cP cS)
% 77.89/78.05 Found x2 as proof of (cP cS)
% 77.89/78.05 Found x100:=(x10 x2):(cP cT)
% 77.89/78.05 Found (x10 x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found x2:(cP cS)
% 77.89/78.05 Found x2 as proof of (cP cS)
% 77.89/78.05 Found x100:=(x10 x2):(cP cT)
% 77.89/78.05 Found (x10 x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found x100:=(x10 x2):(cP cT)
% 77.89/78.05 Found (x10 x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 77.89/78.05 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 77.89/78.05 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 77.89/78.05 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found x100:=(x10 x2):(cP cT)
% 77.89/78.05 Found (x10 x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 77.89/78.05 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 77.89/78.05 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 77.89/78.05 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found x100:=(x10 x2):(cP cT)
% 77.89/78.05 Found (x10 x2) as proof of (cP cT)
% 77.89/78.05 Found ((x1 cP) x2) as proof of (cP cT)
% 77.89/78.05 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 77.89/78.05 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 77.89/78.05 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 77.89/78.05 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 77.89/78.05 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 84.16/84.34 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 84.16/84.34 Found x2:(cP cS)
% 84.16/84.34 Found x2 as proof of (cP cS)
% 84.16/84.34 Found x100:=(x10 x2):(cP cT)
% 84.16/84.34 Found (x10 x2) as proof of (cP cT)
% 84.16/84.34 Found ((x1 cP) x2) as proof of (cP cT)
% 84.16/84.34 Found ((x1 cP) x2) as proof of (cP cT)
% 84.16/84.34 Found x100:=(x10 x2):(cP cT)
% 84.16/84.34 Found (x10 x2) as proof of (cP cT)
% 84.16/84.34 Found ((x1 cP) x2) as proof of (cP cT)
% 84.16/84.34 Found ((x1 cP) x2) as proof of (cP cT)
% 84.16/84.34 Found x100:=(x10 x2):(cP cT)
% 84.16/84.34 Found (x10 x2) as proof of (cP cT)
% 84.16/84.34 Found ((x1 cP) x2) as proof of (cP cT)
% 84.16/84.34 Found ((x1 cP) x2) as proof of (cP cT)
% 84.16/84.34 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 84.16/84.34 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 84.16/84.34 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 84.16/84.34 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 84.16/84.34 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 84.16/84.34 Found (eq_ref0 b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cX)
% 84.16/84.34 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 84.16/84.34 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 84.16/84.34 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 84.16/84.34 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 84.16/84.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 84.16/84.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 84.16/84.34 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 84.16/84.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 84.16/84.34 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 84.16/84.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 84.16/84.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 84.16/84.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 84.16/84.34 Found x100:=(x10 x2):(cP cT)
% 84.16/84.34 Found (x10 x2) as proof of (cP cT)
% 84.16/84.34 Found ((x1 cP) x2) as proof of (cP cT)
% 84.16/84.34 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 84.16/84.34 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 84.16/84.34 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 84.16/84.34 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 84.16/84.34 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 84.16/84.34 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 84.16/84.34 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 84.16/84.34 Found x100:=(x10 x2):(cP cT)
% 84.16/84.34 Found (x10 x2) as proof of (cP cT)
% 84.16/84.34 Found ((x1 cP) x2) as proof of (cP cT)
% 84.16/84.34 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 84.16/84.34 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 84.16/84.34 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 88.95/89.12 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 88.95/89.12 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 88.95/89.12 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 88.95/89.12 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 88.95/89.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 88.95/89.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 88.95/89.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 88.95/89.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 88.95/89.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 88.95/89.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 88.95/89.12 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 88.95/89.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 88.95/89.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 88.95/89.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 88.95/89.12 Found x2:(cP cS)
% 88.95/89.12 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 88.95/89.12 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 88.95/89.12 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 88.95/89.12 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 88.95/89.12 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 88.95/89.12 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 88.95/89.12 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 88.95/89.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 88.95/89.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 88.95/89.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 88.95/89.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 88.95/89.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 88.95/89.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 88.95/89.12 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 88.95/89.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 88.95/89.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 88.95/89.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 88.95/89.12 Found x100:=(x10 x2):(cP cT)
% 88.95/89.12 Found (x10 x2) as proof of (cP cT)
% 88.95/89.12 Found ((x1 cP) x2) as proof of (cP cT)
% 88.95/89.12 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 88.95/89.12 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 88.95/89.12 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 88.95/89.12 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 88.95/89.12 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 88.95/89.12 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 88.95/89.12 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 88.95/89.12 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 88.95/89.12 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 88.95/89.12 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 89.14/89.35 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 89.14/89.35 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 89.14/89.35 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 89.14/89.35 Found x2:(cP cS)
% 89.14/89.35 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 89.14/89.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 89.14/89.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 89.14/89.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found x2:(cP cS)
% 89.14/89.35 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 89.14/89.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 89.14/89.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 89.14/89.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found x2:(cP cS)
% 89.14/89.35 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 89.14/89.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 89.14/89.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 89.14/89.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found x2:(cP cS)
% 89.14/89.35 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 89.14/89.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 89.14/89.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 89.14/89.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.14/89.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found x2:(cP cS)
% 89.83/90.01 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 89.83/90.01 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found x2:(cP cS)
% 89.83/90.01 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 89.83/90.01 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found x100:=(x10 x2):(cP cT)
% 89.83/90.01 Found (x10 x2) as proof of (cP cT)
% 89.83/90.01 Found ((x1 cP) x2) as proof of (cP cT)
% 89.83/90.01 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 89.83/90.01 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 89.83/90.01 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 89.83/90.01 Found x2:(cP cS)
% 89.83/90.01 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 89.83/90.01 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 89.83/90.01 Found x100:=(x10 x2):(cP cT)
% 89.83/90.01 Found (x10 x2) as proof of (cP cT)
% 89.83/90.01 Found ((x1 cP) x2) as proof of (cP cT)
% 89.83/90.01 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 89.83/90.01 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 89.83/90.01 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 89.83/90.01 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 89.83/90.01 Found x2:(cP cS)
% 89.83/90.01 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 89.83/90.01 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.19/90.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found x2:(cP cS)
% 90.19/90.35 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.19/90.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found x100:=(x10 x2):(cP cT)
% 90.19/90.35 Found (x10 x2) as proof of (cP cT)
% 90.19/90.35 Found ((x1 cP) x2) as proof of (cP cT)
% 90.19/90.35 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 90.19/90.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.19/90.35 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.19/90.35 Found x2:(cP cS)
% 90.19/90.35 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.19/90.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found x2:(cP cS)
% 90.19/90.35 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.19/90.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found x2:(cP cS)
% 90.19/90.35 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.19/90.35 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.19/90.35 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.19/90.35 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found x2:(cP cS)
% 90.47/90.62 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.47/90.62 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found x2:(cP cS)
% 90.47/90.62 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.47/90.62 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found x100:=(x10 x2):(cP cT)
% 90.47/90.62 Found (x10 x2) as proof of (cP cT)
% 90.47/90.62 Found ((x1 cP) x2) as proof of (cP cT)
% 90.47/90.62 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 90.47/90.62 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.47/90.62 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.47/90.62 Found x2:(cP cS)
% 90.47/90.62 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.47/90.62 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.47/90.62 Found x100:=(x10 x2):(cP cT)
% 90.47/90.62 Found (x10 x2) as proof of (cP cT)
% 90.47/90.62 Found ((x1 cP) x2) as proof of (cP cT)
% 90.47/90.62 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 90.47/90.62 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 90.47/90.62 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.47/90.62 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.47/90.62 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found x2:(cP cS)
% 90.64/90.85 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.64/90.85 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.64/90.85 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.64/90.85 Found x100:=(x10 x2):(cP cT)
% 90.64/90.85 Found (x10 x2) as proof of (cP cT)
% 90.64/90.85 Found ((x1 cP) x2) as proof of (cP cT)
% 90.64/90.85 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 90.64/90.85 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found x100:=(x10 x2):(cP cT)
% 90.64/90.85 Found (x10 x2) as proof of (cP cT)
% 90.64/90.85 Found ((x1 cP) x2) as proof of (cP cT)
% 90.64/90.85 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 90.64/90.85 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found x100:=(x10 x2):(cP cT)
% 90.64/90.85 Found (x10 x2) as proof of (cP cT)
% 90.64/90.85 Found ((x1 cP) x2) as proof of (cP cT)
% 90.64/90.85 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 90.64/90.85 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 90.64/90.85 Found x2:(cP cS)
% 90.64/90.85 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 90.64/90.85 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 90.64/90.85 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.64/90.85 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 90.64/90.85 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found x2:(cP cS)
% 91.02/91.25 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 91.02/91.25 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found x100:=(x10 x2):(cP cT)
% 91.02/91.25 Found (x10 x2) as proof of (cP cT)
% 91.02/91.25 Found ((x1 cP) x2) as proof of (cP cT)
% 91.02/91.25 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 91.02/91.25 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.02/91.25 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.02/91.25 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.02/91.25 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.02/91.25 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 91.02/91.25 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 91.02/91.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 91.02/91.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 91.02/91.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 91.02/91.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 91.02/91.25 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 91.02/91.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 91.02/91.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 91.02/91.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 91.02/91.25 Found x2:(cP cS)
% 91.02/91.25 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 91.02/91.25 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 91.02/91.25 Found x100:=(x10 x2):(cP cT)
% 91.02/91.25 Found (x10 x2) as proof of (cP cT)
% 91.02/91.25 Found ((x1 cP) x2) as proof of (cP cT)
% 91.02/91.25 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 91.02/91.25 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.02/91.25 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.02/91.25 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.02/91.25 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.02/91.25 Found x100:=(x10 x2):(cP cT)
% 91.02/91.25 Found (x10 x2) as proof of (cP cT)
% 91.02/91.25 Found ((x1 cP) x2) as proof of (cP cT)
% 91.02/91.25 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 91.02/91.25 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 91.74/91.93 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found x100:=(x10 x2):(cP cT)
% 91.74/91.93 Found (x10 x2) as proof of (cP cT)
% 91.74/91.93 Found ((x1 cP) x2) as proof of (cP cT)
% 91.74/91.93 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 91.74/91.93 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 91.74/91.93 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 91.74/91.93 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found x100:=(x10 x2):(cP cT)
% 91.74/91.93 Found (x10 x2) as proof of (cP cT)
% 91.74/91.93 Found ((x1 cP) x2) as proof of (cP cT)
% 91.74/91.93 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 91.74/91.93 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 91.74/91.93 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 91.74/91.93 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 91.74/91.93 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 91.74/91.93 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 91.74/91.93 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 91.74/91.93 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 91.74/91.93 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 91.74/91.93 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 91.74/91.93 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.29/93.48 Found x100:=(x10 x2):(cP cT)
% 93.29/93.48 Found (x10 x2) as proof of (cP cT)
% 93.29/93.48 Found ((x1 cP) x2) as proof of (cP cT)
% 93.29/93.48 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 93.29/93.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 93.29/93.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 93.29/93.48 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.29/93.48 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.29/93.48 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.29/93.48 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 93.29/93.48 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 93.29/93.48 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 93.29/93.48 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.29/93.48 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.29/93.48 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.29/93.48 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.29/93.48 Found x100:=(x10 x2):(cP cT)
% 93.29/93.48 Found (x10 x2) as proof of (cP cT)
% 93.29/93.48 Found ((x1 cP) x2) as proof of (cP cT)
% 93.29/93.48 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 93.29/93.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 93.29/93.48 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 93.29/93.48 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.29/93.48 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.29/93.48 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.29/93.48 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 93.37/93.56 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 93.37/93.56 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 93.37/93.56 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.37/93.56 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.37/93.56 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.37/93.56 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.37/93.56 Found x100:=(x10 x2):(cP cT)
% 93.37/93.56 Found (x10 x2) as proof of (cP cT)
% 93.37/93.56 Found ((x1 cP) x2) as proof of (cP cT)
% 93.37/93.56 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 93.37/93.56 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 93.37/93.56 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 93.37/93.56 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.37/93.56 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.37/93.56 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 93.37/93.56 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 93.37/93.56 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 93.37/93.56 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 93.37/93.56 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.37/93.56 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 93.37/93.56 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 99.77/99.92 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 99.77/99.92 Found x100:=(x10 x2):(cP cT)
% 99.77/99.92 Found (x10 x2) as proof of (cP cT)
% 99.77/99.92 Found ((x1 cP) x2) as proof of (cP cT)
% 99.77/99.92 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 99.77/99.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 99.77/99.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 99.77/99.92 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 99.77/99.92 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 99.77/99.92 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 99.77/99.92 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 99.77/99.92 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 99.77/99.92 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 99.77/99.92 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 99.77/99.92 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 99.77/99.92 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 99.77/99.92 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 99.77/99.92 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 99.77/99.92 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 99.77/99.92 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 99.77/99.92 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 99.77/99.92 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 99.77/99.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 99.77/99.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 114.44/114.61 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found x100:=(x10 x2):(cP cT)
% 114.44/114.61 Found (x10 x2) as proof of (cP cT)
% 114.44/114.61 Found ((x1 cP) x2) as proof of (cP cT)
% 114.44/114.61 Found ((x1 cP) x2) as proof of (cP cT)
% 114.44/114.61 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 114.44/114.61 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 114.44/114.61 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 114.44/114.61 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 114.44/114.61 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 114.44/114.61 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 114.44/114.61 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 114.44/114.61 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 114.44/114.61 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 114.44/114.61 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.44/114.61 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 114.44/114.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.44/114.61 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 114.44/114.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.44/114.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.44/114.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.44/114.61 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.44/114.61 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 114.44/114.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.44/114.61 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 114.44/114.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.44/114.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.44/114.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.44/114.61 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 114.44/114.61 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found x100:=(x10 x2):(cP cT)
% 114.44/114.61 Found (x10 x2) as proof of (cP cT)
% 114.44/114.61 Found ((x1 cP) x2) as proof of (cP cT)
% 114.44/114.61 Found ((x1 cP) x2) as proof of (cP cT)
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 114.44/114.61 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 114.44/114.61 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 114.44/114.61 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 114.44/114.61 Found x2:(cP cS)
% 114.44/114.61 Found x2 as proof of (cP cS)
% 114.44/114.61 Found x100:=(x10 x2):(cP cT)
% 114.44/114.61 Found (x10 x2) as proof of (cP cT)
% 127.52/127.69 Found ((x1 cP) x2) as proof of (cP cT)
% 127.52/127.69 Found ((x1 cP) x2) as proof of (cP cT)
% 127.52/127.69 Found x100:=(x10 x2):(cP cT)
% 127.52/127.69 Found (x10 x2) as proof of (cP cT)
% 127.52/127.69 Found ((x1 cP) x2) as proof of (cP cT)
% 127.52/127.69 Found ((x1 cP) x2) as proof of (cP cT)
% 127.52/127.69 Found x100:=(x10 x2):(cP cT)
% 127.52/127.69 Found (x10 x2) as proof of (cP cT)
% 127.52/127.69 Found ((x1 cP) x2) as proof of (cP cT)
% 127.52/127.69 Found ((x1 cP) x2) as proof of (cP cT)
% 127.52/127.69 Found x100:=(x10 x2):(cP cT)
% 127.52/127.69 Found (x10 x2) as proof of (cP cT)
% 127.52/127.69 Found ((x1 cP) x2) as proof of (cP cT)
% 127.52/127.69 Found ((x1 cP) x2) as proof of (cP cT)
% 127.52/127.69 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 127.52/127.69 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 127.52/127.69 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 127.52/127.69 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 127.52/127.69 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 127.52/127.69 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 127.52/127.69 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.52/127.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 127.52/127.69 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 127.52/127.69 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 127.52/127.69 Instantiate: b0:=(forall (P:Prop), ((iff P) P)):Prop
% 127.52/127.69 Found iff_refl as proof of b0
% 127.52/127.69 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 127.52/127.69 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 127.52/127.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.52/127.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 127.52/127.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.52/127.69 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 127.52/127.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 127.52/127.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 127.52/127.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 127.52/127.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 127.52/127.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 127.52/127.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 127.52/127.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 127.52/127.69 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 127.52/127.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 127.52/127.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 127.52/127.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 127.52/127.69 Found x2:(cP cS)
% 127.52/127.69 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 127.52/127.69 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 127.52/127.69 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 127.52/127.69 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 127.52/127.69 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 127.52/127.69 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 127.52/127.69 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 127.52/127.69 Found x2:(cP cS)
% 127.52/127.69 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 128.70/128.90 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 128.70/128.90 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 128.70/128.90 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 128.70/128.90 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 128.70/128.90 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 128.70/128.90 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 128.70/128.90 Found x2:(cP cS)
% 128.70/128.90 Found (fun (x3:(cT cX))=> x2) as proof of (cP cS)
% 128.70/128.90 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cT cX)->(cP cS))
% 128.70/128.90 Found (fun (x2:(cP cS)) (x3:(cT cX))=> x2) as proof of ((cP cS)->((cT cX)->(cP cS)))
% 128.70/128.90 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 128.70/128.90 Found ((and_rect1 (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 128.70/128.90 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 128.70/128.90 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cS)) (fun (x2:(cP cS)) (x3:(cT cX))=> x2)) as proof of (cP cS)
% 128.70/128.90 Found x100:=(x10 x2):(cP cT)
% 128.70/128.90 Found (x10 x2) as proof of (cP cT)
% 128.70/128.90 Found ((x1 cP) x2) as proof of (cP cT)
% 128.70/128.90 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 128.70/128.90 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 128.70/128.90 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 128.70/128.90 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 128.70/128.90 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 128.70/128.90 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 128.70/128.90 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 128.70/128.90 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 128.70/128.90 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 128.70/128.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 128.70/128.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 128.70/128.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 128.70/128.90 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.70/128.90 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 128.70/128.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.70/128.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.70/128.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.70/128.90 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 128.70/128.90 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 128.70/128.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 128.70/128.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 128.70/128.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 128.70/128.90 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 128.70/128.90 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 128.70/128.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.70/128.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.70/128.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 128.70/128.90 Found x100:=(x10 x2):(cP cT)
% 128.70/128.90 Found (x10 x2) as proof of (cP cT)
% 128.70/128.90 Found ((x1 cP) x2) as proof of (cP cT)
% 128.70/128.90 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 128.70/128.90 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 128.70/128.90 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 128.70/128.90 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 128.70/128.90 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 128.70/128.90 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 132.34/132.54 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 132.34/132.54 Found x100:=(x10 x2):(cP cT)
% 132.34/132.54 Found (x10 x2) as proof of (cP cT)
% 132.34/132.54 Found ((x1 cP) x2) as proof of (cP cT)
% 132.34/132.54 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 132.34/132.54 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 132.34/132.54 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 132.34/132.54 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 132.34/132.54 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 132.34/132.54 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 132.34/132.54 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 132.34/132.54 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 132.34/132.54 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 132.34/132.54 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 132.34/132.54 Found (eq_ref0 b0) as proof of (P0 b0)
% 132.34/132.54 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 132.34/132.54 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 132.34/132.54 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 132.34/132.54 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 132.34/132.54 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 132.34/132.54 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 132.34/132.54 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 132.34/132.54 Found (eq_ref0 a) as proof of (((eq Prop) a) b0)
% 132.34/132.54 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 132.34/132.54 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 132.34/132.54 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 132.34/132.54 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 132.34/132.54 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 132.34/132.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 132.34/132.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 132.34/132.54 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 132.34/132.54 Found x2:(P0 (cS cX))
% 132.34/132.54 Instantiate: b0:=(cS cX):Prop
% 132.34/132.54 Found x2 as proof of (P1 b0)
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 140.40/140.64 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 140.40/140.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 140.40/140.64 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 140.40/140.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 140.40/140.64 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found eq_ref000:=(eq_ref00 P0):((P0 a)->(P0 a))
% 140.40/140.64 Found (eq_ref00 P0) as proof of (P1 a)
% 140.40/140.64 Found ((eq_ref0 a) P0) as proof of (P1 a)
% 140.40/140.64 Found (((eq_ref Prop) a) P0) as proof of (P1 a)
% 140.40/140.64 Found (((eq_ref Prop) a) P0) as proof of (P1 a)
% 140.40/140.64 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 140.40/140.64 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 140.40/140.64 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 140.40/140.64 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b)
% 140.40/140.64 Found (eq_sym0000 ((eq_ref Prop) (cS cX))) as proof of (P0 b0)
% 140.40/140.64 Found (eq_sym0000 ((eq_ref Prop) (cS cX))) as proof of (P0 b0)
% 140.40/140.64 Found (eq_sym0000 ((eq_ref Prop) (cS cX))) as proof of (P0 b0)
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 140.40/140.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 140.40/140.64 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 140.40/140.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 140.40/140.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 140.40/140.64 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 140.40/140.64 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 140.40/140.64 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 140.40/140.64 Found or_ind as proof of b
% 140.40/140.64 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 140.40/140.64 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 140.40/140.64 Found or_ind as proof of b
% 140.40/140.64 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 140.40/140.64 Instantiate: b0:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 140.40/140.64 Found or_ind as proof of b0
% 140.40/140.64 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 140.40/140.64 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 140.40/140.64 Found or_ind as proof of b
% 140.40/140.64 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 140.40/140.64 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 142.73/142.92 Found or_ind as proof of b
% 142.73/142.92 Found x1:(((eq (fofType->Prop)) cS) cT)
% 142.73/142.92 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 142.73/142.92 Found x1 as proof of (P0 b0)
% 142.73/142.92 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 142.73/142.92 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 142.73/142.92 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 142.73/142.92 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 142.73/142.92 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 142.73/142.92 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 142.73/142.92 Instantiate: b0:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 142.73/142.92 Found or_ind as proof of b0
% 142.73/142.92 Found x1:(((eq (fofType->Prop)) cS) cT)
% 142.73/142.92 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 142.73/142.92 Found x1 as proof of (P0 b0)
% 142.73/142.92 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 142.73/142.92 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 142.73/142.92 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 142.73/142.92 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 142.73/142.92 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 142.73/142.92 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 142.73/142.92 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 142.73/142.92 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 142.73/142.92 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 142.73/142.92 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 142.73/142.92 Found x100:=(x10 x2):(cP cT)
% 142.73/142.92 Found (x10 x2) as proof of (cP cT)
% 142.73/142.92 Found ((x1 cP) x2) as proof of (cP cT)
% 142.73/142.92 Found (fun (x3:(cT cX))=> ((x1 cP) x2)) as proof of (cP cT)
% 142.73/142.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cT cX)->(cP cT))
% 142.73/142.92 Found (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)) as proof of ((cP cS)->((cT cX)->(cP cT)))
% 142.73/142.92 Found (and_rect10 (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 142.73/142.92 Found ((and_rect1 (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 142.73/142.92 Found (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))) as proof of (cP cT)
% 142.73/142.92 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (cP cT)
% 142.73/142.92 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of ((((eq (fofType->Prop)) cS) cT)->(cP cT))
% 142.73/142.92 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2)))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(cP cT)))
% 142.73/142.92 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 142.73/142.92 Found ((and_rect0 (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 142.73/142.92 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 142.73/142.92 Found (((fun (P0:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P0)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P0) x0) x)) (cP cT)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P0:Type) (x2:((cP cS)->((cT cX)->P0)))=> (((((and_rect (cP cS)) (cT cX)) P0) x2) x0)) (cP cT)) (fun (x2:(cP cS)) (x3:(cT cX))=> ((x1 cP) x2))))) as proof of (cP cT)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 145.87/146.07 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 145.87/146.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 145.87/146.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 145.87/146.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 145.87/146.07 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 145.87/146.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 145.87/146.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 145.87/146.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 145.87/146.07 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 145.87/146.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 145.87/146.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 145.87/146.07 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 145.87/146.07 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 145.87/146.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 145.87/146.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 145.87/146.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 145.87/146.07 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 145.87/146.07 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 145.87/146.07 Instantiate: b0:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 145.87/146.07 Found or_ind as proof of b0
% 145.87/146.07 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 145.87/146.07 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 145.87/146.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 145.87/146.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 145.87/146.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 145.87/146.07 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 145.87/146.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 145.87/146.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 145.87/146.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 145.87/146.07 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 145.87/146.07 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found x0:((and (cP cS)) (cT cX))
% 145.87/146.07 Instantiate: b:=(cT cX):Prop
% 145.87/146.07 Found x0 as proof of (P0 b)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 145.87/146.07 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 145.87/146.07 Found x0:((and (cP cS)) (cT cX))
% 145.87/146.07 Instantiate: b:=(cT cX):Prop
% 145.87/146.07 Found x0 as proof of (P0 b)
% 145.87/146.07 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 145.87/146.07 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found x0:((and (cP cS)) (cT cX))
% 148.26/148.46 Instantiate: b:=(cT cX):Prop
% 148.26/148.46 Found x0 as proof of (P0 b)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 148.26/148.46 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 148.26/148.46 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 148.26/148.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 148.26/148.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 148.26/148.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 148.26/148.46 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 148.26/148.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 148.26/148.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 148.26/148.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 148.26/148.46 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 148.26/148.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 148.26/148.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 148.26/148.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 148.26/148.46 Found x2:(P0 b)
% 148.26/148.46 Instantiate: b0:=b:Prop
% 148.26/148.46 Found x2 as proof of (P1 b0)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 148.26/148.46 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 148.26/148.46 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b0)
% 148.26/148.46 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 148.26/148.46 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 148.26/148.46 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 148.26/148.46 Found x0:((and (cP cS)) (cT cX))
% 148.26/148.46 Instantiate: b:=(cT cX):Prop
% 148.26/148.46 Found x0 as proof of (P0 b)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 148.26/148.46 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found x0:((and (cP cS)) (cT cX))
% 148.26/148.46 Instantiate: b:=(cT cX):Prop
% 148.26/148.46 Found x0 as proof of (P0 b)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 148.26/148.46 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 148.26/148.46 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found x0:((and (cP cS)) (cT cX))
% 148.26/148.46 Instantiate: b:=(cT cX):Prop
% 148.26/148.46 Found x0 as proof of (P0 b)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 148.26/148.46 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 148.26/148.46 Found x1:(((eq (fofType->Prop)) cS) cT)
% 148.26/148.46 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 148.26/148.46 Found x1 as proof of (P0 b0)
% 148.26/148.46 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 148.26/148.46 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 148.26/148.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 152.43/152.65 Found (eq_ref0 b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 152.43/152.65 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 152.43/152.65 Found (eq_ref0 b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 152.43/152.65 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 152.43/152.65 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b0)
% 152.43/152.65 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 152.43/152.65 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 152.43/152.65 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 152.43/152.65 Found (eq_ref0 b) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 152.43/152.65 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 152.43/152.65 Found (eq_ref0 a) as proof of (((eq Prop) a) b0)
% 152.43/152.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 152.43/152.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 152.43/152.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 152.43/152.65 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 152.43/152.65 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 152.43/152.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 152.43/152.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 152.43/152.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 152.43/152.65 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 152.43/152.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 152.43/152.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 152.43/152.65 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 152.43/152.65 Found (eq_ref0 b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 152.43/152.65 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 152.43/152.65 Found x4:(P0 (cS cX))
% 152.43/152.65 Instantiate: b0:=(cS cX):Prop
% 152.43/152.65 Found x4 as proof of (P1 b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 152.43/152.65 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 152.43/152.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 152.43/152.65 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 152.43/152.65 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 152.43/152.65 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 155.89/156.08 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 155.89/156.08 Found (eq_ref0 a) as proof of (((eq Prop) a) b0)
% 155.89/156.08 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 155.89/156.08 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 155.89/156.08 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 155.89/156.08 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 155.89/156.08 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 155.89/156.08 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 155.89/156.08 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 155.89/156.08 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 155.89/156.08 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 155.89/156.08 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 155.89/156.08 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 155.89/156.08 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 155.89/156.08 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 155.89/156.08 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 155.89/156.08 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 155.89/156.08 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 155.89/156.08 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 155.89/156.08 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 155.89/156.08 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found x0:((and (cP cS)) (cT cX))
% 155.89/156.08 Instantiate: b:=(cT cX):Prop
% 155.89/156.08 Found x0 as proof of (P0 b)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 155.89/156.08 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 155.89/156.08 Found x4:(P0 (cS cX))
% 155.89/156.08 Instantiate: b0:=(cS cX):Prop
% 155.89/156.08 Found x4 as proof of (P1 b0)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 155.89/156.08 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 155.89/156.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 155.89/156.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 155.89/156.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 155.89/156.08 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 155.89/156.08 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 155.89/156.08 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 163.99/164.20 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 163.99/164.20 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 163.99/164.20 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 163.99/164.20 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 163.99/164.20 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 163.99/164.20 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 163.99/164.20 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 163.99/164.20 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 163.99/164.20 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 163.99/164.20 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 163.99/164.20 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 163.99/164.20 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 163.99/164.20 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 163.99/164.20 Found proj1 as proof of b
% 163.99/164.20 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 163.99/164.20 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 163.99/164.20 Found proj1 as proof of b
% 163.99/164.20 Found x0:((and (cP cS)) (cT cX))
% 163.99/164.20 Instantiate: b:=(cT cX):Prop
% 163.99/164.20 Found x0 as proof of (P0 b)
% 163.99/164.20 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 163.99/164.20 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 163.99/164.20 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 163.99/164.20 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 163.99/164.20 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 163.99/164.20 Found eq_ref000:=(eq_ref00 P0):((P0 a)->(P0 a))
% 163.99/164.20 Found (eq_ref00 P0) as proof of (P1 a)
% 163.99/164.20 Found ((eq_ref0 a) P0) as proof of (P1 a)
% 163.99/164.20 Found (((eq_ref Prop) a) P0) as proof of (P1 a)
% 163.99/164.20 Found (((eq_ref Prop) a) P0) as proof of (P1 a)
% 163.99/164.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 163.99/164.20 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 163.99/164.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 163.99/164.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 163.99/164.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 163.99/164.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 163.99/164.20 Found (eq_ref0 b0) as proof of (((eq Prop) b0) a)
% 163.99/164.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 163.99/164.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 163.99/164.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 163.99/164.20 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 163.99/164.20 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 163.99/164.20 Found proj1 as proof of b
% 163.99/164.20 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 163.99/164.20 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 163.99/164.20 Found proj1 as proof of b
% 163.99/164.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 163.99/164.20 Found (eq_ref0 b0) as proof of (P0 b0)
% 163.99/164.20 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 163.99/164.20 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 163.99/164.20 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 163.99/164.20 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 163.99/164.20 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 163.99/164.20 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 163.99/164.20 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 163.99/164.20 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 163.99/164.20 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 163.99/164.20 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 163.99/164.20 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 163.99/164.20 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 163.99/164.20 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 163.99/164.20 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 163.99/164.20 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 163.99/164.20 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 163.99/164.20 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 163.99/164.20 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 163.99/164.20 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 163.99/164.20 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 163.99/164.20 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 163.99/164.20 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 163.99/164.20 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 163.99/164.20 Found eq_ref000:=(eq_ref00 P0):((P0 a)->(P0 a))
% 163.99/164.20 Found (eq_ref00 P0) as proof of (P1 a)
% 163.99/164.20 Found ((eq_ref0 a) P0) as proof of (P1 a)
% 163.99/164.20 Found (((eq_ref Prop) a) P0) as proof of (P1 a)
% 163.99/164.20 Found (((eq_ref Prop) a) P0) as proof of (P1 a)
% 163.99/164.20 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 167.47/167.66 Found (eq_ref0 a) as proof of (((eq Prop) a) b0)
% 167.47/167.66 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 167.47/167.66 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 167.47/167.66 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 167.47/167.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 167.47/167.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 167.47/167.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 167.47/167.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 167.47/167.66 Found x1:(((eq (fofType->Prop)) cS) cT)
% 167.47/167.66 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 167.47/167.66 Found x1 as proof of (P0 b0)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 167.47/167.66 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 167.47/167.66 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 167.47/167.66 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 167.47/167.66 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 167.47/167.66 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 167.47/167.66 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 167.47/167.66 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 167.47/167.66 Found proj1 as proof of b0
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 167.47/167.66 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 167.47/167.66 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 167.47/167.66 Found x4:(P0 (cS cX))
% 167.47/167.66 Instantiate: b0:=(cS cX):Prop
% 167.47/167.66 Found x4 as proof of (P1 b0)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 167.47/167.66 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 167.47/167.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 167.47/167.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 167.47/167.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 167.47/167.66 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 167.47/167.66 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 167.47/167.66 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 167.47/167.66 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 167.47/167.66 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 167.47/167.66 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 167.47/167.66 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 167.47/167.66 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 167.47/167.66 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 167.47/167.66 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 167.47/167.66 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 167.47/167.66 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 171.52/171.74 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 171.52/171.74 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 171.52/171.74 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 171.52/171.74 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 171.52/171.74 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 171.52/171.74 Found (eq_ref00 P0) as proof of (P1 b)
% 171.52/171.74 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 171.52/171.74 Found (((eq_ref Prop) b) P0) as proof of (P1 b)
% 171.52/171.74 Found (((eq_ref Prop) b) P0) as proof of (P1 b)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 171.52/171.74 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 171.52/171.74 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 171.52/171.74 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 171.52/171.74 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 171.52/171.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 171.52/171.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 171.52/171.74 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 171.52/171.74 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 171.52/171.74 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 171.52/171.74 Found proj1 as proof of b0
% 171.52/171.74 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 171.52/171.74 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 171.52/171.74 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 171.52/171.74 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 171.52/171.74 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 171.52/171.74 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 171.52/171.74 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 171.52/171.74 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 171.52/171.74 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 171.52/171.74 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 171.52/171.74 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 171.52/171.74 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 171.52/171.74 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 171.52/171.74 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 171.52/171.74 Found x2:(P0 (cS cX))
% 171.52/171.74 Instantiate: b0:=(cS cX):Prop
% 171.52/171.74 Found x2 as proof of (P1 b0)
% 171.52/171.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.52/171.74 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 171.52/171.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 174.33/174.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.33/174.56 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 174.33/174.56 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 174.33/174.56 Found proj1 as proof of b0
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 174.33/174.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.33/174.56 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 174.33/174.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.33/174.56 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 174.33/174.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.33/174.56 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 174.33/174.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 174.33/174.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 174.33/174.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 174.33/174.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 174.33/174.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 174.33/174.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 174.33/174.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 174.33/174.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 174.33/174.56 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 174.33/174.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 174.33/174.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 174.33/174.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 174.33/174.56 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 174.33/174.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 174.33/174.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 174.33/174.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 174.33/174.56 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 174.33/174.56 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 174.33/174.56 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 174.33/174.56 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 174.33/174.56 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 174.33/174.56 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 174.33/174.56 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.14/179.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.14/179.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.14/179.42 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 179.14/179.42 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 179.14/179.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 179.14/179.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.14/179.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.14/179.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.14/179.42 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 179.14/179.42 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 179.14/179.42 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 179.14/179.42 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 179.14/179.42 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 179.14/179.42 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 179.14/179.42 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found x100:=(x10 x2):(cP cT)
% 179.14/179.42 Found (x10 x2) as proof of (cP cT)
% 179.14/179.42 Found ((x1 cP) x2) as proof of (cP cT)
% 179.14/179.42 Found ((x1 cP) x2) as proof of (cP cT)
% 179.14/179.42 Found ((conj00 ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 179.14/179.42 Found (((conj0 b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 179.14/179.42 Found ((((conj (cP cT)) b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 179.14/179.42 Found ((((conj (cP cT)) b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 179.14/179.42 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 179.14/179.42 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 179.14/179.42 Found proj1 as proof of b
% 179.14/179.42 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 179.14/179.42 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 179.14/179.42 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 179.14/179.42 Found proj1 as proof of b
% 179.14/179.42 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 179.14/179.42 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 179.14/179.42 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 179.14/179.42 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 179.14/179.42 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 179.14/179.42 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 179.14/179.42 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 179.14/179.42 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 179.14/179.42 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 179.14/179.42 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 179.14/179.42 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 179.14/179.42 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 179.14/179.42 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 179.14/179.42 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 179.14/179.42 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 179.14/179.42 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 179.14/179.42 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 179.14/179.42 Found x100:=(x10 x2):(cP cT)
% 179.14/179.42 Found (x10 x2) as proof of (cP cT)
% 179.14/179.42 Found ((x1 cP) x2) as proof of (cP cT)
% 179.14/179.42 Found ((x1 cP) x2) as proof of (cP cT)
% 179.14/179.42 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 179.14/179.42 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 179.14/179.42 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 179.14/179.42 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 179.14/179.42 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b0))
% 179.14/179.42 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b0)))
% 180.66/180.91 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 180.66/180.91 Found ((and_rect1 (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 180.66/180.91 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 180.66/180.91 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 180.66/180.91 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 180.66/180.91 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 180.66/180.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 180.66/180.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 180.66/180.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 180.66/180.91 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 180.66/180.91 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 180.66/180.91 Found proj1 as proof of b
% 180.66/180.91 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 180.66/180.91 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 180.66/180.91 Found proj1 as proof of b
% 180.66/180.91 Found x0:((and (cP cS)) (cT cX))
% 180.66/180.91 Instantiate: b:=(cT cX):Prop
% 180.66/180.91 Found x0 as proof of (P0 b)
% 180.66/180.91 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 180.66/180.91 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 180.66/180.91 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 180.66/180.91 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 180.66/180.91 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 180.66/180.91 Found x100:=(x10 x2):(cP cT)
% 180.66/180.91 Found (x10 x2) as proof of (cP cT)
% 180.66/180.91 Found ((x1 cP) x2) as proof of (cP cT)
% 180.66/180.91 Found ((x1 cP) x2) as proof of (cP cT)
% 180.66/180.91 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 180.66/180.91 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 180.66/180.91 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 180.66/180.91 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 180.66/180.91 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b0))
% 180.66/180.91 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b0)))
% 180.66/180.91 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 180.66/180.91 Found ((and_rect1 (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 180.66/180.91 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 180.66/180.91 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (P0 b0)
% 180.66/180.91 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of ((((eq (fofType->Prop)) cS) cT)->(P0 b0))
% 180.66/180.91 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(P0 b0)))
% 180.66/180.91 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b0)
% 180.66/180.91 Found ((and_rect0 (P0 b0)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b0)
% 180.66/180.91 Found (((fun (P1:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P1)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P1) x0) x)) (P0 b0)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b0)
% 184.81/185.03 Found (((fun (P1:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P1)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P1) x0) x)) (P0 b0)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b0)
% 184.81/185.03 Found x0:((and (cP cS)) (cT cX))
% 184.81/185.03 Instantiate: b:=(cT cX):Prop
% 184.81/185.03 Found x0 as proof of (P0 b)
% 184.81/185.03 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 184.81/185.03 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 184.81/185.03 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 184.81/185.03 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 184.81/185.03 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 184.81/185.03 Found x0:((and (cP cS)) (cT cX))
% 184.81/185.03 Instantiate: b:=(cT cX):Prop
% 184.81/185.03 Found x0 as proof of (P0 b)
% 184.81/185.03 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 184.81/185.03 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 184.81/185.03 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 184.81/185.03 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 184.81/185.03 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 184.81/185.03 Found x1:(((eq (fofType->Prop)) cS) cT)
% 184.81/185.03 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 184.81/185.03 Found x1 as proof of (P0 b0)
% 184.81/185.03 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 184.81/185.03 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found x1:(((eq (fofType->Prop)) cS) cT)
% 184.81/185.03 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 184.81/185.03 Found x1 as proof of (P0 b0)
% 184.81/185.03 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 184.81/185.03 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 184.81/185.03 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 184.81/185.03 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 184.81/185.03 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 184.81/185.03 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 184.81/185.03 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 184.81/185.03 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 184.81/185.03 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 184.81/185.03 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 184.81/185.03 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 184.81/185.03 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 184.81/185.03 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 184.81/185.03 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 184.81/185.03 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 184.81/185.03 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 184.81/185.03 Found proj1 as proof of b0
% 184.81/185.03 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 184.81/185.03 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 184.81/185.03 Found proj1 as proof of b0
% 184.81/185.03 Found eq_ref000:=(eq_ref00 P0):((P0 a)->(P0 a))
% 191.62/191.84 Found (eq_ref00 P0) as proof of (P1 a)
% 191.62/191.84 Found ((eq_ref0 a) P0) as proof of (P1 a)
% 191.62/191.84 Found (((eq_ref Prop) a) P0) as proof of (P1 a)
% 191.62/191.84 Found (((eq_ref Prop) a) P0) as proof of (P1 a)
% 191.62/191.84 Found x0:((and (cP cS)) (cT cX))
% 191.62/191.84 Instantiate: b:=(cT cX):Prop
% 191.62/191.84 Found x0 as proof of (P0 b)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 191.62/191.84 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found x0:((and (cP cS)) (cT cX))
% 191.62/191.84 Instantiate: b:=(cT cX):Prop
% 191.62/191.84 Found x0 as proof of (P0 b)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 191.62/191.84 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found x0:((and (cP cS)) (cT cX))
% 191.62/191.84 Instantiate: b:=(cT cX):Prop
% 191.62/191.84 Found x0 as proof of (P0 b)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 191.62/191.84 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 191.62/191.84 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b0)
% 191.62/191.84 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 191.62/191.84 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 191.62/191.84 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 191.62/191.84 Found x4:(P0 b)
% 191.62/191.84 Instantiate: b0:=b:Prop
% 191.62/191.84 Found x4 as proof of (P1 b0)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 191.62/191.84 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 191.62/191.84 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 191.62/191.84 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 191.62/191.84 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 191.62/191.84 Found x0:((and (cP cS)) (cT cX))
% 191.62/191.84 Instantiate: b:=(cT cX):Prop
% 191.62/191.84 Found x0 as proof of (P0 b)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 191.62/191.84 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found x0:((and (cP cS)) (cT cX))
% 191.62/191.84 Instantiate: b:=(cT cX):Prop
% 191.62/191.84 Found x0 as proof of (P0 b)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 191.62/191.84 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 191.62/191.84 Found (eq_ref0 b0) as proof of (P0 b0)
% 191.62/191.84 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 191.62/191.84 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 191.62/191.84 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 191.62/191.84 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 191.62/191.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 191.62/191.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 191.62/191.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 191.62/191.84 Found (eq_ref0 b) as proof of (P0 b0)
% 191.62/191.84 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 191.62/191.84 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 191.62/191.84 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 191.62/191.84 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 191.62/191.84 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 191.62/191.84 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 191.62/191.84 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 191.62/191.84 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 191.62/191.84 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 191.62/191.84 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 191.62/191.84 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 194.04/194.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 194.04/194.29 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 194.04/194.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 194.04/194.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 194.04/194.29 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 194.04/194.29 Found x1:(((eq (fofType->Prop)) cS) cT)
% 194.04/194.29 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 194.04/194.29 Found x1 as proof of (P0 b0)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 194.04/194.29 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found x1:(((eq (fofType->Prop)) cS) cT)
% 194.04/194.29 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 194.04/194.29 Found x1 as proof of (P0 b0)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 194.04/194.29 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found x1:(((eq (fofType->Prop)) cS) cT)
% 194.04/194.29 Instantiate: b0:=(forall (P:((fofType->Prop)->Prop)), ((P cS)->(P cT))):Prop
% 194.04/194.29 Found x1 as proof of (P0 b0)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 194.04/194.29 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 194.04/194.29 Found x100:=(x10 x2):(cP cT)
% 194.04/194.29 Found (x10 x2) as proof of (cP cT)
% 194.04/194.29 Found ((x1 cP) x2) as proof of (cP cT)
% 194.04/194.29 Found ((x1 cP) x2) as proof of (cP cT)
% 194.04/194.29 Found ((conj00 ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 194.04/194.29 Found (((conj0 b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 194.04/194.29 Found ((((conj (cP cT)) b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 194.04/194.29 Found ((((conj (cP cT)) b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 194.04/194.29 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found x100:=(x10 x2):(cP cT)
% 194.04/194.29 Found (x10 x2) as proof of (cP cT)
% 194.04/194.29 Found ((x1 cP) x2) as proof of (cP cT)
% 194.04/194.29 Found ((x1 cP) x2) as proof of (cP cT)
% 194.04/194.29 Found ((conj00 ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 194.04/194.29 Found (((conj0 b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 194.04/194.29 Found ((((conj (cP cT)) b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 194.04/194.29 Found ((((conj (cP cT)) b0) ((x1 cP) x2)) proj1) as proof of (P0 b0)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 194.04/194.29 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 194.04/194.29 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 194.04/194.29 Found x0:((and (cP cS)) (cT cX))
% 194.04/194.29 Instantiate: b:=(cT cX):Prop
% 194.04/194.29 Found x0 as proof of (P0 b)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 194.04/194.29 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 194.04/194.29 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 194.04/194.29 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 194.04/194.29 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 194.04/194.29 Found x0:((and (cP cS)) (cT cX))
% 194.04/194.29 Instantiate: b:=(cT cX):Prop
% 194.04/194.29 Found x0 as proof of (P0 b)
% 194.04/194.29 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 194.04/194.29 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 194.04/194.29 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 197.24/197.48 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 197.24/197.48 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 197.24/197.48 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 197.24/197.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 197.24/197.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 197.24/197.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 197.24/197.48 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 197.24/197.48 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b0)
% 197.24/197.48 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 197.24/197.48 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 197.24/197.48 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 197.24/197.48 Found x4:(P0 b)
% 197.24/197.48 Instantiate: b0:=b:Prop
% 197.24/197.48 Found x4 as proof of (P1 b0)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 197.24/197.48 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 197.24/197.48 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 197.24/197.48 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 197.24/197.48 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 197.24/197.48 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 197.24/197.48 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 197.24/197.48 Found proj1 as proof of b
% 197.24/197.48 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 197.24/197.48 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 197.24/197.48 Found proj1 as proof of b
% 197.24/197.48 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 197.24/197.48 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 197.24/197.48 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 197.24/197.48 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 197.24/197.48 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 197.24/197.48 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 197.24/197.48 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 197.24/197.48 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 197.24/197.48 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 197.24/197.48 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 197.24/197.48 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 197.24/197.48 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 197.24/197.48 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 197.24/197.48 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.97/201.24 Found (eq_ref0 b0) as proof of (P0 b0)
% 200.97/201.24 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 200.97/201.24 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 200.97/201.24 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 200.97/201.24 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 200.97/201.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 200.97/201.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 200.97/201.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 200.97/201.24 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 200.97/201.24 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 200.97/201.24 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 200.97/201.24 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 200.97/201.24 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 200.97/201.24 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 200.97/201.24 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 200.97/201.24 Found (eq_ref0 b) as proof of (P0 b0)
% 200.97/201.24 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 200.97/201.24 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 200.97/201.24 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 200.97/201.24 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 200.97/201.24 Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 200.97/201.24 Found proj1 as proof of b0
% 200.97/201.24 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 200.97/201.24 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 200.97/201.24 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 200.97/201.24 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 200.97/201.24 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 200.97/201.24 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 200.97/201.24 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 200.97/201.24 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 200.97/201.24 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 200.97/201.24 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 200.97/201.24 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 200.97/201.24 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 200.97/201.24 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 200.97/201.24 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 200.97/201.24 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 200.97/201.24 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 200.97/201.24 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 200.97/201.24 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 200.97/201.24 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 200.97/201.24 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 200.97/201.24 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 203.98/204.22 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 203.98/204.22 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 203.98/204.22 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 203.98/204.22 Found proj1 as proof of b
% 203.98/204.22 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 203.98/204.22 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 203.98/204.22 Found proj1 as proof of b
% 203.98/204.22 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 203.98/204.22 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 203.98/204.22 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 203.98/204.22 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 203.98/204.22 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 203.98/204.22 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 203.98/204.22 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 203.98/204.22 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 203.98/204.22 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 203.98/204.22 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 203.98/204.22 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 203.98/204.22 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 203.98/204.22 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 203.98/204.22 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 203.98/204.22 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 203.98/204.22 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 203.98/204.22 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 203.98/204.22 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 203.98/204.22 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 203.98/204.22 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 203.98/204.22 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 203.98/204.22 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 203.98/204.22 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 203.98/204.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 203.98/204.22 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 203.98/204.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 203.98/204.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 203.98/204.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 208.88/209.12 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 208.88/209.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 208.88/209.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 208.88/209.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 208.88/209.12 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 208.88/209.12 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 208.88/209.12 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b0)
% 208.88/209.12 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 208.88/209.12 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 208.88/209.12 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 208.88/209.12 Found x0:((and (cP cS)) (cT cX))
% 208.88/209.12 Instantiate: b:=(cT cX):Prop
% 208.88/209.12 Found x0 as proof of (P0 b)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 208.88/209.12 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 208.88/209.12 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 208.88/209.12 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 208.88/209.12 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 208.88/209.12 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 208.88/209.12 Found x0:((and (cP cS)) (cT cX))
% 208.88/209.12 Instantiate: b:=(cT cX):Prop
% 208.88/209.12 Found x0 as proof of (P0 b)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 208.88/209.12 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 208.88/209.12 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 208.88/209.12 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 208.88/209.12 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 208.88/209.12 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 208.88/209.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 208.88/209.12 Found x100:=(x10 x2):(cP cT)
% 208.88/209.12 Found (x10 x2) as proof of (cP cT)
% 208.88/209.12 Found ((x1 cP) x2) as proof of (cP cT)
% 208.88/209.12 Found ((x1 cP) x2) as proof of (cP cT)
% 208.88/209.12 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 208.88/209.12 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 208.88/209.12 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 208.88/209.12 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b0))
% 208.88/209.12 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b0))
% 208.88/209.12 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b0)))
% 208.88/209.12 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 208.88/209.12 Found ((and_rect1 (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 208.88/209.12 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 208.88/209.12 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b0)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b0)
% 208.88/209.12 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 208.88/209.12 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 208.88/209.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 208.88/209.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 208.88/209.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 216.88/217.13 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 216.88/217.13 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 216.88/217.13 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 216.88/217.13 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 b00):(((eq Prop) b00) b00)
% 216.88/217.13 Found (eq_ref0 b00) as proof of (((eq Prop) b00) b0)
% 216.88/217.13 Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% 216.88/217.13 Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% 216.88/217.13 Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 216.88/217.13 Found (eq_ref0 b) as proof of (((eq Prop) b) b00)
% 216.88/217.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% 216.88/217.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% 216.88/217.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% 216.88/217.13 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 216.88/217.13 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 216.88/217.13 Found iff_trans as proof of b
% 216.88/217.13 Found x0:((and (cP cS)) (cT cX))
% 216.88/217.13 Instantiate: b:=(cT cX):Prop
% 216.88/217.13 Found x0 as proof of (P0 b)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 216.88/217.13 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found x0:((and (cP cS)) (cT cX))
% 216.88/217.13 Instantiate: b:=(cT cX):Prop
% 216.88/217.13 Found x0 as proof of (P0 b)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 216.88/217.13 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 216.88/217.13 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 216.88/217.13 Found iff_trans as proof of b
% 216.88/217.13 Found x100:=(x10 x2):(cP cT)
% 216.88/217.13 Found (x10 x2) as proof of (cP cT)
% 216.88/217.13 Found ((x1 cP) x2) as proof of (cP cT)
% 216.88/217.13 Found ((x1 cP) x2) as proof of (cP cT)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 216.88/217.13 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 216.88/217.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 216.88/217.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 216.88/217.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 216.88/217.13 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 216.88/217.13 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 216.88/217.13 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 216.88/217.13 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 216.88/217.13 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 216.88/217.13 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 216.88/217.13 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 216.88/217.13 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 216.88/217.13 Found x0:((and (cP cS)) (cT cX))
% 216.88/217.13 Instantiate: b:=(cT cX):Prop
% 216.88/217.13 Found x0 as proof of (P0 b)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 216.88/217.13 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 216.88/217.13 Found x0:((and (cP cS)) (cT cX))
% 216.88/217.13 Instantiate: b:=(cT cX):Prop
% 216.88/217.13 Found x0 as proof of (P0 b)
% 216.88/217.13 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 223.30/223.53 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found x0:((and (cP cS)) (cT cX))
% 223.30/223.53 Instantiate: b:=(cT cX):Prop
% 223.30/223.53 Found x0 as proof of (P0 b)
% 223.30/223.53 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 223.30/223.53 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found x0:((and (cP cS)) (cT cX))
% 223.30/223.53 Instantiate: b:=(cT cX):Prop
% 223.30/223.53 Found x0 as proof of (P0 b)
% 223.30/223.53 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 223.30/223.53 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 223.30/223.53 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 223.30/223.53 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 223.30/223.53 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 223.30/223.53 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 223.30/223.53 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 223.30/223.53 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 223.30/223.53 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 223.30/223.53 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 223.30/223.53 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 223.30/223.53 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 223.30/223.53 Found x4:(P0 b)
% 223.30/223.53 Instantiate: b0:=b:Prop
% 223.30/223.53 Found x4 as proof of (P1 b0)
% 223.30/223.53 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 223.30/223.53 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 223.30/223.53 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 223.30/223.53 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 223.30/223.53 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 223.30/223.53 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 223.30/223.53 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 223.30/223.53 Found iff_trans as proof of b
% 223.30/223.53 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 223.30/223.53 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 223.30/223.53 Found iff_trans as proof of b
% 223.30/223.53 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 223.30/223.53 Found (eq_ref0 b0) as proof of (P0 b0)
% 223.30/223.53 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 223.30/223.53 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 223.30/223.53 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 223.30/223.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 223.30/223.53 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 223.30/223.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 223.30/223.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 223.30/223.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 223.30/223.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 223.30/223.53 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 223.30/223.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 223.30/223.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 223.30/223.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 223.30/223.53 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 223.30/223.53 Found (eq_ref0 b0) as proof of (((eq Prop) b0) a)
% 223.30/223.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 223.30/223.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 223.30/223.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 223.30/223.53 Found x100:=(x10 x2):(cP cT)
% 223.30/223.53 Found (x10 x2) as proof of (cP cT)
% 227.70/227.98 Found ((x1 cP) x2) as proof of (cP cT)
% 227.70/227.98 Found ((x1 cP) x2) as proof of (cP cT)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 227.70/227.98 Found (eq_ref0 b) as proof of (P0 b0)
% 227.70/227.98 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 227.70/227.98 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 227.70/227.98 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 227.70/227.98 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 227.70/227.98 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 227.70/227.98 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 227.70/227.98 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 227.70/227.98 Found x0:((and (cP cS)) (cT cX))
% 227.70/227.98 Instantiate: b:=(cT cX):Prop
% 227.70/227.98 Found x0 as proof of (P0 b)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 227.70/227.98 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found x0:((and (cP cS)) (cT cX))
% 227.70/227.98 Instantiate: b:=(cT cX):Prop
% 227.70/227.98 Found x0 as proof of (P0 b)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 227.70/227.98 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found x0:((and (cP cS)) (cT cX))
% 227.70/227.98 Instantiate: b:=(cT cX):Prop
% 227.70/227.98 Found x0 as proof of (P0 b)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 227.70/227.98 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found x100:=(x10 x2):(cP cT)
% 227.70/227.98 Found (x10 x2) as proof of (cP cT)
% 227.70/227.98 Found ((x1 cP) x2) as proof of (cP cT)
% 227.70/227.98 Found ((x1 cP) x2) as proof of (cP cT)
% 227.70/227.98 Found x0:((and (cP cS)) (cT cX))
% 227.70/227.98 Instantiate: b:=(cT cX):Prop
% 227.70/227.98 Found x0 as proof of (P0 b)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 (cS a)):(((eq Prop) (cS a)) (cS a))
% 227.70/227.98 Found (eq_ref0 (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found ((eq_ref Prop) (cS a)) as proof of (((eq Prop) (cS a)) b)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 227.70/227.98 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 227.70/227.98 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 227.70/227.98 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 227.70/227.98 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 227.70/227.98 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 227.70/227.98 Found (eq_ref0 a) as proof of (((eq fofType) a) cX)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) cX)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 227.70/227.98 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (cS cX))
% 227.70/227.98 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (cS cX))
% 227.70/227.98 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (cS cX))
% 227.70/227.98 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (cS cX))
% 227.70/227.98 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 227.70/227.98 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% 227.70/227.98 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 227.70/227.98 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 227.70/227.98 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 227.70/227.98 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 227.70/227.98 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 227.70/227.98 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 227.70/227.98 Found eq_ref000:=(eq_ref00 P0):((P0 b0)->(P0 b0))
% 233.48/233.72 Found (eq_ref00 P0) as proof of (P1 b0)
% 233.48/233.72 Found ((eq_ref0 b0) P0) as proof of (P1 b0)
% 233.48/233.72 Found (((eq_ref Prop) b0) P0) as proof of (P1 b0)
% 233.48/233.72 Found (((eq_ref Prop) b0) P0) as proof of (P1 b0)
% 233.48/233.72 Found x100:=(x10 x2):(cP cT)
% 233.48/233.72 Found (x10 x2) as proof of (cP cT)
% 233.48/233.72 Found ((x1 cP) x2) as proof of (cP cT)
% 233.48/233.72 Found ((x1 cP) x2) as proof of (cP cT)
% 233.48/233.72 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 233.48/233.72 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 233.48/233.72 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 233.48/233.72 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 233.48/233.72 Found x100:=(x10 x2):(cP cT)
% 233.48/233.72 Found (x10 x2) as proof of (cP cT)
% 233.48/233.72 Found ((x1 cP) x2) as proof of (cP cT)
% 233.48/233.72 Found ((x1 cP) x2) as proof of (cP cT)
% 233.48/233.72 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 233.48/233.72 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 233.48/233.72 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 233.48/233.72 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 233.48/233.72 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 233.48/233.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 233.48/233.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 233.48/233.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 233.48/233.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) a)
% 233.48/233.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 233.48/233.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 233.48/233.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 233.48/233.72 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 233.48/233.72 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 233.48/233.72 Found x4:(P0 b)
% 233.48/233.72 Instantiate: b0:=b:Prop
% 233.48/233.72 Found x4 as proof of (P1 b0)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 233.48/233.72 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 233.48/233.72 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 233.48/233.72 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 233.48/233.72 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 233.48/233.72 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 233.48/233.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 233.48/233.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 233.48/233.72 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 233.48/233.72 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 233.48/233.72 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 233.48/233.72 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 233.48/233.72 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 233.48/233.72 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 233.48/233.72 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 233.48/233.72 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 233.48/233.72 Found eq_ref00:=(eq_ref0 cX):(((eq fofType) cX) cX)
% 233.48/233.72 Found (eq_ref0 cX) as proof of (((eq fofType) cX) b0)
% 238.77/239.07 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 238.77/239.07 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 238.77/239.07 Found ((eq_ref fofType) cX) as proof of (((eq fofType) cX) b0)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 238.77/239.07 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 238.77/239.07 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 238.77/239.07 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 238.77/239.07 Found (eq_ref0 b0) as proof of (P0 b0)
% 238.77/239.07 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 238.77/239.07 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 238.77/239.07 Found ((eq_ref Prop) b0) as proof of (P0 b0)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 238.77/239.07 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 238.77/239.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 238.77/239.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 238.77/239.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 238.77/239.07 Found x100:=(x10 x2):(cP cT)
% 238.77/239.07 Found (x10 x2) as proof of (cP cT)
% 238.77/239.07 Found ((x1 cP) x2) as proof of (cP cT)
% 238.77/239.07 Found ((x1 cP) x2) as proof of (cP cT)
% 238.77/239.07 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 238.77/239.07 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 238.77/239.07 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 238.77/239.07 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 238.77/239.07 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 238.77/239.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 238.77/239.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 238.77/239.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 238.77/239.07 Found x100:=(x10 x2):(cP cT)
% 238.77/239.07 Found (x10 x2) as proof of (cP cT)
% 238.77/239.07 Found ((x1 cP) x2) as proof of (cP cT)
% 238.77/239.07 Found ((x1 cP) x2) as proof of (cP cT)
% 238.77/239.07 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 238.77/239.07 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 238.77/239.07 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 238.77/239.07 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 238.77/239.07 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 238.77/239.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 238.77/239.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 238.77/239.07 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 238.77/239.07 Found (eq_ref0 b) as proof of (P0 b0)
% 238.77/239.07 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 238.77/239.07 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 238.77/239.07 Found ((eq_ref Prop) b) as proof of (P0 b0)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 238.77/239.07 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 238.77/239.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 238.77/239.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 238.77/239.07 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 238.77/239.07 Found eq_ref000:=(eq_ref00 P0):((P0 b0)->(P0 b0))
% 238.77/239.07 Found (eq_ref00 P0) as proof of (P1 b0)
% 238.77/239.07 Found ((eq_ref0 b0) P0) as proof of (P1 b0)
% 238.77/239.07 Found (((eq_ref Prop) b0) P0) as proof of (P1 b0)
% 238.77/239.07 Found (((eq_ref Prop) b0) P0) as proof of (P1 b0)
% 238.77/239.07 Found x100:=(x10 x2):(cP cT)
% 238.77/239.07 Found (x10 x2) as proof of (cP cT)
% 238.77/239.07 Found ((x1 cP) x2) as proof of (cP cT)
% 238.77/239.07 Found ((x1 cP) x2) as proof of (cP cT)
% 238.77/239.07 Found x100:=(x10 x2):(cP cT)
% 238.77/239.07 Found (x10 x2) as proof of (cP cT)
% 238.77/239.07 Found ((x1 cP) x2) as proof of (cP cT)
% 238.77/239.07 Found ((x1 cP) x2) as proof of (cP cT)
% 238.77/239.07 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 238.77/239.07 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 238.77/239.07 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 243.68/243.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 243.68/243.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 243.68/243.99 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 243.68/243.99 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 243.68/243.99 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 243.68/243.99 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 243.68/243.99 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 243.68/243.99 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 243.68/243.99 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 243.68/243.99 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 243.68/243.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 243.68/243.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 243.68/243.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 243.68/243.99 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 243.68/243.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 243.68/243.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 243.68/243.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 243.68/243.99 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 243.68/243.99 Found (eq_ref00 P0) as proof of (P1 b)
% 243.68/243.99 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 243.68/243.99 Found (((eq_ref Prop) b) P0) as proof of (P1 b)
% 243.68/243.99 Found (((eq_ref Prop) b) P0) as proof of (P1 b)
% 243.68/243.99 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 243.68/243.99 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 243.68/243.99 Found iff_trans as proof of b
% 243.68/243.99 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 243.68/243.99 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 243.68/243.99 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 243.68/243.99 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 248.83/249.10 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 248.83/249.10 Found iff_trans as proof of b
% 248.83/249.10 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 248.83/249.10 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 248.83/249.10 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 248.83/249.10 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 248.83/249.10 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 248.83/249.10 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 248.83/249.10 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 248.83/249.10 Found iff_trans as proof of b
% 248.83/249.10 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 248.83/249.10 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 248.83/249.10 Found iff_trans as proof of b
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 248.83/249.10 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 248.83/249.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 248.83/249.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 248.83/249.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 248.83/249.10 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 248.83/249.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 248.83/249.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 248.83/249.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 248.83/249.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 248.83/249.10 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 248.83/249.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 248.83/249.10 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 248.83/249.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 248.83/249.10 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 248.83/249.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 248.83/249.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 248.83/249.10 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 248.83/249.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 261.08/261.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 261.08/261.37 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 261.08/261.37 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 261.08/261.37 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 261.08/261.37 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 261.08/261.37 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 261.08/261.37 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 261.08/261.37 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 261.08/261.37 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 261.08/261.37 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 261.08/261.37 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 261.08/261.37 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 261.08/261.37 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 261.08/261.37 Found iff_trans as proof of b
% 261.08/261.37 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 261.08/261.37 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 261.08/261.37 Found iff_trans as proof of b
% 261.08/261.37 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 261.08/261.37 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 261.08/261.38 Found iff_trans as proof of b
% 261.08/261.38 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 261.08/261.38 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 261.08/261.38 Found iff_trans as proof of b
% 261.08/261.38 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 261.08/261.38 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 261.08/261.38 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 261.08/261.38 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 261.08/261.38 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 261.08/261.38 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 261.08/261.38 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 261.08/261.38 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 261.08/261.38 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 261.08/261.38 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 261.08/261.38 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 261.08/261.38 Found (eq_ref00 P0) as proof of (P1 b)
% 261.08/261.38 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 261.08/261.38 Found (((eq_ref Prop) b) P0) as proof of (P1 b)
% 261.08/261.38 Found (((eq_ref Prop) b) P0) as proof of (P1 b)
% 261.08/261.38 Found x100:=(x10 x2):(cP cT)
% 261.08/261.38 Found (x10 x2) as proof of (cP cT)
% 261.08/261.38 Found ((x1 cP) x2) as proof of (cP cT)
% 261.08/261.38 Found ((x1 cP) x2) as proof of (cP cT)
% 261.08/261.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 261.08/261.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 261.08/261.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 261.08/261.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 261.08/261.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 261.08/261.38 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 261.08/261.38 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 261.08/261.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 261.08/261.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 261.08/261.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 270.04/270.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 270.04/270.31 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 270.04/270.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 270.04/270.31 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 270.04/270.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 270.04/270.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 270.04/270.31 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found x100:=(x10 x2):(cP cT)
% 270.04/270.31 Found (x10 x2) as proof of (cP cT)
% 270.04/270.31 Found ((x1 cP) x2) as proof of (cP cT)
% 270.04/270.31 Found ((x1 cP) x2) as proof of (cP cT)
% 270.04/270.31 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 270.04/270.31 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 270.04/270.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 270.04/270.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) a)
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 270.04/270.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 270.04/270.31 Found x100:=(x10 x2):(cP cT)
% 270.04/270.31 Found (x10 x2) as proof of (cP cT)
% 270.04/270.31 Found ((x1 cP) x2) as proof of (cP cT)
% 270.04/270.31 Found ((x1 cP) x2) as proof of (cP cT)
% 270.04/270.31 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found x100:=(x10 x2):(cP cT)
% 270.04/270.31 Found (x10 x2) as proof of (cP cT)
% 270.04/270.31 Found ((x1 cP) x2) as proof of (cP cT)
% 270.04/270.31 Found ((x1 cP) x2) as proof of (cP cT)
% 270.04/270.31 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found x100:=(x10 x2):(cP cT)
% 270.04/270.31 Found (x10 x2) as proof of (cP cT)
% 270.04/270.31 Found ((x1 cP) x2) as proof of (cP cT)
% 270.04/270.31 Found ((x1 cP) x2) as proof of (cP cT)
% 270.04/270.31 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 270.04/270.31 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 270.04/270.31 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 270.04/270.31 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 270.04/270.31 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 270.04/270.31 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 270.04/270.31 Found x2:(cP cS)
% 275.28/275.56 Found x2 as proof of (cP cS)
% 275.28/275.56 Found x2:(cP cS)
% 275.28/275.56 Found x2 as proof of (cP cS)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 275.28/275.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 275.28/275.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 275.28/275.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 275.28/275.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 275.28/275.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 275.28/275.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 275.28/275.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 275.28/275.56 Found (eq_ref0 a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) cX)
% 275.28/275.56 Found x100:=(x10 x2):(cP cT)
% 275.28/275.56 Found (x10 x2) as proof of (cP cT)
% 275.28/275.56 Found ((x1 cP) x2) as proof of (cP cT)
% 275.28/275.56 Found ((x1 cP) x2) as proof of (cP cT)
% 275.28/275.56 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found x100:=(x10 x2):(cP cT)
% 275.28/275.56 Found (x10 x2) as proof of (cP cT)
% 275.28/275.56 Found ((x1 cP) x2) as proof of (cP cT)
% 275.28/275.56 Found ((x1 cP) x2) as proof of (cP cT)
% 275.28/275.56 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 275.28/275.56 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 275.28/275.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 275.28/275.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 275.28/275.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 275.28/275.56 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 275.28/275.56 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 275.28/275.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 275.28/275.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 275.28/275.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 275.28/275.56 Found x100:=(x10 x2):(cP cT)
% 275.28/275.56 Found (x10 x2) as proof of (cP cT)
% 275.28/275.56 Found ((x1 cP) x2) as proof of (cP cT)
% 275.28/275.56 Found ((x1 cP) x2) as proof of (cP cT)
% 275.28/275.56 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 275.28/275.56 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 279.25/279.53 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 279.25/279.53 Found x100:=(x10 x2):(cP cT)
% 279.25/279.53 Found (x10 x2) as proof of (cP cT)
% 279.25/279.53 Found ((x1 cP) x2) as proof of (cP cT)
% 279.25/279.53 Found ((x1 cP) x2) as proof of (cP cT)
% 279.25/279.53 Found ((conj00 ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 279.25/279.53 Found (((conj0 b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 279.25/279.53 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 279.25/279.53 Found ((((conj (cP cT)) b) ((x1 cP) x2)) iff_trans) as proof of (P0 b)
% 279.25/279.53 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 279.25/279.53 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 279.25/279.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 279.25/279.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 279.25/279.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 279.25/279.53 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 279.25/279.53 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 279.25/279.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 279.25/279.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 279.25/279.53 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 279.25/279.53 Found x2:(cP cS)
% 279.25/279.53 Found x2 as proof of (cP cS)
% 279.25/279.53 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.53 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 279.25/279.53 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 279.25/279.53 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 279.25/279.53 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 279.25/279.53 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 279.25/279.53 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 279.25/279.53 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 279.25/279.53 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 279.25/279.53 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 279.25/279.53 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 279.25/279.53 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.53 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found x2:(cP cS)
% 279.25/279.53 Found x2 as proof of (cP cS)
% 279.25/279.53 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.53 Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% 279.25/279.53 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 279.25/279.53 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 279.25/279.53 Found iff_trans as proof of b
% 279.25/279.53 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 279.25/279.53 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 279.25/279.53 Found iff_trans as proof of b
% 279.25/279.53 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 279.25/279.53 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 279.25/279.53 Found iff_trans as proof of b
% 279.25/279.53 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 284.15/284.46 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 284.15/284.46 Found iff_trans as proof of b
% 284.15/284.46 Found x2:(P0 b)
% 284.15/284.46 Instantiate: b0:=b:Prop
% 284.15/284.46 Found x2 as proof of (P1 b0)
% 284.15/284.46 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 284.15/284.46 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 284.15/284.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 284.15/284.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 284.15/284.46 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b0)
% 284.15/284.46 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 284.15/284.47 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 284.15/284.47 Found iff_trans as proof of b
% 284.15/284.47 Found x2:(cP cS)
% 284.15/284.47 Found x2 as proof of (cP cS)
% 284.15/284.47 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 284.15/284.47 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 284.15/284.47 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 284.15/284.47 Found iff_trans as proof of b
% 284.15/284.47 Found x2:(cP cS)
% 284.15/284.47 Found x2 as proof of (cP cS)
% 284.15/284.47 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 284.15/284.47 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 284.15/284.47 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 284.15/284.47 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 284.15/284.47 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 284.15/284.47 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 284.15/284.47 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 284.15/284.47 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 284.15/284.47 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 284.15/284.47 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 284.15/284.47 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 284.15/284.47 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 284.15/284.47 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 284.15/284.47 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 284.15/284.47 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 284.15/284.47 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 284.15/284.47 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 288.75/289.06 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 288.75/289.06 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 288.75/289.06 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 288.75/289.06 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 288.75/289.06 Found x100:=(x10 x2):(cP cT)
% 288.75/289.06 Found (x10 x2) as proof of (cP cT)
% 288.75/289.06 Found ((x1 cP) x2) as proof of (cP cT)
% 288.75/289.06 Found ((x1 cP) x2) as proof of (cP cT)
% 288.75/289.06 Found x100:=(x10 x2):(cP cT)
% 288.75/289.06 Found (x10 x2) as proof of (cP cT)
% 288.75/289.06 Found ((x1 cP) x2) as proof of (cP cT)
% 288.75/289.06 Found ((x1 cP) x2) as proof of (cP cT)
% 288.75/289.06 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 288.75/289.06 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 288.75/289.06 Found iff_trans as proof of b
% 288.75/289.06 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 288.75/289.06 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 288.75/289.06 Found iff_trans as proof of b
% 288.75/289.06 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 288.75/289.06 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 288.75/289.06 Found iff_trans as proof of b
% 288.75/289.06 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 288.75/289.06 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 288.75/289.06 Found iff_trans as proof of b
% 288.75/289.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.75/289.06 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 288.75/289.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.75/289.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.75/289.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.75/289.06 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 288.75/289.06 Found (eq_ref0 b0) as proof of (((eq Prop) b0) a)
% 288.75/289.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 288.75/289.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 288.75/289.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% 288.75/289.06 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 288.75/289.06 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 288.75/289.06 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 294.02/294.30 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found x2:(cP cS)
% 294.02/294.30 Found x2 as proof of (cP cS)
% 294.02/294.30 Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% 294.02/294.30 Found (eq_ref00 P0) as proof of (P1 b)
% 294.02/294.30 Found ((eq_ref0 b) P0) as proof of (P1 b)
% 294.02/294.30 Found (((eq_ref Prop) b) P0) as proof of (P1 b)
% 294.02/294.30 Found (((eq_ref Prop) b) P0) as proof of (P1 b)
% 294.02/294.30 Found x2:(cP cS)
% 294.02/294.30 Found x2 as proof of (cP cS)
% 294.02/294.30 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 294.02/294.30 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 294.02/294.30 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 294.02/294.30 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 294.02/294.30 Found iff_trans as proof of b
% 294.02/294.30 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 294.02/294.30 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% 294.02/294.30 Instantiate: b:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% 294.02/294.30 Found iff_trans as proof of b
% 294.02/294.30 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 294.02/294.30 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 294.02/294.30 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 294.02/294.30 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 294.02/294.30 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 294.02/294.30 Found x100:=(x10 x2):(cP cT)
% 294.02/294.30 Found (x10 x2) as proof of (cP cT)
% 294.02/294.30 Found ((x1 cP) x2) as proof of (cP cT)
% 294.02/294.30 Found ((x1 cP) x2) as proof of (cP cT)
% 294.02/294.30 Found x100:=(x10 x2):(cP cT)
% 294.02/294.30 Found (x10 x2) as proof of (cP cT)
% 294.02/294.30 Found ((x1 cP) x2) as proof of (cP cT)
% 294.02/294.30 Found ((x1 cP) x2) as proof of (cP cT)
% 294.02/294.30 Found x100:=(x10 x2):(cP cT)
% 294.02/294.30 Found (x10 x2) as proof of (cP cT)
% 294.02/294.30 Found ((x1 cP) x2) as proof of (cP cT)
% 294.02/294.30 Found ((x1 cP) x2) as proof of (cP cT)
% 294.02/294.30 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b)))
% 294.54/294.83 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found ((and_rect1 (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found x100:=(x10 x2):(cP cT)
% 294.54/294.83 Found (x10 x2) as proof of (cP cT)
% 294.54/294.83 Found ((x1 cP) x2) as proof of (cP cT)
% 294.54/294.83 Found ((x1 cP) x2) as proof of (cP cT)
% 294.54/294.83 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b)))
% 294.54/294.83 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found ((and_rect1 (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found eq_ref000:=(eq_ref00 P0):((P0 (cS cX))->(P0 (cS cX)))
% 294.54/294.83 Found (eq_ref00 P0) as proof of (P1 (cS cX))
% 294.54/294.83 Found ((eq_ref0 (cS cX)) P0) as proof of (P1 (cS cX))
% 294.54/294.83 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 294.54/294.83 Found (((eq_ref Prop) (cS cX)) P0) as proof of (P1 (cS cX))
% 294.54/294.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 294.54/294.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 294.54/294.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 294.54/294.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 294.54/294.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 294.54/294.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 294.54/294.83 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 294.54/294.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 294.54/294.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 294.54/294.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 294.54/294.83 Found x100:=(x10 x2):(cP cT)
% 294.54/294.83 Found (x10 x2) as proof of (cP cT)
% 294.54/294.83 Found ((x1 cP) x2) as proof of (cP cT)
% 294.54/294.83 Found ((x1 cP) x2) as proof of (cP cT)
% 294.54/294.83 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b))
% 294.54/294.83 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b)))
% 294.54/294.83 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found ((and_rect1 (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 294.54/294.83 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 295.75/296.12 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 295.75/296.12 Found x100:=(x10 x2):(cP cT)
% 295.75/296.12 Found (x10 x2) as proof of (cP cT)
% 295.75/296.12 Found ((x1 cP) x2) as proof of (cP cT)
% 295.75/296.12 Found ((x1 cP) x2) as proof of (cP cT)
% 295.75/296.12 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 295.75/296.12 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 295.75/296.12 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 295.75/296.12 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 295.75/296.12 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b))
% 295.75/296.12 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b)))
% 295.75/296.12 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 295.75/296.12 Found ((and_rect1 (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 295.75/296.12 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 295.75/296.12 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 295.75/296.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 295.75/296.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 295.75/296.12 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 295.75/296.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 295.75/296.12 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 295.75/296.12 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (cS cX))
% 295.75/296.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 295.75/296.12 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 295.75/296.12 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 295.75/296.12 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 295.75/296.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 295.75/296.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 295.75/296.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 295.75/296.12 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 295.75/296.12 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 295.75/296.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 295.75/296.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 295.75/296.12 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 295.75/296.12 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 295.75/296.12 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 295.75/296.12 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 295.75/296.12 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 295.75/296.12 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 295.75/296.12 Found eq_ref00:=(eq_ref0 (cS cX)):(((eq Prop) (cS cX)) (cS cX))
% 295.75/296.12 Found (eq_ref0 (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 295.75/296.12 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 297.97/298.27 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 297.97/298.27 Found ((eq_ref Prop) (cS cX)) as proof of (((eq Prop) (cS cX)) b1)
% 297.97/298.27 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 297.97/298.27 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 297.97/298.27 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 297.97/298.27 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 297.97/298.27 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 297.97/298.27 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% 297.97/298.27 Found (eq_ref0 a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) a)
% 297.97/298.27 Found x100:=(x10 x2):(cP cT)
% 297.97/298.27 Found (x10 x2) as proof of (cP cT)
% 297.97/298.27 Found ((x1 cP) x2) as proof of (cP cT)
% 297.97/298.27 Found ((x1 cP) x2) as proof of (cP cT)
% 297.97/298.27 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 297.97/298.27 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 297.97/298.27 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 297.97/298.27 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 297.97/298.27 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b))
% 297.97/298.27 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b)))
% 297.97/298.27 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 297.97/298.27 Found ((and_rect1 (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 297.97/298.27 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 297.97/298.27 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (P0 b)
% 297.97/298.27 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of ((((eq (fofType->Prop)) cS) cT)->(P0 b))
% 297.97/298.27 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(P0 b)))
% 297.97/298.27 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b)
% 297.97/298.27 Found ((and_rect0 (P0 b)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b)
% 298.26/298.55 Found (((fun (P1:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P1)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P1) x0) x)) (P0 b)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b)
% 298.26/298.55 Found (((fun (P1:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P1)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P1) x0) x)) (P0 b)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b)
% 298.26/298.55 Found x100:=(x10 x2):(cP cT)
% 298.26/298.55 Found (x10 x2) as proof of (cP cT)
% 298.26/298.55 Found ((x1 cP) x2) as proof of (cP cT)
% 298.26/298.55 Found ((x1 cP) x2) as proof of (cP cT)
% 298.26/298.55 Found (conj00 ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 298.26/298.55 Found ((conj0 (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 298.26/298.55 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 298.26/298.55 Found (((conj (cP cT)) (cT cX)) ((x1 cP) x2)) as proof of ((cT cX)->(P0 b))
% 298.26/298.55 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cT cX)->(P0 b))
% 298.26/298.55 Found (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))) as proof of ((cP cS)->((cT cX)->(P0 b)))
% 298.26/298.55 Found (and_rect10 (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 298.26/298.55 Found ((and_rect1 (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 298.26/298.55 Found (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))) as proof of (P0 b)
% 298.26/298.55 Found (fun (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (P0 b)
% 298.26/298.55 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of ((((eq (fofType->Prop)) cS) cT)->(P0 b))
% 298.26/298.55 Found (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2))))) as proof of (((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->(P0 b)))
% 298.26/298.55 Found (and_rect00 (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b)
% 298.26/298.55 Found ((and_rect0 (P0 b)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b)
% 298.26/298.55 Found (((fun (P1:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P1)))=> (((((and_rect ((and (cP cS)) (cT cX))) (((eq (fofType->Prop)) cS) cT)) P1) x0) x)) (P0 b)) (fun (x0:((and (cP cS)) (cT cX))) (x1:(((eq (fofType->Prop)) cS) cT))=> (((fun (P1:Type) (x2:((cP cS)->((cT cX)->P1)))=> (((((and_rect (cP cS)) (cT cX)) P1) x2) x0)) (P0 b)) (fun (x2:(cP cS))=> (((conj (cP cT)) (cT cX)) ((x1 cP) x2)))))) as proof of (P0 b)
% 298.26/298.55 Found (((fun (P1:Type) (x0:(((and (cP cS)) (cT cX))->((((eq (fofType->Prop)) cS) cT)->P1)))=> (((((and_rect ((and (cP cS)
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