TSTP Solution File: NUM813^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM813^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n071.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:49 EST 2018
% Result : Timeout 285.78s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM813^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n071.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 14:41:05 CST 2018
% 0.02/0.23 % CPUTime :
% 0.09/0.28 Python 2.7.13
% 4.33/4.80 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 4.33/4.80 FOF formula (<kernel.Constant object at 0x2abb690fc098>, <kernel.Constant object at 0x2abb690fc3f8>) of role type named c0_type
% 4.33/4.80 Using role type
% 4.33/4.80 Declaring c0:fofType
% 4.33/4.80 FOF formula (<kernel.Constant object at 0x2abb690fc638>, <kernel.DependentProduct object at 0x2abb6945ca70>) of role type named cEVEN_type
% 4.33/4.80 Using role type
% 4.33/4.80 Declaring cEVEN:(fofType->Prop)
% 4.33/4.80 FOF formula (<kernel.Constant object at 0x2abb69b79050>, <kernel.DependentProduct object at 0x2abb6945cf80>) of role type named cNUMBER_type
% 4.33/4.80 Using role type
% 4.33/4.80 Declaring cNUMBER:(fofType->Prop)
% 4.33/4.80 FOF formula (<kernel.Constant object at 0x2abb690fc3f8>, <kernel.DependentProduct object at 0x2abb6945cb48>) of role type named cODD_type
% 4.33/4.80 Using role type
% 4.33/4.80 Declaring cODD:(fofType->Prop)
% 4.33/4.80 FOF formula (<kernel.Constant object at 0x2abb690fcfc8>, <kernel.DependentProduct object at 0x2abb6945cfc8>) of role type named cS_type
% 4.33/4.80 Using role type
% 4.33/4.80 Declaring cS:(fofType->fofType)
% 4.33/4.80 FOF formula (<kernel.Constant object at 0x2abb690fc3f8>, <kernel.Sort object at 0x2abb617c5fc8>) of role type named cIND_type
% 4.33/4.80 Using role type
% 4.33/4.80 Declaring cIND:Prop
% 4.33/4.80 FOF formula (((eq Prop) cIND) (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx))))) of role definition named cIND_def
% 4.33/4.80 A new definition: (((eq Prop) cIND) (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx)))))
% 4.33/4.80 Defined: cIND:=(forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx))))
% 4.33/4.80 FOF formula (((and ((and ((and ((and ((and (cEVEN c0)) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) cIND)) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn))) of role conjecture named cTHM303
% 4.33/4.80 Conjecture to prove = (((and ((and ((and ((and ((and (cEVEN c0)) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) cIND)) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn))):Prop
% 4.33/4.80 We need to prove ['(((and ((and ((and ((and ((and (cEVEN c0)) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) cIND)) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn)))']
% 4.33/4.80 Parameter fofType:Type.
% 4.33/4.80 Parameter c0:fofType.
% 4.33/4.80 Parameter cEVEN:(fofType->Prop).
% 4.33/4.80 Parameter cNUMBER:(fofType->Prop).
% 4.33/4.80 Parameter cODD:(fofType->Prop).
% 4.33/4.80 Parameter cS:(fofType->fofType).
% 4.33/4.80 Definition cIND:=(forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx)))):Prop.
% 4.33/4.80 Trying to prove (((and ((and ((and ((and ((and (cEVEN c0)) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) cIND)) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn)))
% 4.33/4.80 Found x30:(cNUMBER Xn0)
% 4.33/4.80 Instantiate: Xn0:=Xn:fofType
% 4.33/4.80 Found x30 as proof of (cNUMBER Xn)
% 4.33/4.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 4.33/4.80 Instantiate: Xn0:=Xn:fofType
% 4.33/4.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.33/4.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.33/4.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 4.33/4.80 Instantiate: Xn0:=Xn:fofType
% 4.33/4.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.33/4.80 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 4.33/4.80 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 4.33/4.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 4.33/4.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.33/4.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.33/4.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.33/4.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 10.34/10.83 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 10.34/10.83 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 10.34/10.83 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 10.34/10.83 Found x50:(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found x50 as proof of (cNUMBER Xn)
% 10.34/10.83 Found x30:(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found x30 as proof of (cNUMBER Xn)
% 10.34/10.83 Found x30:(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found (fun (x5:cIND)=> x30) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x5:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 10.34/10.83 Found x30:(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found (fun (x5:cIND)=> x30) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 10.34/10.83 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 10.34/10.83 Found x50:=(x5 x40):(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 10.34/10.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found x50:=(x5 x40):(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 10.34/10.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 10.34/10.83 Found x50:=(x5 x40):(cNUMBER Xn0)
% 10.34/10.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 10.34/10.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 10.34/10.83 Instantiate: Xn0:=Xn:fofType
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 10.34/10.83 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 10.34/10.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.34/10.83 Found x50:=(x5 x40):(cNUMBER Xn0)
% 10.34/10.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 18.17/18.66 Found x30:=(x3 x20):(cNUMBER Xn0)
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 18.17/18.66 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 18.17/18.66 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 18.17/18.66 Found x30:=(x3 x20):(cNUMBER Xn0)
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 18.17/18.66 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 18.17/18.66 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 18.17/18.66 Found x30:(cNUMBER Xn0)
% 18.17/18.66 Instantiate: Xn0:=Xn:fofType
% 18.17/18.66 Found x30 as proof of (cNUMBER Xn)
% 18.17/18.66 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 18.17/18.66 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 18.17/18.66 Found x30:(cNUMBER Xn0)
% 18.17/18.66 Instantiate: Xn0:=Xn:fofType
% 18.17/18.66 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 18.17/18.66 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 18.17/18.66 Found x70:(cNUMBER Xn0)
% 18.17/18.66 Instantiate: Xn0:=Xn:fofType
% 18.17/18.66 Found x70 as proof of (cNUMBER Xn)
% 18.17/18.66 Found x50:(cNUMBER Xn0)
% 18.17/18.66 Instantiate: Xn0:=Xn:fofType
% 18.17/18.66 Found x50 as proof of (cNUMBER Xn)
% 18.17/18.66 Found x30:(cNUMBER Xn0)
% 18.17/18.66 Instantiate: Xn0:=Xn:fofType
% 18.17/18.66 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 20.57/21.06 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 20.57/21.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 20.57/21.06 Instantiate: Xn0:=Xn:fofType
% 20.57/21.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 20.57/21.06 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 20.57/21.06 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20))) as proof of (cNUMBER Xn)
% 20.57/21.06 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20))) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20))) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20))) as proof of (cNUMBER Xn)
% 20.57/21.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 20.57/21.06 Instantiate: Xn0:=Xn:fofType
% 20.57/21.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.57/21.06 Found x50:(cNUMBER Xn0)
% 20.57/21.06 Instantiate: Xn0:=Xn:fofType
% 20.57/21.06 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 20.57/21.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 20.57/21.06 Instantiate: Xn0:=Xn:fofType
% 20.57/21.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 20.57/21.06 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 22.06/22.52 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 22.06/22.52 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20))) as proof of (cNUMBER Xn)
% 22.06/22.52 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20))) as proof of (cNUMBER Xn)
% 22.06/22.52 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20))) as proof of (cNUMBER Xn)
% 22.06/22.52 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)))) as proof of (cNUMBER Xn)
% 22.06/22.52 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 22.06/22.52 Found x30:=(x3 x20):(cNUMBER Xn0)
% 22.06/22.52 Instantiate: Xn0:=Xn:fofType
% 22.06/22.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 22.06/22.52 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 22.06/22.52 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 22.06/22.52 Found x50:(cNUMBER Xn0)
% 22.06/22.52 Instantiate: Xn0:=Xn:fofType
% 22.06/22.52 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 22.06/22.52 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 22.06/22.52 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 27.38/27.93 Found x70:=(x7 x60):(cNUMBER Xn0)
% 27.38/27.93 Instantiate: Xn0:=Xn:fofType
% 27.38/27.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 27.38/27.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 27.38/27.93 Instantiate: Xn0:=Xn:fofType
% 27.38/27.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 27.38/27.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 27.38/27.93 Instantiate: Xn0:=Xn:fofType
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 27.38/27.93 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 27.38/27.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found x70:=(x7 x60):(cNUMBER Xn0)
% 27.38/27.93 Instantiate: Xn0:=Xn:fofType
% 27.38/27.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 27.38/27.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 27.38/27.93 Instantiate: Xn0:=Xn:fofType
% 27.38/27.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 27.38/27.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 27.38/27.93 Found x70:=(x7 x60):(cNUMBER Xn0)
% 27.38/27.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 27.38/27.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 27.38/27.93 Instantiate: Xn0:=Xn:fofType
% 27.38/27.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 27.38/27.93 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 27.38/27.93 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 27.38/27.93 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.38/27.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 27.38/27.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found x30:=(x3 x20):(cNUMBER Xn0)
% 33.17/33.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 33.17/33.69 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 33.17/33.69 Found x70:=(x7 x60):(cNUMBER Xn0)
% 33.17/33.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 33.17/33.69 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 33.17/33.69 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 33.17/33.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 33.17/33.69 Found x50:=(x5 x40):(cNUMBER Xn0)
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 33.17/33.69 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 33.17/33.69 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 33.17/33.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 33.17/33.69 Found x30:(cNUMBER Xn0)
% 33.17/33.69 Instantiate: Xn0:=Xn:fofType
% 33.17/33.69 Found x30 as proof of (cNUMBER Xn)
% 33.17/33.69 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 33.17/33.69 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 33.17/33.69 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 33.17/33.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 33.17/33.69 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 33.17/33.69 Found x50:=(x5 x40):(cNUMBER Xn0)
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 33.17/33.69 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 36.98/37.53 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 36.98/37.53 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 36.98/37.53 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 36.98/37.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 36.98/37.53 Found x30:=(x3 x20):(cNUMBER Xn0)
% 36.98/37.53 Found (x3 x20) as proof of (cNUMBER Xn0)
% 36.98/37.53 Found (x3 x20) as proof of (cNUMBER Xn0)
% 36.98/37.53 Found x30:=(x3 x21):(cNUMBER Xn0)
% 36.98/37.53 Instantiate: Xn0:=Xn:fofType
% 36.98/37.53 Found (x3 x21) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (x3 x21) as proof of (cNUMBER Xn)
% 36.98/37.53 Found x30:=(x3 x21):(cNUMBER Xn0)
% 36.98/37.53 Found (x3 x21) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (x3 x21) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (x3 x21) as proof of (cNUMBER Xn)
% 36.98/37.53 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 36.98/37.53 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 36.98/37.53 Found (x3 x21) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (x3 x21) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (x3 x21) as proof of (cNUMBER Xn)
% 36.98/37.53 Found x30:(cNUMBER Xn0)
% 36.98/37.53 Instantiate: Xn0:=Xn:fofType
% 36.98/37.53 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 36.98/37.53 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 36.98/37.53 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 36.98/37.53 Found (x5 x40) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (x5 x40) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 36.98/37.53 Found x30:=(x3 x20):(cNUMBER Xn0)
% 36.98/37.53 Instantiate: Xn0:=Xn:fofType
% 36.98/37.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 36.98/37.53 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 36.98/37.53 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 36.98/37.53 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 36.98/37.53 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 40.81/41.29 Found x30:=(x3 x20):(cNUMBER Xn0)
% 40.81/41.29 Found (x3 x20) as proof of (cNUMBER Xn0)
% 40.81/41.29 Found (x3 x20) as proof of (cNUMBER Xn0)
% 40.81/41.29 Found x30:=(x3 x21):(cNUMBER Xn0)
% 40.81/41.29 Instantiate: Xn0:=Xn:fofType
% 40.81/41.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.81/41.29 Found x30:=(x3 x21):(cNUMBER Xn0)
% 40.81/41.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.81/41.29 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 40.81/41.29 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.81/41.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.81/41.29 Found x50:(cNUMBER Xn0)
% 40.81/41.29 Instantiate: Xn0:=Xn:fofType
% 40.81/41.29 Found x50 as proof of (cNUMBER Xn)
% 40.81/41.29 Found x30:(cNUMBER Xn0)
% 40.81/41.29 Instantiate: Xn0:=Xn:fofType
% 40.81/41.29 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 40.81/41.29 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x30) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 40.81/41.29 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 40.81/41.29 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.81/41.29 Found (x5 x40) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (x5 x40) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 40.81/41.29 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 40.81/41.29 Found x30:=(x3 x20):(cNUMBER Xn0)
% 40.81/41.29 Instantiate: Xn0:=Xn:fofType
% 40.81/41.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 40.81/41.29 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 40.81/41.29 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 40.81/41.29 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 40.81/41.29 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 42.23/42.75 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 42.23/42.75 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 42.23/42.75 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cIND->(cNUMBER Xn))
% 42.23/42.75 Found x30:=(x3 x20):(cNUMBER Xn0)
% 42.23/42.75 Instantiate: Xn0:=Xn:fofType
% 42.23/42.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.23/42.75 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 42.23/42.75 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.23/42.75 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 42.23/42.75 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 42.23/42.76 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 42.23/42.76 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 42.23/42.76 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 45.07/45.57 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cIND->(cNUMBER Xn))
% 45.07/45.57 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 45.07/45.57 Found x30:=(x3 x21):(cNUMBER Xn0)
% 45.07/45.57 Instantiate: Xn0:=Xn:fofType
% 45.07/45.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 45.07/45.57 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 45.07/45.57 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 45.07/45.57 Found x50:(cNUMBER Xn0)
% 45.07/45.57 Instantiate: Xn0:=c0:fofType
% 45.07/45.57 Found x50 as proof of (cNUMBER c0)
% 45.07/45.57 Found x50:(cNUMBER Xn0)
% 45.07/45.57 Instantiate: Xn0:=Xn:fofType
% 45.07/45.57 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 45.07/45.57 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 45.07/45.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 45.07/45.57 Instantiate: Xn0:=Xn:fofType
% 45.07/45.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 45.07/45.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 45.07/45.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 45.07/45.57 Instantiate: Xn0:=Xn:fofType
% 45.07/45.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 45.07/45.57 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 45.07/45.57 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 45.07/45.57 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 45.07/45.57 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.91/51.38 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.91/51.38 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.91/51.38 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.91/51.38 Found x90:(cNUMBER Xn0)
% 50.91/51.38 Instantiate: Xn0:=Xn:fofType
% 50.91/51.38 Found x90 as proof of (cNUMBER Xn)
% 50.91/51.38 Found x30:(cNUMBER Xn0)
% 50.91/51.38 Instantiate: Xn0:=c0:fofType
% 50.91/51.38 Found x30 as proof of (cNUMBER c0)
% 50.91/51.38 Found x70:(cNUMBER Xn0)
% 50.91/51.38 Instantiate: Xn0:=Xn:fofType
% 50.91/51.38 Found x70 as proof of (cNUMBER Xn)
% 50.91/51.38 Found x50:(cNUMBER Xn0)
% 50.91/51.38 Instantiate: Xn0:=Xn:fofType
% 50.91/51.38 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 50.91/51.38 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 50.91/51.38 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x50) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 50.91/51.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 50.91/51.38 Instantiate: Xn0:=Xn:fofType
% 50.91/51.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 50.91/51.38 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 50.91/51.38 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 50.91/51.38 Found x50:=(x5 x40):(cNUMBER Xn0)
% 50.91/51.38 Instantiate: Xn0:=Xn:fofType
% 50.91/51.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.91/51.38 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 50.91/51.38 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 50.91/51.38 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 50.91/51.38 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.91/51.38 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.91/51.38 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 56.99/57.45 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 56.99/57.45 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 56.99/57.45 Found x50:(cNUMBER Xn0)
% 56.99/57.45 Instantiate: Xn0:=c0:fofType
% 56.99/57.45 Found x50 as proof of (cNUMBER c0)
% 56.99/57.45 Found x70:(cNUMBER Xn0)
% 56.99/57.45 Instantiate: Xn0:=Xn:fofType
% 56.99/57.45 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 56.99/57.45 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 56.99/57.45 Found x50:(cNUMBER Xn0)
% 56.99/57.45 Instantiate: Xn0:=c0:fofType
% 56.99/57.45 Found x50 as proof of (cNUMBER c0)
% 56.99/57.45 Found x50:=(x5 x40):(cNUMBER Xn0)
% 56.99/57.45 Instantiate: Xn0:=Xn:fofType
% 56.99/57.45 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.99/57.45 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.99/57.45 Found x30:=(x3 x20):(cNUMBER Xn0)
% 56.99/57.45 Instantiate: Xn0:=Xn:fofType
% 56.99/57.45 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.99/57.45 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 56.99/57.45 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 56.99/57.45 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 56.99/57.45 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 56.99/57.45 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.99/57.45 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.99/57.45 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.99/57.45 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.99/57.45 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 56.99/57.45 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.24/66.72 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.24/66.72 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.24/66.72 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.24/66.72 Found x30:=(x3 x20):(cNUMBER Xn0)
% 66.24/66.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 66.24/66.72 Found x30:(cNUMBER Xn0)
% 66.24/66.72 Instantiate: Xn0:=c0:fofType
% 66.24/66.72 Found x30 as proof of (cNUMBER c0)
% 66.24/66.72 Found x30:=(x3 x21):(cNUMBER Xn0)
% 66.24/66.72 Found (x3 x21) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (x3 x21) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 66.24/66.72 Found x70:(cNUMBER Xn0)
% 66.24/66.72 Instantiate: Xn0:=Xn:fofType
% 66.24/66.72 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 66.24/66.72 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x70) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 66.24/66.72 Found x50:=(x5 x40):(cNUMBER Xn0)
% 66.24/66.72 Instantiate: Xn0:=Xn:fofType
% 66.24/66.72 Found (x5 x40) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 66.24/66.72 Found x90:=(x9 x80):(cNUMBER Xn0)
% 66.24/66.72 Instantiate: Xn0:=Xn:fofType
% 66.24/66.72 Found (x9 x80) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (x9 x80) as proof of (cNUMBER Xn)
% 66.24/66.72 Found x50:(cNUMBER Xn0)
% 66.24/66.72 Instantiate: Xn0:=c0:fofType
% 66.24/66.72 Found x50 as proof of (cNUMBER c0)
% 66.24/66.72 Found x30:=(x3 x20):(cNUMBER Xn0)
% 66.24/66.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 66.24/66.72 Found x50:=(x5 x40):(cNUMBER Xn0)
% 66.24/66.72 Instantiate: Xn0:=c0:fofType
% 66.24/66.72 Found (x5 x40) as proof of (cNUMBER c0)
% 66.24/66.72 Found (x5 x40) as proof of (cNUMBER c0)
% 66.24/66.72 Found x70:=(x7 x60):(cNUMBER Xn0)
% 66.24/66.72 Instantiate: Xn0:=Xn:fofType
% 66.24/66.72 Found (x7 x60) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (x7 x60) as proof of (cNUMBER Xn)
% 66.24/66.72 Found x50:=(x5 x40):(cNUMBER Xn0)
% 66.24/66.72 Instantiate: Xn0:=Xn:fofType
% 66.24/66.72 Found (x5 x40) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 66.24/66.72 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 66.24/66.72 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 66.24/66.72 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 66.64/67.14 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.64/67.14 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.64/67.14 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.64/67.14 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.64/67.14 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 66.64/67.14 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.64/67.14 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.64/67.14 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.64/67.14 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.64/67.14 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 66.64/67.14 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.64/67.14 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.64/67.14 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.64/67.14 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.64/67.14 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 66.64/67.14 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.64/67.14 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.64/67.14 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.64/67.14 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.72/72.20 Found x90:=(x9 x80):(cNUMBER Xn0)
% 71.72/72.20 Instantiate: Xn0:=Xn:fofType
% 71.72/72.20 Found (x9 x80) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 71.72/72.20 Found x30:=(x3 x20):(cNUMBER Xn0)
% 71.72/72.20 Instantiate: Xn0:=c0:fofType
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER c0)
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER c0)
% 71.72/72.20 Found x50:=(x5 x40):(cNUMBER Xn0)
% 71.72/72.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 71.72/72.20 Found x6:(cNUMBER Xx)
% 71.72/72.20 Instantiate: Xn0:=Xx:fofType
% 71.72/72.20 Found x6 as proof of (cNUMBER Xn0)
% 71.72/72.20 Found x30:=(x3 x20):(cNUMBER Xn0)
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 71.72/72.20 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 71.72/72.20 Found x50:(cNUMBER Xn0)
% 71.72/72.20 Instantiate: Xn0:=(cS Xx):fofType
% 71.72/72.20 Found x50 as proof of (cNUMBER (cS Xx))
% 71.72/72.20 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 71.72/72.20 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 71.72/72.20 Found x30:=(x3 x20):(cNUMBER Xn0)
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER Xn0)
% 71.72/72.20 Found (x3 x20) as proof of (cNUMBER Xn0)
% 71.72/72.20 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 71.72/72.20 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.72/72.20 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.72/72.20 Found x31:(cNUMBER Xn0)
% 71.72/72.20 Instantiate: Xn0:=Xn:fofType
% 71.72/72.20 Found (fun (x5:cIND)=> x31) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> x31) as proof of (cIND->(cNUMBER Xn))
% 71.72/72.20 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> x31) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 71.72/72.20 Found x70:=(x7 x60):(cNUMBER Xn0)
% 71.72/72.20 Instantiate: Xn0:=Xn:fofType
% 71.72/72.20 Found (x7 x60) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 71.72/72.20 Found x6:(cNUMBER Xx)
% 71.72/72.20 Instantiate: Xn0:=Xx:fofType
% 71.72/72.20 Found x6 as proof of (cNUMBER Xn0)
% 71.72/72.20 Found x30:(cNUMBER Xn0)
% 71.72/72.20 Instantiate: Xn0:=(cS Xx):fofType
% 71.72/72.20 Found x30 as proof of (cNUMBER (cS Xx))
% 71.72/72.20 Found x50:=(x5 x40):(cNUMBER Xn0)
% 71.72/72.20 Instantiate: Xn0:=c0:fofType
% 71.72/72.20 Found (x5 x40) as proof of (cNUMBER c0)
% 71.72/72.20 Found (x5 x40) as proof of (cNUMBER c0)
% 71.72/72.20 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 71.72/72.20 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.72/72.20 Found (x3 x21) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (x3 x21) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 71.72/72.20 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 71.72/72.20 Found x31:(cNUMBER Xn0)
% 76.59/77.06 Instantiate: Xn0:=Xn:fofType
% 76.59/77.06 Found (fun (x5:cIND)=> x31) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x5:cIND)=> x31) as proof of (cIND->(cNUMBER Xn))
% 76.59/77.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 76.59/77.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 76.59/77.06 Found x50:(cNUMBER Xn0)
% 76.59/77.06 Instantiate: Xn0:=(cS Xx):fofType
% 76.59/77.06 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 76.59/77.06 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 76.59/77.06 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 76.59/77.06 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.59/77.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 76.59/77.06 Found x30:=(x3 x21):(cNUMBER Xn0)
% 76.59/77.06 Instantiate: Xn0:=Xn:fofType
% 76.59/77.06 Found (x3 x21) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x5:cIND)=> (x3 x21)) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21)) as proof of (cIND->(cNUMBER Xn))
% 76.59/77.06 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 76.59/77.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 76.59/77.06 Found (x3 x20) as proof of (cNUMBER Xn0)
% 76.59/77.06 Found (x3 x20) as proof of (cNUMBER Xn0)
% 76.59/77.06 Found x30:=(x3 x21):(cNUMBER Xn0)
% 76.59/77.06 Instantiate: Xn0:=Xn:fofType
% 76.59/77.06 Found (x3 x21) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x5:cIND)=> (x3 x21)) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x5:cIND)=> (x3 x21)) as proof of (cIND->(cNUMBER Xn))
% 76.59/77.06 Found x90:=(x9 x80):(cNUMBER Xn0)
% 76.59/77.06 Found (x9 x80) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (x9 x80) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (x9 x80) as proof of (cNUMBER Xn)
% 76.59/77.06 Found x30:(cNUMBER Xn0)
% 76.59/77.06 Instantiate: Xn0:=Xn:fofType
% 76.59/77.06 Found x30 as proof of (cNUMBER Xn)
% 76.59/77.06 Found x50:(cNUMBER Xn00)
% 76.59/77.06 Instantiate: Xn00:=Xn:fofType
% 76.59/77.06 Found x50 as proof of (cNUMBER Xn)
% 76.59/77.06 Found x50:(cNUMBER Xn0)
% 76.59/77.06 Instantiate: Xn0:=(cS Xx):fofType
% 76.59/77.06 Found x50 as proof of (cNUMBER (cS Xx))
% 76.59/77.06 Found x6:(cNUMBER Xx)
% 76.59/77.06 Instantiate: Xn0:=Xx:fofType
% 76.59/77.06 Found x6 as proof of (cNUMBER Xn0)
% 76.59/77.06 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 76.59/77.06 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.59/77.06 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.59/77.06 Found x70:=(x7 x60):(cNUMBER Xn0)
% 76.59/77.06 Instantiate: Xn0:=Xn:fofType
% 76.59/77.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 76.59/77.06 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 76.59/77.06 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 76.59/77.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 76.59/77.06 Instantiate: Xn0:=c0:fofType
% 76.59/77.06 Found (x5 x40) as proof of (cNUMBER c0)
% 76.59/77.06 Found (x5 x40) as proof of (cNUMBER c0)
% 76.59/77.06 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 76.59/77.06 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 76.59/77.06 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 76.59/77.06 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 76.59/77.06 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 79.68/80.18 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 79.68/80.18 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.68/80.18 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.68/80.18 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.68/80.18 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.68/80.18 Found x30:(cNUMBER Xn0)
% 79.68/80.18 Instantiate: Xn0:=(cS Xx):fofType
% 79.68/80.18 Found (fun (x6:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 79.68/80.18 Found (fun (x6:(cNUMBER Xx))=> x30) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 79.68/80.18 Found x31:(cNUMBER Xn0)
% 79.68/80.18 Instantiate: Xn0:=Xn:fofType
% 79.68/80.18 Found (fun (x5:cIND)=> x31) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (fun (x5:cIND)=> x31) as proof of (cIND->(cNUMBER Xn))
% 79.68/80.18 Found x70:=(x7 x60):(cNUMBER Xn0)
% 79.68/80.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 79.68/80.18 Found x50:=(x5 x40):(cNUMBER Xn0)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn0)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn0)
% 79.68/80.18 Found x50:=(x5 x41):(cNUMBER Xn0)
% 79.68/80.18 Instantiate: Xn0:=Xn:fofType
% 79.68/80.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 79.68/80.18 Found x50:=(x5 x40):(cNUMBER Xn0)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.68/80.18 Found x50:=(x5 x40):(cNUMBER Xn0)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 79.68/80.18 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 79.68/80.18 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 79.68/80.18 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.68/80.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 79.68/80.18 Instantiate: Xn0:=c0:fofType
% 79.68/80.18 Found (x3 x20) as proof of (cNUMBER c0)
% 79.68/80.18 Found (x3 x20) as proof of (cNUMBER c0)
% 79.68/80.18 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 79.68/80.18 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.68/80.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 79.68/80.18 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 79.68/80.18 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 84.30/84.76 Found x90:=(x9 x80):(cNUMBER Xn0)
% 84.30/84.76 Found (x9 x80) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (x9 x80) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 84.30/84.76 Found x30:=(x3 x20):(cNUMBER Xn0)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 84.30/84.76 Found x30:(cNUMBER Xn0)
% 84.30/84.76 Instantiate: Xn0:=Xn:fofType
% 84.30/84.76 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 84.30/84.76 Found x30:=(x3 x20):(cNUMBER Xn0)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn0)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn0)
% 84.30/84.76 Found x30:=(x3 x21):(cNUMBER Xn0)
% 84.30/84.76 Instantiate: Xn0:=Xn:fofType
% 84.30/84.76 Found (x3 x21) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x5:cIND)=> (x3 x21)) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x5:cIND)=> (x3 x21)) as proof of (cIND->(cNUMBER Xn))
% 84.30/84.76 Found x50:(cNUMBER Xn0)
% 84.30/84.76 Instantiate: Xn0:=(cS Xx):fofType
% 84.30/84.76 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 84.30/84.76 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 84.30/84.76 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 84.30/84.76 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 84.30/84.76 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 84.30/84.76 Found x30:=(x3 x20):(cNUMBER Xn0)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn0)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn0)
% 84.30/84.76 Found x30:=(x3 x21):(cNUMBER Xn0)
% 84.30/84.76 Instantiate: Xn0:=Xn:fofType
% 84.30/84.76 Found (x3 x21) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (x3 x21) as proof of (cNUMBER Xn)
% 84.30/84.76 Found x30:=(x3 x20):(cNUMBER Xn0)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn)
% 84.30/84.76 Found x30:(cNUMBER Xn0)
% 84.30/84.76 Instantiate: Xn0:=Xn:fofType
% 84.30/84.76 Found x30 as proof of (cNUMBER Xn)
% 84.30/84.76 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 84.30/84.76 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 84.30/84.76 Found (x5 x40) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (x5 x40) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (x5 x40) as proof of (cNUMBER Xn)
% 84.30/84.76 Found x50:(cNUMBER Xn0)
% 84.30/84.76 Found x50 as proof of (cNUMBER (cS Xx))
% 84.30/84.76 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 84.30/84.76 Found x30:=(x3 x20):(cNUMBER Xn0)
% 84.30/84.76 Instantiate: Xn0:=Xn:fofType
% 84.30/84.76 Found (x3 x20) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 84.30/84.76 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 84.30/84.76 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 84.30/84.76 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 84.30/84.76 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 87.90/88.36 Found x50:=(x5 x40):(cNUMBER Xn0)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER c0)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER c0)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER c0)
% 87.90/88.36 Found x50:=(x5 x40):(cNUMBER Xn0)
% 87.90/88.36 Instantiate: Xn0:=c0:fofType
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER c0)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER c0)
% 87.90/88.36 Found x70:=(x7 x60):(cNUMBER Xn0)
% 87.90/88.36 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 87.90/88.36 Found x50:=(x5 x40):(cNUMBER Xn0)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER Xn0)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER Xn0)
% 87.90/88.36 Found x50:=(x5 x41):(cNUMBER Xn0)
% 87.90/88.36 Instantiate: Xn0:=Xn:fofType
% 87.90/88.36 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.90/88.36 Found x50:=(x5 x40):(cNUMBER Xn0)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.90/88.36 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 87.90/88.36 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 87.90/88.36 Found x50:=(x5 x40):(cNUMBER Xn0)
% 87.90/88.36 Instantiate: Xn0:=(cS Xx):fofType
% 87.90/88.36 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 87.90/88.36 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 87.90/88.36 Found x50:(cNUMBER Xn0)
% 87.90/88.36 Instantiate: Xn0:=(cS Xx):fofType
% 87.90/88.36 Found x50 as proof of (cNUMBER (cS Xx))
% 87.90/88.36 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 87.90/88.36 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 87.90/88.36 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.90/88.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.90/88.36 Found x30:(cNUMBER Xn0)
% 87.90/88.36 Found x30 as proof of (cNUMBER (cS Xx))
% 87.90/88.36 Found (fun (x6:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 87.90/88.36 Found x30:(cNUMBER Xn0)
% 87.90/88.36 Instantiate: Xn0:=Xn:fofType
% 87.90/88.36 Found (fun (x6:cIND)=> x30) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 87.90/88.36 Found (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30) as proof of ((cEVEN Xn0)->(cIND->(cNUMBER Xn)))
% 87.90/88.36 Found x30:(cNUMBER Xn0)
% 87.90/88.36 Instantiate: Xn0:=Xn:fofType
% 87.90/88.36 Found (fun (x6:cIND)=> x30) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (fun (x5:(cODD Xn0)) (x6:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 87.90/88.36 Found (fun (x5:(cODD Xn0)) (x6:cIND)=> x30) as proof of ((cODD Xn0)->(cIND->(cNUMBER Xn)))
% 87.90/88.36 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 87.90/88.36 Found (((or_ind0 (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 87.90/88.36 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 87.90/88.36 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 87.90/88.36 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 87.90/88.36 Found x30:=(x3 x20):(cNUMBER Xn0)
% 87.90/88.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 87.90/88.36 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 88.22/88.69 Found x30:(cNUMBER Xn0)
% 88.22/88.69 Instantiate: Xn0:=Xn:fofType
% 88.22/88.69 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 88.22/88.69 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 88.22/88.69 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 88.22/88.69 Found x30:=(x3 x20):(cNUMBER Xn0)
% 88.22/88.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 88.22/88.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 88.22/88.69 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 88.22/88.69 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 88.22/88.69 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 88.22/88.69 Found x30:=(x3 x20):(cNUMBER Xn0)
% 88.22/88.69 Found (x3 x20) as proof of (cNUMBER c0)
% 88.22/88.69 Found (x3 x20) as proof of (cNUMBER c0)
% 88.22/88.69 Found (x3 x20) as proof of (cNUMBER c0)
% 88.22/88.69 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 88.22/88.69 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.22/88.69 Found (x9 x80) as proof of (cNUMBER Xn)
% 88.22/88.69 Found (x9 x80) as proof of (cNUMBER Xn)
% 88.22/88.69 Found (x9 x80) as proof of (cNUMBER Xn)
% 88.22/88.69 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 88.22/88.69 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 88.22/88.69 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 88.22/88.69 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 88.22/88.69 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 88.22/88.69 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 88.22/88.69 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.22/88.69 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.22/88.69 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.22/88.69 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.18/89.64 Found (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 89.18/89.64 Found (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 89.18/89.64 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 89.18/89.64 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.18/89.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 89.18/89.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 89.18/89.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 89.18/89.64 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 89.18/89.64 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 89.18/89.64 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 89.18/89.64 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 89.18/89.64 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 89.18/89.64 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 89.18/89.64 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.18/89.64 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.18/89.64 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.18/89.64 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.18/89.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 89.18/89.64 Found (x3 x20) as proof of (cNUMBER Xn0)
% 89.18/89.64 Found (x3 x20) as proof of (cNUMBER Xn0)
% 89.18/89.64 Found x30:=(x3 x21):(cNUMBER Xn0)
% 89.18/89.64 Instantiate: Xn0:=Xn:fofType
% 89.18/89.64 Found (x3 x21) as proof of (cNUMBER Xn)
% 89.18/89.64 Found (x3 x21) as proof of (cNUMBER Xn)
% 89.18/89.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 89.18/89.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 89.18/89.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 89.18/89.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 89.18/89.64 Found x30:(cNUMBER Xn0)
% 89.18/89.64 Instantiate: Xn0:=Xn:fofType
% 89.18/89.64 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 89.18/89.64 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 92.94/93.46 Found x30:=(x3 x20):(cNUMBER Xn0)
% 92.94/93.46 Instantiate: Xn0:=(cS Xx):fofType
% 92.94/93.46 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 92.94/93.46 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 92.94/93.46 Found x30:(cNUMBER Xn0)
% 92.94/93.46 Instantiate: Xn0:=(cS Xx):fofType
% 92.94/93.46 Found x30 as proof of (cNUMBER (cS Xx))
% 92.94/93.46 Found (fun (x6:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 92.94/93.46 Found x30:=(x3 x20):(cNUMBER Xn0)
% 92.94/93.46 Instantiate: Xn0:=Xn:fofType
% 92.94/93.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 92.94/93.46 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 92.94/93.46 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 92.94/93.46 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 92.94/93.46 Found x50:=(x5 x40):(cNUMBER Xn0)
% 92.94/93.46 Instantiate: Xn0:=c0:fofType
% 92.94/93.46 Found (x5 x40) as proof of (cNUMBER c0)
% 92.94/93.46 Found (x5 x40) as proof of (cNUMBER c0)
% 92.94/93.46 Found x70:=(x7 x60):(cNUMBER Xn0)
% 92.94/93.46 Found (x7 x60) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (x7 x60) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 92.94/93.46 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 92.94/93.46 Found x50:(cNUMBER Xn0)
% 92.94/93.46 Found x50 as proof of (cNUMBER (cS Xx))
% 92.94/93.46 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 92.94/93.46 Found x50:=(x5 x41):(cNUMBER Xn0)
% 92.94/93.46 Instantiate: Xn0:=Xn:fofType
% 92.94/93.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 92.94/93.46 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x41)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 92.94/93.46 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 92.94/93.46 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.38/93.91 Found (x7 x60) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (x7 x60) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (x7 x60) as proof of (cNUMBER Xn)
% 93.38/93.91 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 93.38/93.91 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.38/93.91 Found (x3 x20) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (x3 x20) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 93.38/93.91 Found x30:=(x3 x20):(cNUMBER Xn0)
% 93.38/93.91 Instantiate: Xn0:=Xn:fofType
% 93.38/93.91 Found (x3 x20) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.38/93.91 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 93.38/93.91 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 93.38/93.91 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 93.38/93.91 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 93.38/93.91 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 93.38/93.91 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.38/93.91 Found (x5 x40) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (x5 x40) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 93.38/93.91 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 95.44/95.90 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 95.44/95.90 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.90 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 95.44/95.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 95.44/95.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 95.44/95.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 95.44/95.90 Found (x5 x40) as proof of (cNUMBER c0)
% 95.44/95.90 Found (x5 x40) as proof of (cNUMBER c0)
% 95.44/95.90 Found (x5 x40) as proof of (cNUMBER c0)
% 95.44/95.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 95.44/95.90 Instantiate: Xn0:=Xn:fofType
% 95.44/95.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 95.44/95.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 95.44/95.90 Found x50:=(x5 x40):(cNUMBER Xn00)
% 95.44/95.90 Instantiate: Xn00:=Xn:fofType
% 95.44/95.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 95.44/95.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 95.44/95.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 95.44/95.90 Instantiate: Xn0:=(cS Xx):fofType
% 95.44/95.90 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 95.44/95.90 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 95.44/95.90 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 95.44/95.90 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 95.44/95.90 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 95.44/95.90 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 95.44/95.90 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 95.44/95.90 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 95.44/95.90 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.90 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.90 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.90 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.90 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 95.44/95.91 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 95.44/95.91 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.91 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.91 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.44/95.91 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.87/99.36 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 98.87/99.36 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.87/99.36 Found (x9 x80) as proof of (cNUMBER Xn)
% 98.87/99.36 Found (x9 x80) as proof of (cNUMBER Xn)
% 98.87/99.36 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 98.87/99.36 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 98.87/99.36 Found x50:=(x5 x40):(cNUMBER Xn0)
% 98.87/99.36 Instantiate: Xn0:=(cS Xx):fofType
% 98.87/99.36 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 98.87/99.36 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 98.87/99.36 Found x50:(cNUMBER Xn0)
% 98.87/99.36 Instantiate: Xn0:=(cS Xx):fofType
% 98.87/99.36 Found x50 as proof of (cNUMBER (cS Xx))
% 98.87/99.36 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 98.87/99.36 Found x30:(cNUMBER Xn0)
% 98.87/99.36 Instantiate: Xn0:=Xn:fofType
% 98.87/99.36 Found (fun (x6:cIND)=> x30) as proof of (cNUMBER Xn)
% 98.87/99.36 Found (fun (x5:(cODD Xn0)) (x6:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 98.87/99.36 Found (fun (x5:(cODD Xn0)) (x6:cIND)=> x30) as proof of ((cODD Xn0)->(cIND->(cNUMBER Xn)))
% 98.87/99.36 Found x30:(cNUMBER Xn0)
% 98.87/99.36 Instantiate: Xn0:=Xn:fofType
% 98.87/99.36 Found (fun (x6:cIND)=> x30) as proof of (cNUMBER Xn)
% 98.87/99.36 Found (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 98.87/99.36 Found (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30) as proof of ((cEVEN Xn0)->(cIND->(cNUMBER Xn)))
% 98.87/99.36 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 98.87/99.36 Found (((or_ind0 (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 98.87/99.36 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 98.87/99.36 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30)) as proof of (cIND->(cNUMBER Xn))
% 98.87/99.36 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30))) as proof of (cIND->(cNUMBER Xn))
% 98.87/99.36 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) (cIND->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:cIND)=> x30)) (fun (x5:(cODD Xn0)) (x6:cIND)=> x30))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 98.87/99.36 Found x50:(cNUMBER Xn0)
% 98.87/99.36 Instantiate: Xn0:=Xn:fofType
% 98.87/99.36 Found x50 as proof of (cNUMBER Xn)
% 98.87/99.36 Found x30:=(x3 x20):(cNUMBER Xn0)
% 98.87/99.36 Found (x3 x20) as proof of (cNUMBER Xn0)
% 98.87/99.36 Found (x3 x20) as proof of (cNUMBER Xn0)
% 98.87/99.36 Found x30:=(x3 x21):(cNUMBER Xn0)
% 98.87/99.36 Instantiate: Xn0:=Xn:fofType
% 98.87/99.36 Found (x3 x21) as proof of (cNUMBER Xn)
% 98.87/99.36 Found (x3 x21) as proof of (cNUMBER Xn)
% 98.87/99.36 Found x30:=(x3 x20):(cNUMBER Xn0)
% 98.87/99.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.87/99.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.87/99.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.87/99.36 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 98.87/99.36 Instantiate: Xn00:=Xn:fofType
% 98.87/99.36 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.07/102.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 102.07/102.53 Instantiate: Xn0:=Xn:fofType
% 102.07/102.53 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 102.07/102.53 Found x30:(cNUMBER Xn0)
% 102.07/102.53 Instantiate: Xn0:=Xn:fofType
% 102.07/102.53 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 102.07/102.53 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 102.07/102.53 Found x50:=(x5 x40):(cNUMBER Xn0)
% 102.07/102.53 Instantiate: Xn0:=Xn:fofType
% 102.07/102.53 Found (x5 x40) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 102.07/102.53 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 102.07/102.53 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 102.07/102.53 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 102.07/102.53 Found x30:=(x3 x20):(cNUMBER Xn0)
% 102.07/102.53 Instantiate: Xn0:=(cS Xx):fofType
% 102.07/102.53 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 102.07/102.53 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 102.07/102.53 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 102.07/102.53 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.07/102.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 102.07/102.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 102.07/102.53 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.07/102.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 102.07/102.53 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 102.07/102.53 Found x30:=(x3 x20):(cNUMBER Xn0)
% 102.07/102.53 Instantiate: Xn0:=Xn:fofType
% 102.07/102.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 102.07/102.53 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 103.07/103.57 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 103.07/103.57 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.07/103.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.07/103.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.07/103.57 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 103.07/103.57 Found (fun (x5:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 103.07/103.57 Found x50:=(x5 x40):(cNUMBER Xn00)
% 103.07/103.57 Instantiate: Xn00:=Xn:fofType
% 103.07/103.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 103.07/103.57 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 103.07/103.57 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 103.07/103.57 Found x30:(cNUMBER Xn0)
% 103.07/103.57 Instantiate: Xn0:=c0:fofType
% 103.07/103.57 Found x30 as proof of (cNUMBER c0)
% 103.07/103.57 Found x30:(cNUMBER Xn0)
% 103.07/103.57 Instantiate: Xn0:=Xn:fofType
% 103.07/103.57 Found (fun (x6:cIND)=> x30) as proof of (cNUMBER Xn)
% 103.07/103.57 Found (fun (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 103.07/103.57 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 103.07/103.57 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30) as proof of ((cEVEN Xn0)->(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn))))
% 103.07/103.57 Found x30:(cNUMBER Xn0)
% 103.07/103.57 Instantiate: Xn0:=Xn:fofType
% 103.07/103.57 Found (fun (x6:cIND)=> x30) as proof of (cNUMBER Xn)
% 103.07/103.57 Found (fun (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 103.07/103.57 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 103.07/103.57 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30) as proof of ((cODD Xn0)->(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn))))
% 103.07/103.57 Found ((or_ind00 (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 103.07/103.57 Found (((or_ind0 (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:cIND)=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 103.25/103.72 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->(cIND->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:cIND)=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:cIND)=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 103.25/103.72 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) (x2 x30))) (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->(cIND->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:cIND)=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:cIND)=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 103.25/103.72 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) (x2 x30))) (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->(cIND->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:cIND)=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:cIND)=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 103.25/103.72 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 103.25/103.72 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.25/103.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.25/103.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.25/103.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.25/103.72 Found x50:=(x5 x40):(cNUMBER Xn0)
% 103.25/103.72 Instantiate: Xn0:=(cS Xx):fofType
% 103.25/103.72 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 103.25/103.72 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 103.25/103.72 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 104.77/105.28 Found x50:=(x5 x40):(cNUMBER Xn0)
% 104.77/105.28 Instantiate: Xn0:=(cS Xx):fofType
% 104.77/105.28 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 104.77/105.28 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 104.77/105.28 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 104.77/105.28 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 104.77/105.28 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 104.77/105.28 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 104.77/105.28 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 104.77/105.28 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 104.77/105.28 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 104.77/105.28 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 104.77/105.28 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 104.77/105.28 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 104.77/105.28 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 104.77/105.28 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 104.77/105.28 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 104.77/105.28 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 104.77/105.28 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 104.77/105.28 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 104.77/105.28 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 104.77/105.28 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 107.50/107.96 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found (x5 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 107.50/107.96 Found (x5 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 107.50/107.96 Found x50:=(x5 x40):(cNUMBER Xn0)
% 107.50/107.96 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 107.50/107.96 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 107.50/107.96 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 107.50/107.96 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 107.50/107.96 Instantiate: Xn00:=Xn:fofType
% 107.50/107.96 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found x50:(cNUMBER Xn0)
% 107.50/107.96 Instantiate: Xn0:=Xn:fofType
% 107.50/107.96 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 107.50/107.96 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 107.50/107.96 Found x50:=(x5 x40):(cNUMBER Xn0)
% 107.50/107.96 Instantiate: Xn0:=(cS Xx):fofType
% 107.50/107.96 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 107.50/107.96 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 107.50/107.96 Found x50:(cNUMBER Xn0)
% 107.50/107.96 Instantiate: Xn0:=c0:fofType
% 107.50/107.96 Found x50 as proof of (cNUMBER c0)
% 107.50/107.96 Found x9:(cODD (cS c0))
% 107.50/107.96 Instantiate: Xn0:=(cS c0):fofType
% 107.50/107.96 Found x9 as proof of (cODD Xn0)
% 107.50/107.96 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.50/107.96 Found x50:=(x5 x40):(cNUMBER Xn0)
% 107.50/107.96 Instantiate: Xn0:=Xn:fofType
% 107.50/107.96 Found (x5 x40) as proof of (cNUMBER Xn)
% 107.50/107.96 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 107.50/107.96 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 107.50/107.96 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 110.38/110.90 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 110.38/110.90 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 110.38/110.90 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 110.38/110.90 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 110.38/110.90 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 110.38/110.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 110.38/110.90 Instantiate: Xn0:=(cS Xx):fofType
% 110.38/110.90 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 110.38/110.90 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 110.38/110.90 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 110.38/110.90 Found x50:(cNUMBER Xn0)
% 110.38/110.90 Found x50 as proof of (cNUMBER (cS Xx))
% 110.38/110.90 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 110.38/110.90 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 110.38/110.90 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.38/110.90 Found (x5 x40) as proof of (cNUMBER c0)
% 110.38/110.90 Found (x5 x40) as proof of (cNUMBER c0)
% 110.38/110.90 Found (x5 x40) as proof of (cNUMBER c0)
% 110.38/110.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 110.38/110.90 Instantiate: Xn0:=Xn:fofType
% 110.38/110.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.38/110.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.38/110.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 110.38/110.90 Instantiate: Xn0:=c0:fofType
% 110.38/110.90 Found (x5 x40) as proof of (cNUMBER c0)
% 110.38/110.90 Found (x5 x40) as proof of (cNUMBER c0)
% 110.38/110.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 110.38/110.90 Instantiate: Xn0:=Xn:fofType
% 110.38/110.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 110.38/110.90 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 110.38/110.90 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 110.38/110.90 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 110.38/110.90 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 110.38/110.90 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 110.38/110.90 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 111.81/112.30 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 111.81/112.30 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 111.81/112.30 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 111.81/112.30 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 111.81/112.30 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.81/112.30 Found (x7 x60) as proof of (cNUMBER Xn)
% 111.81/112.30 Found (x7 x60) as proof of (cNUMBER Xn)
% 111.81/112.30 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 111.81/112.30 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 111.81/112.30 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 111.81/112.30 Found x30:=(x3 x20):(cNUMBER Xn0)
% 111.81/112.30 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 111.81/112.30 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 111.81/112.30 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 111.81/112.30 Found x30:=(x3 x20):(cNUMBER Xn0)
% 111.81/112.30 Instantiate: Xn0:=Xn:fofType
% 111.81/112.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.81/112.30 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 111.81/112.30 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 111.81/112.30 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 111.81/112.30 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 111.81/112.30 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 111.81/112.30 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 111.81/112.30 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 111.81/112.30 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 111.84/112.31 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 111.84/112.31 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.84/112.31 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.84/112.31 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.84/112.31 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.84/112.31 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 111.84/112.31 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 111.84/112.31 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.46/114.97 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.46/114.97 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.46/114.97 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.46/114.97 Found x50:=(x5 x40):(cNUMBER Xn0)
% 114.46/114.97 Instantiate: Xn0:=(cS Xx):fofType
% 114.46/114.97 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 114.46/114.97 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 114.46/114.97 Found x50:=(x5 x40):(cNUMBER Xn00)
% 114.46/114.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 114.46/114.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 114.46/114.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 114.46/114.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 114.46/114.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 114.46/114.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 114.46/114.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 114.46/114.97 Found x50:(cNUMBER Xn0)
% 114.46/114.97 Instantiate: Xn0:=(cS Xx):fofType
% 114.46/114.97 Found x50 as proof of (cNUMBER (cS Xx))
% 114.46/114.97 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 114.46/114.97 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 114.46/114.97 Instantiate: Xn00:=Xn:fofType
% 114.46/114.97 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.46/114.97 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x40) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 114.46/114.97 Found x30:(cNUMBER Xn0)
% 114.46/114.97 Found x30 as proof of (cNUMBER (cS Xx))
% 114.46/114.97 Found (fun (x6:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 114.46/114.97 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 114.46/114.97 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 120.88/121.39 Found (x3 x20) as proof of (cNUMBER c0)
% 120.88/121.39 Found (x3 x20) as proof of (cNUMBER c0)
% 120.88/121.39 Found (x3 x20) as proof of (cNUMBER c0)
% 120.88/121.39 Found x70:(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=Xn:fofType
% 120.88/121.39 Found x70 as proof of (cNUMBER Xn)
% 120.88/121.39 Found x50:=(x5 x40):(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=(cS Xx):fofType
% 120.88/121.39 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 120.88/121.39 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 120.88/121.39 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 120.88/121.39 Found x30:=(x3 x20):(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=c0:fofType
% 120.88/121.39 Found (x3 x20) as proof of (cNUMBER c0)
% 120.88/121.39 Found (x3 x20) as proof of (cNUMBER c0)
% 120.88/121.39 Found x70:(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=c0:fofType
% 120.88/121.39 Found x70 as proof of (cNUMBER c0)
% 120.88/121.39 Found x30:(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=c0:fofType
% 120.88/121.39 Found x30 as proof of (cNUMBER c0)
% 120.88/121.39 Found x50:(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=Xn:fofType
% 120.88/121.39 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 120.88/121.39 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 120.88/121.39 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 120.88/121.39 Found x70:=(x7 x60):(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=Xn:fofType
% 120.88/121.39 Found (x7 x60) as proof of (cNUMBER Xn)
% 120.88/121.39 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 120.88/121.39 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 120.88/121.39 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 120.88/121.39 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 120.88/121.39 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 120.88/121.39 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 120.88/121.39 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 120.88/121.39 Found x50:=(x5 x40):(cNUMBER Xn0)
% 120.88/121.39 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 120.88/121.39 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 120.88/121.39 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 120.88/121.39 Found x30:=(x3 x20):(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=(cS Xx):fofType
% 120.88/121.39 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 120.88/121.39 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 120.88/121.39 Found x30:=(x3 x20):(cNUMBER Xn0)
% 120.88/121.39 Instantiate: Xn0:=Xn:fofType
% 120.88/121.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 120.88/121.39 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 120.88/121.39 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 120.88/121.39 Found x30:(cNUMBER Xn0)
% 120.88/121.39 Found (fun (x5:cIND)=> x30) as proof of (cNUMBER Xn0)
% 120.88/121.39 Found (fun (x5:cIND)=> x30) as proof of (cIND->(cNUMBER Xn0))
% 120.88/121.39 Found x50:=(x5 x40):(cNUMBER Xn0)
% 124.15/124.63 Instantiate: Xn0:=c0:fofType
% 124.15/124.63 Found (x5 x40) as proof of (cNUMBER c0)
% 124.15/124.63 Found (x5 x40) as proof of (cNUMBER c0)
% 124.15/124.63 Found x30:(cNUMBER Xn0)
% 124.15/124.63 Instantiate: Xn0:=(cS Xx):fofType
% 124.15/124.63 Found x30 as proof of (cNUMBER (cS Xx))
% 124.15/124.63 Found (fun (x6:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 124.15/124.63 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 124.15/124.63 Found (fun (x5:cIND)=> x20) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.15/124.63 Found (fun (x5:cIND)=> x20) as proof of (cIND->((or (cEVEN Xn0)) (cODD Xn0)))
% 124.15/124.63 Found x50:(cNUMBER Xn0)
% 124.15/124.63 Instantiate: Xn0:=c0:fofType
% 124.15/124.63 Found x50 as proof of (cNUMBER c0)
% 124.15/124.63 Found x50:(cNUMBER Xn0)
% 124.15/124.63 Found x50 as proof of (cNUMBER (cS Xx))
% 124.15/124.63 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 124.15/124.63 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 124.15/124.63 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.15/124.63 Found (x5 x40) as proof of (cNUMBER c0)
% 124.15/124.63 Found (x5 x40) as proof of (cNUMBER c0)
% 124.15/124.63 Found (x5 x40) as proof of (cNUMBER c0)
% 124.15/124.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 124.15/124.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 124.15/124.63 Found x30:=(x3 x21):(cNUMBER Xn0)
% 124.15/124.63 Instantiate: Xn0:=Xn:fofType
% 124.15/124.63 Found (x3 x21) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (fun (x5:cIND)=> (x3 x21)) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21)) as proof of (cIND->(cNUMBER Xn))
% 124.15/124.63 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 124.15/124.63 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21))) as proof of (cNUMBER Xn)
% 124.15/124.63 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21))) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21))) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21))) as proof of (cNUMBER Xn)
% 124.15/124.63 Found x50:=(x5 x40):(cNUMBER Xn0)
% 124.15/124.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 124.15/124.63 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 126.28/126.83 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 126.28/126.83 Found x50:=(x5 x40):(cNUMBER Xn00)
% 126.28/126.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 126.28/126.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 126.28/126.83 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 126.28/126.83 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 126.28/126.83 Found x6:(cNUMBER Xx)
% 126.28/126.83 Instantiate: Xn0:=Xx:fofType
% 126.28/126.83 Found x6 as proof of (cNUMBER Xn0)
% 126.28/126.83 Found (x4 x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.28/126.83 Found (x4 x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.28/126.83 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 126.28/126.83 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.28/126.83 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.28/126.83 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.28/126.83 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.28/126.83 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 126.28/126.83 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.28/126.83 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.28/126.83 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.28/126.83 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.28/126.83 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 126.28/126.83 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 126.28/126.83 Found x30:(cNUMBER Xn0)
% 126.28/126.83 Instantiate: Xn0:=c0:fofType
% 126.28/126.83 Found x30 as proof of (cNUMBER c0)
% 126.28/126.83 Found x50:=(x5 x40):(cNUMBER Xn0)
% 126.28/126.83 Instantiate: Xn0:=(cS Xx):fofType
% 126.28/126.83 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 128.60/129.07 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 128.60/129.07 Found x30:=(x3 x20):(cNUMBER Xn0)
% 128.60/129.07 Instantiate: Xn0:=c0:fofType
% 128.60/129.07 Found (x3 x20) as proof of (cNUMBER c0)
% 128.60/129.07 Found (x3 x20) as proof of (cNUMBER c0)
% 128.60/129.07 Found x70:(cNUMBER Xn0)
% 128.60/129.07 Instantiate: Xn0:=Xn:fofType
% 128.60/129.07 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 128.60/129.07 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 128.60/129.07 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 128.60/129.07 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.60/129.07 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 128.60/129.07 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 128.60/129.07 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 128.60/129.07 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 128.60/129.07 Instantiate: Xn0:=Xn:fofType
% 128.60/129.07 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 128.60/129.07 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 128.60/129.07 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 128.60/129.07 Instantiate: Xn00:=Xn:fofType
% 128.60/129.07 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.60/129.07 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.60/129.07 Found x50:=(x5 x40):(cNUMBER Xn0)
% 128.60/129.07 Instantiate: Xn0:=(cS Xx):fofType
% 128.60/129.07 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 128.60/129.07 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 128.60/129.07 Found x70:=(x7 x60):(cNUMBER Xn0)
% 128.60/129.07 Instantiate: Xn0:=Xn:fofType
% 128.60/129.07 Found (x7 x60) as proof of (cNUMBER Xn)
% 128.60/129.07 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 128.60/129.07 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 128.60/129.07 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 128.60/129.07 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 128.60/129.07 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 128.60/129.07 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 128.60/129.07 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 128.60/129.07 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 128.60/129.07 Found x9:(cODD (cS c0))
% 128.60/129.07 Instantiate: Xn0:=(cS c0):fofType
% 128.60/129.07 Found x9 as proof of (cODD Xn0)
% 128.60/129.07 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.60/129.07 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.60/129.07 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.60/129.07 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found x50:(cNUMBER Xn0)
% 134.31/134.77 Instantiate: Xn0:=(cS Xx):fofType
% 134.31/134.77 Found x50 as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found x120:(cNUMBER Xn0)
% 134.31/134.77 Instantiate: Xn0:=Xn:fofType
% 134.31/134.77 Found x120 as proof of (cNUMBER Xn)
% 134.31/134.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 134.31/134.77 Instantiate: Xn0:=Xn:fofType
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 134.31/134.77 Found x6:(cNUMBER Xx)
% 134.31/134.77 Instantiate: Xn0:=Xx:fofType
% 134.31/134.77 Found x6 as proof of (cNUMBER Xn0)
% 134.31/134.77 Found (x2 x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found (x2 x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found x70:(cNUMBER Xn0)
% 134.31/134.77 Instantiate: Xn0:=c0:fofType
% 134.31/134.77 Found x70 as proof of (cNUMBER c0)
% 134.31/134.77 Found x30:=(x3 x20):(cNUMBER Xn0)
% 134.31/134.77 Instantiate: Xn0:=Xn:fofType
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 134.31/134.77 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 134.31/134.77 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 134.31/134.77 Instantiate: Xn00:=Xn:fofType
% 134.31/134.77 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found (x3 x40) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x3 x40) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x3 x40) as proof of (cNUMBER Xn)
% 134.31/134.77 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 134.31/134.77 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 134.31/134.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Instantiate: Xn0:=Xn:fofType
% 134.31/134.77 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.31/134.77 Found (x5 x20) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x5 x20) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x5 x20) as proof of (cNUMBER Xn)
% 134.31/134.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 134.31/134.77 Found x30:(cNUMBER Xn0)
% 134.31/134.77 Found (fun (x5:cIND)=> x30) as proof of (cNUMBER Xn0)
% 134.31/134.77 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> x30) as proof of (cIND->(cNUMBER Xn0))
% 134.31/134.77 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->(cIND->(cNUMBER Xn0)))
% 134.31/134.77 Found x30:=(x3 x20):(cNUMBER Xn0)
% 134.31/134.77 Instantiate: Xn0:=(cS Xx):fofType
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found x30:=(x3 x20):(cNUMBER Xn0)
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER Xn0)
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER Xn0)
% 134.31/134.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 134.31/134.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found (fun (x5:cIND)=> x20) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.31/134.77 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> x20) as proof of (cIND->((or (cEVEN Xn0)) (cODD Xn0)))
% 134.37/134.88 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> x20) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->(cIND->((or (cEVEN Xn0)) (cODD Xn0))))
% 134.37/134.88 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 134.37/134.88 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 134.37/134.88 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 134.37/134.88 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 134.37/134.88 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 134.37/134.88 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 134.37/134.88 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.37/134.88 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.37/134.88 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.37/134.88 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.37/134.88 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 134.37/134.88 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 134.91/135.39 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.91/135.39 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.91/135.39 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.91/135.39 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.91/135.39 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 134.91/135.39 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.50/135.98 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.50/135.98 Found x31:(cNUMBER Xn0)
% 135.50/135.98 Instantiate: Xn0:=Xn:fofType
% 135.50/135.98 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 135.50/135.98 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 135.50/135.98 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 135.50/135.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 135.50/135.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 135.50/135.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 135.50/135.98 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 135.50/135.98 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 135.50/135.98 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 135.50/135.98 Found x30:=(x3 x21):(cNUMBER Xn0)
% 135.50/135.98 Instantiate: Xn0:=Xn:fofType
% 135.50/135.98 Found (x3 x21) as proof of (cNUMBER Xn)
% 135.50/135.98 Found (fun (x5:cIND)=> (x3 x21)) as proof of (cNUMBER Xn)
% 135.50/135.98 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21)) as proof of (cIND->(cNUMBER Xn))
% 135.50/135.98 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 135.50/135.98 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21))) as proof of (cNUMBER Xn)
% 135.50/135.98 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21))) as proof of (cNUMBER Xn)
% 135.50/135.98 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21))) as proof of (cNUMBER Xn)
% 135.50/135.98 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (x3 x21))) as proof of (cNUMBER Xn)
% 140.46/140.95 Found x30:(cNUMBER Xn0)
% 140.46/140.95 Instantiate: Xn0:=(cS Xx):fofType
% 140.46/140.95 Found x30 as proof of (cNUMBER (cS Xx))
% 140.46/140.95 Found (fun (x6:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 140.46/140.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 140.46/140.95 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 140.46/140.95 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 140.46/140.95 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 140.46/140.95 Found x50:=(x5 x40):(cNUMBER Xn0)
% 140.46/140.95 Instantiate: Xn0:=(cS Xx):fofType
% 140.46/140.95 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 140.46/140.95 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 140.46/140.95 Found x90:(cNUMBER Xn0)
% 140.46/140.95 Instantiate: Xn0:=Xn:fofType
% 140.46/140.95 Found x90 as proof of (cNUMBER Xn)
% 140.46/140.95 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 140.46/140.95 Instantiate: Xn00:=Xn:fofType
% 140.46/140.95 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.46/140.95 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.46/140.95 Found x4:(cNUMBER Xx)
% 140.46/140.95 Instantiate: Xn0:=Xx:fofType
% 140.46/140.95 Found x4 as proof of (cNUMBER Xn0)
% 140.46/140.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 140.46/140.95 Instantiate: Xn0:=c0:fofType
% 140.46/140.95 Found (x3 x20) as proof of (cNUMBER c0)
% 140.46/140.95 Found (x3 x20) as proof of (cNUMBER c0)
% 140.46/140.95 Found x70:(cNUMBER Xn0)
% 140.46/140.95 Instantiate: Xn0:=Xn:fofType
% 140.46/140.95 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 140.46/140.95 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 140.46/140.95 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 140.46/140.95 Found x50:(cNUMBER Xn0)
% 140.46/140.95 Instantiate: Xn0:=c0:fofType
% 140.46/140.95 Found x50 as proof of (cNUMBER c0)
% 140.46/140.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 140.46/140.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.46/140.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.46/140.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.46/140.95 Found x6:(cNUMBER Xx)
% 140.46/140.95 Instantiate: Xn0:=Xx:fofType
% 140.46/140.95 Found x6 as proof of (cNUMBER Xn0)
% 140.46/140.95 Found (x4 x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.46/140.95 Found (x4 x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.46/140.95 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 140.46/140.95 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 140.46/140.95 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 140.46/140.95 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 140.46/140.95 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 140.46/140.95 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 140.46/140.95 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.46/140.95 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.46/140.95 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.46/140.95 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found x70:(cNUMBER Xn0)
% 143.98/144.47 Instantiate: Xn0:=c0:fofType
% 143.98/144.47 Found x70 as proof of (cNUMBER c0)
% 143.98/144.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 143.98/144.47 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 143.98/144.47 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 143.98/144.47 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 143.98/144.47 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 143.98/144.47 Found x31:(cNUMBER Xn0)
% 143.98/144.47 Instantiate: Xn0:=Xn:fofType
% 143.98/144.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 143.98/144.47 Found x30:(cNUMBER Xn0)
% 143.98/144.47 Instantiate: Xn0:=c0:fofType
% 143.98/144.47 Found x30 as proof of (cNUMBER c0)
% 143.98/144.47 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 143.98/144.47 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 143.98/144.47 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 143.98/144.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 143.98/144.47 Instantiate: Xn0:=Xn:fofType
% 143.98/144.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 143.98/144.47 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Instantiate: Xn0:=Xn:fofType
% 143.98/144.47 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 143.98/144.47 Found (x5 x20) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (x5 x20) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 143.98/144.47 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 143.98/144.47 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 143.98/144.47 Instantiate: Xn00:=Xn:fofType
% 143.98/144.47 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found (x3 x40) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (x3 x40) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x40)) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 143.98/144.47 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 143.98/144.47 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 143.98/144.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 143.98/144.47 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 143.98/144.47 Found x30:=(x3 x20):(cNUMBER Xn0)
% 143.98/144.47 Instantiate: Xn0:=(cS Xx):fofType
% 143.98/144.47 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 143.98/144.47 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 143.98/144.47 Found x7:(cODD (cS c0))
% 143.98/144.47 Instantiate: Xn0:=(cS c0):fofType
% 143.98/144.47 Found x7 as proof of (cODD Xn0)
% 143.98/144.47 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 143.98/144.47 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.57/148.07 Found x50:=(x5 x40):(cNUMBER Xn0)
% 147.57/148.07 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 147.57/148.07 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 147.57/148.07 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 147.57/148.07 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 147.57/148.07 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 147.57/148.07 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 147.57/148.07 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 147.57/148.07 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 147.57/148.07 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 147.57/148.07 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.57/148.07 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.57/148.07 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.57/148.07 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.57/148.07 Found (x7 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 147.57/148.07 Found (x7 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 147.57/148.07 Found x30:=(x3 x20):(cNUMBER Xn0)
% 147.57/148.07 Found (x3 x20) as proof of (cNUMBER Xn0)
% 147.57/148.07 Found (x3 x20) as proof of (cNUMBER Xn0)
% 147.57/148.07 Found x30:=(x3 x21):(cNUMBER Xn0)
% 147.57/148.07 Instantiate: Xn0:=Xn:fofType
% 147.57/148.07 Found (x3 x21) as proof of (cNUMBER Xn)
% 147.57/148.07 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 147.57/148.07 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 147.57/148.07 Found x30:=(x3 x20):(cNUMBER Xn0)
% 147.57/148.07 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 147.57/148.07 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 147.57/148.07 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 147.57/148.07 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 154.76/155.29 Found x50:(cNUMBER Xn0)
% 154.76/155.29 Instantiate: Xn0:=c0:fofType
% 154.76/155.29 Found x50 as proof of (cNUMBER c0)
% 154.76/155.29 Found x70:(cNUMBER Xn0)
% 154.76/155.29 Instantiate: Xn0:=c0:fofType
% 154.76/155.29 Found x70 as proof of (cNUMBER c0)
% 154.76/155.29 Found x90:(cNUMBER Xn0)
% 154.76/155.29 Instantiate: Xn0:=Xn:fofType
% 154.76/155.29 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of (cNUMBER Xn)
% 154.76/155.29 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 154.76/155.29 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found x30:=(x3 x21):(cNUMBER Xn0)
% 154.76/155.29 Instantiate: Xn0:=Xn:fofType
% 154.76/155.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 154.76/155.29 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 154.76/155.29 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 154.76/155.29 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 154.76/155.29 Found x30:=(x3 x20):(cNUMBER Xn0)
% 154.76/155.29 Instantiate: Xn0:=c0:fofType
% 154.76/155.29 Found (x3 x20) as proof of (cNUMBER c0)
% 154.76/155.29 Found (x3 x20) as proof of (cNUMBER c0)
% 154.76/155.29 Found x9:(cODD (cS c0))
% 154.76/155.29 Instantiate: Xn0:=(cS c0):fofType
% 154.76/155.29 Found x9 as proof of (cODD Xn0)
% 154.76/155.29 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found x30:=(x3 x20):(cNUMBER Xn0)
% 154.76/155.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 154.76/155.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 154.76/155.29 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 154.76/155.29 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 154.76/155.29 Found x50:=(x5 x40):(cNUMBER Xn0)
% 154.76/155.29 Instantiate: Xn0:=c0:fofType
% 154.76/155.29 Found (x5 x40) as proof of (cNUMBER c0)
% 154.76/155.29 Found (x5 x40) as proof of (cNUMBER c0)
% 154.76/155.29 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 154.76/155.29 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found x70:=(x7 x60):(cNUMBER Xn0)
% 154.76/155.29 Instantiate: Xn0:=Xn:fofType
% 154.76/155.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 154.76/155.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 154.76/155.29 Found x50:=(x5 x40):(cNUMBER Xn0)
% 154.76/155.29 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 154.76/155.29 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 154.76/155.29 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 154.76/155.29 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.29 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 154.76/155.29 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 154.76/155.29 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 154.76/155.29 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 154.76/155.29 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.76/155.29 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.76/155.29 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.76/155.29 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.76/155.30 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 154.76/155.30 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.30 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.30 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.30 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.76/155.30 Found (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 154.76/155.30 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (cNUMBER Xn0)
% 154.76/155.30 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn0))
% 154.76/155.30 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 154.76/155.32 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 154.76/155.32 Found ((and_rect3 (cNUMBER Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 154.76/155.32 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cNUMBER Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 154.76/155.32 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cNUMBER Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 154.76/155.32 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 154.76/155.32 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.76/155.32 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.76/155.32 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.76/155.32 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.85/155.32 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 154.85/155.32 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.85/155.32 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.85/155.32 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.85/155.32 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.85/155.32 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 154.85/155.32 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 154.85/155.32 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.85/155.32 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.85/155.33 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.85/155.33 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.85/155.33 Found (x3 (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 154.85/155.33 Found (x3 (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 158.05/158.56 Found x30:(cNUMBER Xn0)
% 158.05/158.56 Instantiate: Xn0:=c0:fofType
% 158.05/158.56 Found x30 as proof of (cNUMBER c0)
% 158.05/158.56 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 158.05/158.56 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 158.05/158.56 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 158.05/158.56 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 158.05/158.56 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 158.05/158.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 158.05/158.56 Instantiate: Xn0:=Xn:fofType
% 158.05/158.56 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 158.05/158.56 Found (x5 x20) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (x5 x20) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 158.05/158.56 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 158.05/158.56 Found x31:(cNUMBER Xn0)
% 158.05/158.56 Instantiate: Xn0:=Xn:fofType
% 158.05/158.56 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 158.05/158.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 158.05/158.56 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 158.05/158.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 158.05/158.56 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 158.05/158.56 Found x50:=(x5 x40):(cNUMBER Xn0)
% 158.05/158.56 Instantiate: Xn0:=Xn:fofType
% 158.05/158.56 Found (x5 x40) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 158.05/158.56 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 158.05/158.56 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 158.05/158.56 Found x50:=(x5 x40):(cNUMBER Xn0)
% 158.05/158.56 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 158.05/158.56 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 158.05/158.56 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 158.05/158.56 Found x50:(cNUMBER Xn0)
% 158.05/158.56 Instantiate: Xn0:=c0:fofType
% 158.05/158.56 Found x50 as proof of (cNUMBER c0)
% 158.05/158.56 Found x50:=(x5 x40):(cNUMBER Xn0)
% 158.05/158.56 Found (x5 x40) as proof of (cNUMBER Xn0)
% 158.05/158.56 Found (x5 x40) as proof of (cNUMBER Xn0)
% 158.05/158.56 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 158.05/158.56 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 163.73/164.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 163.73/164.21 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 163.73/164.21 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 163.73/164.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 163.73/164.21 Instantiate: Xn0:=(cS Xx):fofType
% 163.73/164.21 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found x70:(cNUMBER Xn0)
% 163.73/164.21 Instantiate: Xn0:=c0:fofType
% 163.73/164.21 Found x70 as proof of (cNUMBER c0)
% 163.73/164.21 Found x50:=(x5 x40):(cNUMBER Xn0)
% 163.73/164.21 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 163.73/164.21 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found x51:(cNUMBER Xn0)
% 163.73/164.21 Instantiate: Xn0:=Xn:fofType
% 163.73/164.21 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 163.73/164.21 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 163.73/164.21 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 163.73/164.21 Found x50:=(x5 x40):(cNUMBER Xn0)
% 163.73/164.21 Found (x5 x40) as proof of (cNUMBER Xn0)
% 163.73/164.21 Found (x5 x40) as proof of (cNUMBER Xn0)
% 163.73/164.21 Found x50:(cNUMBER Xn0)
% 163.73/164.21 Instantiate: Xn0:=(cS Xx):fofType
% 163.73/164.21 Found x50 as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 163.73/164.21 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found x30:(cNUMBER Xn0)
% 163.73/164.21 Instantiate: Xn0:=(cS Xx):fofType
% 163.73/164.21 Found x30 as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found x8:(cNUMBER Xx)
% 163.73/164.21 Instantiate: Xn0:=Xx:fofType
% 163.73/164.21 Found x8 as proof of (cNUMBER Xn0)
% 163.73/164.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 163.73/164.21 Found (x3 x20) as proof of (cNUMBER Xn0)
% 163.73/164.21 Found (x3 x20) as proof of (cNUMBER Xn0)
% 163.73/164.21 Found x30:=(x3 x21):(cNUMBER Xn0)
% 163.73/164.21 Instantiate: Xn0:=Xn:fofType
% 163.73/164.21 Found (x3 x21) as proof of (cNUMBER Xn)
% 163.73/164.21 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 163.73/164.21 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 163.73/164.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 163.73/164.21 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 163.73/164.21 Found x90:(cNUMBER Xn0)
% 163.73/164.21 Instantiate: Xn0:=Xn:fofType
% 163.73/164.21 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of (cNUMBER Xn)
% 163.73/164.21 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 163.73/164.21 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 163.73/164.21 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 163.73/164.21 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found x50:=(x5 x40):(cNUMBER Xn0)
% 165.25/165.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 165.25/165.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 165.25/165.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 165.25/165.73 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 165.25/165.73 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 165.25/165.73 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 165.25/165.73 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 165.25/165.73 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 165.25/165.73 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 165.25/165.73 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 165.25/165.73 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 165.25/165.73 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 165.25/165.73 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 165.25/165.73 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 165.25/165.73 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 165.25/165.73 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 165.25/165.73 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.25/165.73 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.37/166.89 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.37/166.89 Found x30:=(x3 x20):(cNUMBER Xn0)
% 166.37/166.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 166.37/166.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 166.37/166.89 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 166.37/166.89 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 166.37/166.89 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 166.37/166.89 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 166.37/166.89 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 166.37/166.89 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 166.37/166.89 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 166.37/166.89 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 166.37/166.89 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 166.37/166.89 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.37/166.89 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.37/166.89 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.37/166.89 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.37/166.89 Found x50:=(x5 x40):(cNUMBER Xn0)
% 166.37/166.89 Instantiate: Xn0:=c0:fofType
% 166.37/166.89 Found (x5 x40) as proof of (cNUMBER c0)
% 166.37/166.89 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER c0)
% 166.37/166.89 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER c0))
% 166.37/166.89 Found x51:(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=Xn:fofType
% 171.78/172.27 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 171.78/172.27 Found x70:=(x7 x60):(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=Xn:fofType
% 171.78/172.27 Found (x7 x60) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 171.78/172.27 Found x50:(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=c0:fofType
% 171.78/172.27 Found x50 as proof of (cNUMBER c0)
% 171.78/172.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn0)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn0)
% 171.78/172.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 171.78/172.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn0)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn0)
% 171.78/172.27 Found x30:=(x3 x21):(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=Xn:fofType
% 171.78/172.27 Found (x3 x21) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (x3 x21) as proof of (cNUMBER Xn)
% 171.78/172.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.78/172.27 Found x50:=(x5 x40):(cNUMBER Xn0)
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found x70:=(x7 x60):(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=c0:fofType
% 171.78/172.27 Found (x7 x60) as proof of (cNUMBER c0)
% 171.78/172.27 Found (x7 x60) as proof of (cNUMBER c0)
% 171.78/172.27 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found x30:(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=c0:fofType
% 171.78/172.27 Found x30 as proof of (cNUMBER c0)
% 171.78/172.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=c0:fofType
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER c0)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER c0)
% 171.78/172.27 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.78/172.27 Found x4:(cNUMBER Xx)
% 171.78/172.27 Instantiate: Xn0:=Xx:fofType
% 171.78/172.27 Found x4 as proof of (cNUMBER Xn0)
% 171.78/172.27 Found x60:(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=(cS Xx):fofType
% 171.78/172.27 Found x60 as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found x120:=(x12 x110):(cNUMBER Xn0)
% 171.78/172.27 Instantiate: Xn0:=Xn:fofType
% 171.78/172.27 Found (x12 x110) as proof of (cNUMBER Xn)
% 171.78/172.27 Found (x12 x110) as proof of (cNUMBER Xn)
% 171.78/172.27 Found x9:(cODD (cS c0))
% 171.78/172.27 Instantiate: Xn0:=(cS c0):fofType
% 171.78/172.27 Found x9 as proof of (cODD Xn0)
% 171.78/172.27 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.78/172.27 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 171.78/172.27 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 171.78/172.27 Found x50:=(x5 x40):(cNUMBER Xn0)
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 171.78/172.27 Found x50:=(x5 x40):(cNUMBER Xn0)
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER Xn0)
% 171.78/172.27 Found (x5 x40) as proof of (cNUMBER Xn0)
% 177.16/177.66 Found x50:=(x5 x41):(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=Xn:fofType
% 177.16/177.66 Found (x5 x41) as proof of (cNUMBER Xn)
% 177.16/177.66 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 177.16/177.66 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 177.16/177.66 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found x30:(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=(cS Xx):fofType
% 177.16/177.66 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 177.16/177.66 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found x50:=(x5 x41):(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=Xn:fofType
% 177.16/177.66 Found (x5 x41) as proof of (cNUMBER Xn)
% 177.16/177.66 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 177.16/177.66 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 177.16/177.66 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 177.16/177.66 Found x30:=(x3 x20):(cNUMBER Xn0)
% 177.16/177.66 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found x50:=(x5 x40):(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=c0:fofType
% 177.16/177.66 Found (x5 x40) as proof of (cNUMBER c0)
% 177.16/177.66 Found (x5 x40) as proof of (cNUMBER c0)
% 177.16/177.66 Found x30:(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=(cS Xx):fofType
% 177.16/177.66 Found x30 as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found (fun (x6:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found x50:=(x5 x40):(cNUMBER Xn0)
% 177.16/177.66 Found (x5 x40) as proof of (cNUMBER Xn0)
% 177.16/177.66 Found (x5 x40) as proof of (cNUMBER Xn0)
% 177.16/177.66 Found x70:(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=c0:fofType
% 177.16/177.66 Found x70 as proof of (cNUMBER c0)
% 177.16/177.66 Found x50:=(x5 x40):(cNUMBER Xn0)
% 177.16/177.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 177.16/177.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 177.16/177.66 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 177.16/177.66 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 177.16/177.66 Found x50:(cNUMBER Xn00)
% 177.16/177.66 Found x50 as proof of (cNUMBER Xn00)
% 177.16/177.66 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found x30:(cNUMBER Xn0)
% 177.16/177.66 Found x30 as proof of (cNUMBER Xn0)
% 177.16/177.66 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 177.16/177.66 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 177.16/177.66 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 177.16/177.66 Found x50:(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=(cS Xx):fofType
% 177.16/177.66 Found x50 as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 177.16/177.66 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.16/177.66 Found x30:=(x3 x20):(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=c0:fofType
% 177.16/177.66 Found (x3 x20) as proof of (cNUMBER c0)
% 177.16/177.66 Found (x3 x20) as proof of (cNUMBER c0)
% 177.16/177.66 Found x90:=(x9 x80):(cNUMBER Xn0)
% 177.16/177.66 Instantiate: Xn0:=Xn:fofType
% 177.16/177.66 Found (x9 x80) as proof of (cNUMBER Xn)
% 177.16/177.66 Found (x9 x80) as proof of (cNUMBER Xn)
% 177.24/177.74 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 177.24/177.74 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.24/177.74 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.24/177.74 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.24/177.74 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.24/177.74 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 177.24/177.74 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.24/177.74 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.24/177.74 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.24/177.74 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.24/177.74 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.24/177.74 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 177.24/177.74 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.24/177.75 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.24/177.75 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.24/177.75 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.24/177.75 Found (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 177.64/178.14 Found (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 177.64/178.14 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 177.64/178.14 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.64/178.14 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.64/178.14 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.64/178.14 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 177.64/178.14 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 177.64/178.14 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.64/178.14 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.64/178.14 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.64/178.14 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 177.64/178.14 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 177.64/178.14 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (cNUMBER Xn0)
% 177.64/178.15 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn0))
% 177.64/178.15 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 177.64/178.15 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 177.64/178.15 Found ((and_rect3 (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 177.64/178.15 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 179.00/179.51 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 179.00/179.51 Found x70:(cNUMBER Xn0)
% 179.00/179.51 Instantiate: Xn0:=(cS Xx):fofType
% 179.00/179.51 Found x70 as proof of (cNUMBER (cS Xx))
% 179.00/179.51 Found x8:(cNUMBER Xx)
% 179.00/179.51 Instantiate: Xn0:=Xx:fofType
% 179.00/179.51 Found x8 as proof of (cNUMBER Xn0)
% 179.00/179.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn0)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn0)
% 179.00/179.51 Found x30:=(x3 x21):(cNUMBER Xn0)
% 179.00/179.51 Instantiate: Xn0:=Xn:fofType
% 179.00/179.51 Found (x3 x21) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (x3 x21) as proof of (cNUMBER Xn)
% 179.00/179.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.00/179.51 Found x50:(cNUMBER Xn0)
% 179.00/179.51 Instantiate: Xn0:=c0:fofType
% 179.00/179.51 Found x50 as proof of (cNUMBER c0)
% 179.00/179.51 Found x30:(cNUMBER Xn0)
% 179.00/179.51 Instantiate: Xn0:=(cS Xx):fofType
% 179.00/179.51 Found x30 as proof of (cNUMBER (cS Xx))
% 179.00/179.51 Found x8:(cNUMBER Xx)
% 179.00/179.51 Instantiate: Xn0:=Xx:fofType
% 179.00/179.51 Found x8 as proof of (cNUMBER Xn0)
% 179.00/179.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 179.00/179.51 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 179.00/179.51 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 179.00/179.51 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 179.00/179.51 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 179.00/179.51 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 179.00/179.51 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 179.00/179.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 179.00/179.51 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 179.00/179.51 Found x70:=(x7 x60):(cNUMBER Xn0)
% 179.00/179.51 Instantiate: Xn0:=Xn:fofType
% 179.00/179.51 Found (x7 x60) as proof of (cNUMBER Xn)
% 179.00/179.51 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 181.75/182.26 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 181.75/182.26 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 181.75/182.26 Found x51:(cNUMBER Xn0)
% 181.75/182.26 Instantiate: Xn0:=Xn:fofType
% 181.75/182.26 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 181.75/182.26 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 181.75/182.26 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.75/182.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.75/182.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.75/182.26 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.75/182.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.75/182.26 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 181.75/182.26 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 181.75/182.26 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 181.75/182.26 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 181.75/182.26 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 181.75/182.26 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 181.75/182.26 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 181.75/182.26 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 181.75/182.26 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 181.75/182.26 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 181.75/182.26 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 181.75/182.26 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.75/182.26 Found x120:=(x12 x110):(cNUMBER Xn0)
% 181.75/182.26 Instantiate: Xn0:=Xn:fofType
% 181.75/182.26 Found (x12 x110) as proof of (cNUMBER Xn)
% 181.75/182.26 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 184.23/184.75 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 184.23/184.75 Found x50:(cNUMBER Xn0)
% 184.23/184.75 Instantiate: Xn0:=c0:fofType
% 184.23/184.75 Found x50 as proof of (cNUMBER c0)
% 184.23/184.75 Found x70:=(x7 x60):(cNUMBER Xn0)
% 184.23/184.75 Found (x7 x60) as proof of (cNUMBER Xn0)
% 184.23/184.75 Found (x7 x60) as proof of (cNUMBER Xn0)
% 184.23/184.75 Found x70:=(x7 x61):(cNUMBER Xn0)
% 184.23/184.75 Instantiate: Xn0:=Xn:fofType
% 184.23/184.75 Found (x7 x61) as proof of (cNUMBER Xn)
% 184.23/184.75 Found (x7 x61) as proof of (cNUMBER Xn)
% 184.23/184.75 Found x70:=(x7 x60):(cNUMBER Xn0)
% 184.23/184.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 184.23/184.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 184.23/184.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 184.23/184.75 Found x70:=(x7 x60):(cNUMBER Xn0)
% 184.23/184.75 Instantiate: Xn0:=c0:fofType
% 184.23/184.75 Found (x7 x60) as proof of (cNUMBER c0)
% 184.23/184.75 Found (x7 x60) as proof of (cNUMBER c0)
% 184.23/184.75 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 184.23/184.75 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 184.23/184.75 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 184.23/184.75 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 184.23/184.75 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 184.23/184.75 Found x8:(cODD (cS c0))
% 184.23/184.75 Instantiate: Xn0:=(cS c0):fofType
% 184.23/184.75 Found (fun (x8:(cODD (cS c0)))=> x8) as proof of (cODD Xn0)
% 184.23/184.75 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of ((cODD (cS c0))->(cODD Xn0))
% 184.23/184.75 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 184.23/184.75 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 184.23/184.75 Found ((and_rect4 (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 184.23/184.75 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 184.23/184.75 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 184.23/184.75 Found (or_intror00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 184.23/184.75 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 184.23/184.75 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 184.83/185.38 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 184.83/185.38 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 184.83/185.38 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 184.83/185.38 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 184.83/185.38 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 184.83/185.38 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 184.83/185.38 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 184.83/185.38 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 184.83/185.38 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 184.83/185.38 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 184.83/185.38 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 184.83/185.38 Found (or_comm_i00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 184.83/185.38 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 184.83/185.38 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found x50:(cNUMBER Xn0)
% 189.27/189.77 Instantiate: Xn0:=(cS Xx):fofType
% 189.27/189.77 Found x50 as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found x30:=(x3 x20):(cNUMBER Xn0)
% 189.27/189.77 Instantiate: Xn0:=Xn:fofType
% 189.27/189.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 189.27/189.77 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 189.27/189.77 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 189.27/189.77 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 189.27/189.77 Found (and_rect20 (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 189.27/189.77 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 189.27/189.77 Found (((fun (P:Type) (x4:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x4) x11)) (cNUMBER Xn)) (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 189.27/189.77 Found x8:(cNUMBER Xx)
% 189.27/189.77 Instantiate: Xn0:=Xx:fofType
% 189.27/189.77 Found x8 as proof of (cNUMBER Xn0)
% 189.27/189.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 189.27/189.77 Found (x5 x40) as proof of (cNUMBER Xn0)
% 189.27/189.77 Found (x5 x40) as proof of (cNUMBER Xn0)
% 189.27/189.77 Found x50:=(x5 x41):(cNUMBER Xn0)
% 189.27/189.77 Instantiate: Xn0:=Xn:fofType
% 189.27/189.77 Found (x5 x41) as proof of (cNUMBER Xn)
% 189.27/189.77 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 189.27/189.77 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 189.27/189.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 189.27/189.77 Found x50:(cNUMBER Xn00)
% 189.27/189.77 Found x50 as proof of (cNUMBER Xn00)
% 189.27/189.77 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found x30:=(x3 x20):(cNUMBER Xn0)
% 189.27/189.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 189.27/189.77 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 189.27/189.77 Found x70:=(x7 x60):(cNUMBER Xn0)
% 189.27/189.77 Found (x7 x60) as proof of (cNUMBER Xn)
% 190.36/190.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 190.36/190.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 190.36/190.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 190.36/190.87 Found (x5 x40) as proof of (cNUMBER Xn0)
% 190.36/190.87 Found (x5 x40) as proof of (cNUMBER Xn0)
% 190.36/190.87 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 190.36/190.87 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.36/190.87 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.36/190.87 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.36/190.87 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.36/190.87 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 190.36/190.87 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.36/190.87 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.36/190.87 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.36/190.87 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.36/190.87 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 190.36/190.87 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.36/190.87 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.36/190.87 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.36/190.87 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.36/190.87 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 190.36/190.87 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.36/190.87 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.36/190.87 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.10 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.10 Found x50:=(x5 x40):(cNUMBER Xn0)
% 190.58/191.10 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.58/191.10 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.58/191.10 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 190.58/191.10 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 190.58/191.10 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 190.58/191.10 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 190.58/191.10 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.58/191.10 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.58/191.10 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.58/191.10 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.58/191.10 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 190.58/191.10 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.10 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.10 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.10 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.10 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.58/191.11 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 190.58/191.11 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.11 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.11 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.11 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.12 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cIND->((or (cEVEN Xn0)) (cODD Xn0)))
% 190.58/191.12 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->(cIND->((or (cEVEN Xn0)) (cODD Xn0))))
% 190.58/191.12 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.13 Found ((and_rect2 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.13 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.58/191.13 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.59/194.14 Found x90:=(x9 x80):(cNUMBER Xn0)
% 193.59/194.14 Instantiate: Xn0:=Xn:fofType
% 193.59/194.14 Found (x9 x80) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 193.59/194.14 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 193.59/194.14 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 193.59/194.14 Found x50:=(x5 x41):(cNUMBER Xn0)
% 193.59/194.14 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 193.59/194.14 Found x70:(cNUMBER Xn0)
% 193.59/194.14 Instantiate: Xn0:=(cS Xx):fofType
% 193.59/194.14 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 193.59/194.14 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 193.59/194.14 Found x50:=(x5 x40):(cNUMBER Xn0)
% 193.59/194.14 Found (x5 x40) as proof of (cNUMBER Xn0)
% 193.59/194.14 Found (x5 x40) as proof of (cNUMBER Xn0)
% 193.59/194.14 Found x50:=(x5 x41):(cNUMBER Xn0)
% 193.59/194.14 Instantiate: Xn0:=Xn:fofType
% 193.59/194.14 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.59/194.14 Found x50:=(x5 x41):(cNUMBER Xn0)
% 193.59/194.14 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.59/194.14 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 193.59/194.14 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.59/194.14 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 193.59/194.14 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.59/194.14 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 193.59/194.14 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 193.59/194.14 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 193.59/194.14 Found x30:(cNUMBER Xn0)
% 193.59/194.14 Instantiate: Xn0:=(cS Xx):fofType
% 193.59/194.14 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 193.59/194.14 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 193.59/194.14 Found x30:=(x3 x20):(cNUMBER Xn0)
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn0)
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn0)
% 193.59/194.14 Found x30:=(x3 x21):(cNUMBER Xn0)
% 193.59/194.14 Instantiate: Xn0:=Xn:fofType
% 193.59/194.14 Found (x3 x21) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x3 x21) as proof of (cNUMBER Xn)
% 193.59/194.14 Found x30:=(x3 x20):(cNUMBER Xn0)
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.59/194.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 198.39/198.94 Found x50:(cNUMBER Xn0)
% 198.39/198.94 Instantiate: Xn0:=c0:fofType
% 198.39/198.94 Found x50 as proof of (cNUMBER c0)
% 198.39/198.94 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER Xn)
% 198.39/198.94 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 198.39/198.94 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 198.39/198.94 Found x50:=(x5 x40):(cNUMBER Xn0)
% 198.39/198.94 Instantiate: Xn0:=c0:fofType
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER c0)
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER c0)
% 198.39/198.94 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (x3 x20) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (x3 x20) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 198.39/198.94 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 198.39/198.94 Found x9:(cODD (cS c0))
% 198.39/198.94 Instantiate: Xn0:=(cS c0):fofType
% 198.39/198.94 Found x9 as proof of (cODD Xn0)
% 198.39/198.94 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 198.39/198.94 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 198.39/198.94 Found x70:=(x7 x60):(cNUMBER Xn0)
% 198.39/198.94 Instantiate: Xn0:=c0:fofType
% 198.39/198.94 Found (x7 x60) as proof of (cNUMBER c0)
% 198.39/198.94 Found (x7 x60) as proof of (cNUMBER c0)
% 198.39/198.94 Found x8:(cNUMBER Xx)
% 198.39/198.94 Instantiate: Xn0:=Xx:fofType
% 198.39/198.94 Found x8 as proof of (cNUMBER Xn0)
% 198.39/198.94 Found x70:(cNUMBER Xn0)
% 198.39/198.94 Instantiate: Xn0:=(cS Xx):fofType
% 198.39/198.94 Found x70 as proof of (cNUMBER (cS Xx))
% 198.39/198.94 Found x70:=(x7 x60):(cNUMBER Xn0)
% 198.39/198.94 Found (x7 x60) as proof of (cNUMBER Xn0)
% 198.39/198.94 Found (x7 x60) as proof of (cNUMBER Xn0)
% 198.39/198.94 Found x70:=(x7 x61):(cNUMBER Xn0)
% 198.39/198.94 Instantiate: Xn0:=Xn:fofType
% 198.39/198.94 Found (x7 x61) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (x7 x61) as proof of (cNUMBER Xn)
% 198.39/198.94 Found x70:=(x7 x60):(cNUMBER Xn0)
% 198.39/198.94 Found (x7 x60) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (x7 x60) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (x7 x60) as proof of (cNUMBER Xn)
% 198.39/198.94 Found x30:=(x3 x20):(cNUMBER Xn0)
% 198.39/198.94 Instantiate: Xn0:=c0:fofType
% 198.39/198.94 Found (x3 x20) as proof of (cNUMBER c0)
% 198.39/198.94 Found (x3 x20) as proof of (cNUMBER c0)
% 198.39/198.94 Found x50:(cNUMBER Xn0)
% 198.39/198.94 Instantiate: Xn0:=c0:fofType
% 198.39/198.94 Found x50 as proof of (cNUMBER c0)
% 198.39/198.94 Found x9:(cODD (cS c0))
% 198.39/198.94 Instantiate: Xn0:=(cS c0):fofType
% 198.39/198.94 Found x9 as proof of (cODD Xn0)
% 198.39/198.94 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 198.39/198.94 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 198.39/198.94 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 198.39/198.94 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 198.39/198.94 Found x30:=(x3 x20):(cNUMBER Xn0)
% 198.39/198.94 Instantiate: Xn0:=Xn:fofType
% 198.39/198.94 Found (x3 x20) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 198.39/198.94 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 201.39/201.91 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 201.39/201.91 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 201.39/201.91 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 201.39/201.91 Found x30:(cNUMBER Xn0)
% 201.39/201.91 Found x30 as proof of (cNUMBER (cS Xx))
% 201.39/201.91 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 201.39/201.91 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 201.39/201.91 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.39/201.91 Found (x7 x60) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (x7 x60) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (x7 x60) as proof of (cNUMBER Xn)
% 201.39/201.91 Found x50:=(x5 x40):(cNUMBER Xn0)
% 201.39/201.91 Found (x5 x40) as proof of (cNUMBER c0)
% 201.39/201.91 Found (x5 x40) as proof of (cNUMBER c0)
% 201.39/201.91 Found (x5 x40) as proof of (cNUMBER c0)
% 201.39/201.91 Found x30:=(x3 x20):(cNUMBER Xn0)
% 201.39/201.91 Found (x3 x20) as proof of (cNUMBER c0)
% 201.39/201.91 Found (x3 x20) as proof of (cNUMBER c0)
% 201.39/201.91 Found (x3 x20) as proof of (cNUMBER c0)
% 201.39/201.91 Found x70:(cNUMBER Xn00)
% 201.39/201.91 Instantiate: Xn00:=Xn:fofType
% 201.39/201.91 Found x70 as proof of (cNUMBER Xn)
% 201.39/201.91 Found x50:(cNUMBER Xn0)
% 201.39/201.91 Instantiate: Xn0:=Xn:fofType
% 201.39/201.91 Found x50 as proof of (cNUMBER Xn)
% 201.39/201.91 Found x30:=(x3 x20):(cNUMBER Xn0)
% 201.39/201.91 Instantiate: Xn0:=Xn:fofType
% 201.39/201.91 Found (x3 x20) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 201.39/201.91 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 201.39/201.91 Found (and_rect20 (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 201.39/201.91 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (((fun (P:Type) (x4:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x4) x11)) (cNUMBER Xn)) (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 201.39/201.91 Found x30:=(x3 x21):(cNUMBER Xn0)
% 201.39/201.91 Found (x3 x21) as proof of (cNUMBER Xn0)
% 201.39/201.91 Found (x3 x21) as proof of (cNUMBER Xn0)
% 201.39/201.91 Found x30:=(x3 x22):(cNUMBER Xn0)
% 201.39/201.91 Instantiate: Xn0:=Xn:fofType
% 201.39/201.91 Found (x3 x22) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (x3 x22) as proof of (cNUMBER Xn)
% 201.39/201.91 Found x30:=(x3 x22):(cNUMBER Xn0)
% 201.39/201.91 Found (x3 x22) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (x3 x22) as proof of (cNUMBER Xn)
% 201.39/201.91 Found (x3 x22) as proof of (cNUMBER Xn)
% 201.39/201.91 Found x50:(cNUMBER Xn0)
% 201.39/201.91 Instantiate: Xn0:=(cS Xx):fofType
% 201.39/201.91 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 201.39/201.91 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 205.54/206.06 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.06 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.06 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found x50:(cNUMBER Xn0)
% 205.54/206.06 Instantiate: Xn0:=(cS Xx):fofType
% 205.54/206.06 Found x50 as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.06 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.06 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found x70:=(x7 x60):(cNUMBER Xn0)
% 205.54/206.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 205.54/206.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 205.54/206.06 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 205.54/206.06 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 205.54/206.06 Found or_comm_i100:=(or_comm_i10 x20):((or (cODD Xn0)) (cEVEN Xn0))
% 205.54/206.06 Found (or_comm_i10 x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 205.54/206.06 Found ((or_comm_i1 (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 205.54/206.06 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 205.54/206.06 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 205.54/206.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 205.54/206.06 Instantiate: Xn0:=(cS Xx):fofType
% 205.54/206.06 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 205.54/206.06 Instantiate: Xn0:=c0:fofType
% 205.54/206.06 Found (x5 x40) as proof of (cNUMBER c0)
% 205.54/206.06 Found (x5 x40) as proof of (cNUMBER c0)
% 205.54/206.06 Found x70:=(x7 x60):(cNUMBER Xn0)
% 205.54/206.06 Instantiate: Xn0:=c0:fofType
% 205.54/206.06 Found (x7 x60) as proof of (cNUMBER c0)
% 205.54/206.06 Found (x7 x60) as proof of (cNUMBER c0)
% 205.54/206.06 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.06 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.06 Found (x3 x22) as proof of (cNUMBER Xn)
% 205.54/206.06 Found (x3 x22) as proof of (cNUMBER Xn)
% 205.54/206.06 Found (x3 x22) as proof of (cNUMBER Xn)
% 205.54/206.06 Found x30:(cNUMBER Xn0)
% 205.54/206.06 Instantiate: Xn0:=(cS Xx):fofType
% 205.54/206.06 Found x30 as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 205.54/206.06 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 205.54/206.06 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.54/206.06 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.54/206.06 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.54/206.06 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.54/206.06 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 205.54/206.06 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.06 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.06 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.07 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.07 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.54/206.07 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 205.54/206.07 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.07 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.54/206.07 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.59/206.09 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.59/206.09 Found (x5 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 205.59/206.09 Found (x5 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 205.59/206.09 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 205.59/206.09 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.59/206.09 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.59/206.09 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.59/206.09 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 205.59/206.09 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 205.59/206.09 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.59/206.09 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.59/206.09 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.59/206.09 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.59/206.09 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 205.59/206.09 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (cNUMBER Xn0)
% 205.59/206.09 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn0))
% 205.59/206.09 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 205.59/206.11 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 205.59/206.11 Found ((and_rect3 (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 205.59/206.11 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 205.59/206.11 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 205.59/206.11 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 205.59/206.11 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.59/206.11 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.59/206.11 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.59/206.11 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 205.59/206.11 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 207.25/207.81 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 207.25/207.81 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 207.25/207.81 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.25/207.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 207.25/207.81 Found x90:=(x9 x80):(cNUMBER Xn0)
% 207.25/207.81 Instantiate: Xn0:=Xn:fofType
% 207.25/207.81 Found (x9 x80) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 207.25/207.81 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 207.25/207.81 Found x50:=(x5 x40):(cNUMBER Xn0)
% 207.25/207.81 Found (x5 x40) as proof of (cNUMBER Xn0)
% 207.25/207.81 Found (x5 x40) as proof of (cNUMBER Xn0)
% 207.25/207.81 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.25/207.81 Instantiate: Xn0:=Xn:fofType
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found x50:(cNUMBER Xn0)
% 207.25/207.81 Instantiate: Xn0:=(cS Xx):fofType
% 207.25/207.81 Found x50 as proof of (cNUMBER (cS Xx))
% 207.25/207.81 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 207.25/207.81 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 207.25/207.81 Found x120:=(x12 x110):(cNUMBER Xn0)
% 207.25/207.81 Found (x12 x110) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x12 x110) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x12 x110) as proof of (cNUMBER Xn)
% 207.25/207.81 Found x8:(cNUMBER Xx)
% 207.25/207.81 Instantiate: Xn0:=Xx:fofType
% 207.25/207.81 Found x8 as proof of (cNUMBER Xn0)
% 207.25/207.81 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 207.25/207.81 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 207.25/207.81 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 207.25/207.81 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 207.25/207.81 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.25/207.81 Found (x5 x40) as proof of (cNUMBER Xn)
% 211.29/211.82 Found (x5 x40) as proof of (cNUMBER Xn)
% 211.29/211.82 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 211.29/211.82 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 211.29/211.82 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 211.29/211.82 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 211.29/211.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 211.29/211.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 211.29/211.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 211.29/211.82 Found x30:(cNUMBER Xn0)
% 211.29/211.82 Instantiate: Xn0:=Xn:fofType
% 211.29/211.82 Found x30 as proof of (cNUMBER Xn)
% 211.29/211.82 Found x70:(cNUMBER Xn00)
% 211.29/211.82 Instantiate: Xn00:=Xn:fofType
% 211.29/211.82 Found x70 as proof of (cNUMBER Xn)
% 211.29/211.82 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 211.29/211.82 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 211.29/211.82 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 211.29/211.82 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 211.29/211.82 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 211.29/211.82 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 211.29/211.82 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 211.29/211.82 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 211.29/211.82 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 211.29/211.82 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 211.29/211.82 Found x30:=(x3 x20):(cNUMBER Xn0)
% 211.29/211.82 Instantiate: Xn0:=c0:fofType
% 211.29/211.82 Found (x3 x20) as proof of (cNUMBER c0)
% 211.29/211.82 Found (x3 x20) as proof of (cNUMBER c0)
% 211.29/211.82 Found x30:=(x3 x20):(cNUMBER Xn0)
% 211.29/211.82 Instantiate: Xn0:=Xn:fofType
% 211.29/211.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 211.29/211.82 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 211.29/211.82 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 211.29/211.82 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 211.29/211.82 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 211.29/211.82 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 211.29/211.82 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 212.55/213.04 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 212.55/213.04 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 212.55/213.04 Found x70:(cNUMBER Xn0)
% 212.55/213.04 Instantiate: Xn0:=(cS Xx):fofType
% 212.55/213.04 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 212.55/213.04 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 212.55/213.04 Found x70:=(x7 x61):(cNUMBER Xn0)
% 212.55/213.04 Instantiate: Xn0:=Xn:fofType
% 212.55/213.04 Found (x7 x61) as proof of (cNUMBER Xn)
% 212.55/213.04 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 212.55/213.04 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 212.55/213.04 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 212.55/213.04 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 212.55/213.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 212.55/213.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 212.55/213.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 212.55/213.04 Found x50:=(x5 x40):(cNUMBER Xn0)
% 212.55/213.04 Found (x5 x40) as proof of (cNUMBER c0)
% 212.55/213.04 Found (x5 x40) as proof of (cNUMBER c0)
% 212.55/213.04 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER c0)
% 212.55/213.05 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER c0))
% 212.55/213.05 Found x8:(cODD (cS c0))
% 212.55/213.05 Instantiate: Xn0:=(cS c0):fofType
% 212.55/213.05 Found (fun (x8:(cODD (cS c0)))=> x8) as proof of (cODD Xn0)
% 212.55/213.05 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of ((cODD (cS c0))->(cODD Xn0))
% 212.55/213.05 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 212.55/213.05 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 212.55/213.05 Found ((and_rect4 (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 212.55/213.05 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 212.55/213.05 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 212.55/213.05 Found (or_intror00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.14/213.66 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.14/213.66 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.14/213.66 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.14/213.66 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 213.14/213.66 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.14/213.66 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 213.14/213.66 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 213.14/213.66 Found (fun (x6:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 213.14/213.66 Found x50:=(x5 x40):(cNUMBER Xn0)
% 213.14/213.66 Instantiate: Xn0:=c0:fofType
% 213.14/213.66 Found (x5 x40) as proof of (cNUMBER c0)
% 213.14/213.66 Found (x5 x40) as proof of (cNUMBER c0)
% 213.14/213.66 Found x50:(cNUMBER Xn0)
% 213.14/213.66 Instantiate: Xn0:=c0:fofType
% 213.14/213.66 Found x50 as proof of (cNUMBER c0)
% 213.14/213.66 Found x50:(cNUMBER Xn0)
% 213.14/213.66 Instantiate: Xn0:=Xn:fofType
% 213.14/213.66 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 213.14/213.66 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 213.14/213.66 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 213.14/213.66 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 213.14/213.66 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 213.14/213.66 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 213.14/213.66 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 213.14/213.66 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 213.14/213.66 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 213.14/213.66 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 213.14/213.66 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 213.78/214.28 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 213.78/214.28 Found (or_comm_i00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.78/214.28 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.78/214.28 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.78/214.28 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.78/214.28 Found x70:=(x7 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 213.78/214.28 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 213.78/214.28 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 213.78/214.28 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 213.78/214.28 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 213.78/214.28 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 213.78/214.28 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 213.78/214.28 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 213.78/214.28 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 213.78/214.32 Found (or_intror00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.78/214.32 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.78/214.32 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.78/214.32 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.78/214.32 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 213.78/214.32 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 213.78/214.32 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 213.78/214.32 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 213.78/214.32 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 213.78/214.32 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 213.78/214.32 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 213.78/214.32 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 213.78/214.32 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 213.78/214.32 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 216.08/216.64 Found (or_comm_i00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.08/216.64 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.08/216.64 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.08/216.64 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.08/216.64 Found x30:=(x3 x21):(cNUMBER Xn0)
% 216.08/216.64 Found (x3 x21) as proof of (cNUMBER Xn0)
% 216.08/216.64 Found (x3 x21) as proof of (cNUMBER Xn0)
% 216.08/216.64 Found x30:=(x3 x22):(cNUMBER Xn0)
% 216.08/216.64 Instantiate: Xn0:=Xn:fofType
% 216.08/216.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 216.08/216.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 216.08/216.64 Found x30:=(x3 x22):(cNUMBER Xn0)
% 216.08/216.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 216.08/216.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 216.08/216.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 216.08/216.64 Found x7:(cODD (cS c0))
% 216.08/216.64 Instantiate: Xn0:=(cS c0):fofType
% 216.08/216.64 Found x7 as proof of (cODD Xn0)
% 216.08/216.64 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.08/216.64 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.08/216.64 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.08/216.64 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.08/216.64 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 216.08/216.64 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 216.08/216.64 Found x70:=(x7 x60):(cNUMBER Xn0)
% 216.08/216.64 Instantiate: Xn0:=c0:fofType
% 216.08/216.64 Found (x7 x60) as proof of (cNUMBER c0)
% 216.08/216.64 Found (x7 x60) as proof of (cNUMBER c0)
% 216.08/216.64 Found x30:(cNUMBER Xn0)
% 216.08/216.64 Instantiate: Xn0:=Xn:fofType
% 216.08/216.64 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 216.08/216.64 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.08/216.64 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 216.08/216.64 Found x30:(cNUMBER Xn0)
% 216.08/216.64 Instantiate: Xn0:=Xn:fofType
% 216.08/216.64 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 216.08/216.64 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.44/216.96 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 216.44/216.96 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.44/216.96 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.44/216.96 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.44/216.96 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.44/216.96 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.44/216.96 Found x30:=(x3 x20):(cNUMBER Xn0)
% 216.44/216.96 Instantiate: Xn0:=Xn:fofType
% 216.44/216.96 Found (x3 x20) as proof of (cNUMBER Xn)
% 216.44/216.96 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 216.44/216.96 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.44/216.96 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 216.44/216.96 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 216.44/216.96 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 216.44/216.96 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 216.44/216.96 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 218.34/218.86 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 218.34/218.86 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 218.34/218.86 Found x90:=(x9 x80):(cNUMBER Xn0)
% 218.34/218.86 Found (x9 x80) as proof of (cNUMBER Xn)
% 218.34/218.86 Found (x9 x80) as proof of (cNUMBER Xn)
% 218.34/218.86 Found (x9 x80) as proof of (cNUMBER Xn)
% 218.34/218.86 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 218.34/218.86 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 218.34/218.86 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 218.34/218.86 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 218.34/218.86 Found (fun (x6:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 218.34/218.86 Found x30:(cNUMBER Xn0)
% 218.34/218.86 Instantiate: Xn0:=Xn:fofType
% 218.34/218.86 Found x30 as proof of (cNUMBER Xn)
% 218.34/218.86 Found x50:(cNUMBER Xn00)
% 218.34/218.86 Instantiate: Xn00:=Xn:fofType
% 218.34/218.86 Found x50 as proof of (cNUMBER Xn)
% 218.34/218.86 Found x70:(cNUMBER Xn0)
% 218.34/218.86 Found x70 as proof of (cNUMBER (cS Xx))
% 218.34/218.86 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 218.34/218.86 Found x70:=(x7 x60):(cNUMBER Xn0)
% 218.34/218.86 Found (x7 x60) as proof of (cNUMBER c0)
% 218.34/218.86 Found (x7 x60) as proof of (cNUMBER c0)
% 218.34/218.86 Found (x7 x60) as proof of (cNUMBER c0)
% 218.34/218.86 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 218.34/218.86 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 218.34/218.86 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 218.34/218.86 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 218.34/218.86 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 218.34/218.86 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 218.34/218.86 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 218.34/218.86 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 218.34/218.86 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 218.34/218.86 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.22/219.75 Found (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 219.22/219.75 Found (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 219.22/219.75 Found x70:=(x7 x60):(cNUMBER Xn0)
% 219.22/219.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 219.22/219.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 219.22/219.75 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 219.22/219.75 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 219.22/219.75 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 219.22/219.75 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 219.22/219.75 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 219.22/219.75 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 219.22/219.75 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 219.22/219.75 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 219.22/219.75 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 219.22/219.75 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.22/219.75 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.22/219.75 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.22/219.75 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.22/219.75 Found x70:(cNUMBER Xn0)
% 219.22/219.75 Instantiate: Xn0:=(cS Xx):fofType
% 219.22/219.75 Found x70 as proof of (cNUMBER (cS Xx))
% 219.22/219.75 Found x8:(cNUMBER Xx)
% 219.22/219.75 Instantiate: Xn0:=Xx:fofType
% 219.22/219.75 Found x8 as proof of (cNUMBER Xn0)
% 219.22/219.75 Found x30:=(x3 x20):(cNUMBER Xn0)
% 224.04/224.61 Found (x3 x20) as proof of (cNUMBER c0)
% 224.04/224.61 Found (x3 x20) as proof of (cNUMBER c0)
% 224.04/224.61 Found (x3 x20) as proof of (cNUMBER c0)
% 224.04/224.61 Found x30:(cNUMBER Xn0)
% 224.04/224.61 Found x30 as proof of (cNUMBER (cS Xx))
% 224.04/224.61 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 224.04/224.61 Found x30:(cNUMBER Xn0)
% 224.04/224.61 Instantiate: Xn0:=c0:fofType
% 224.04/224.61 Found x30 as proof of (cNUMBER c0)
% 224.04/224.61 Found x50:=(x5 x40):(cNUMBER Xn0)
% 224.04/224.61 Found (x5 x40) as proof of (cNUMBER Xn0)
% 224.04/224.61 Found (x5 x40) as proof of (cNUMBER Xn0)
% 224.04/224.61 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (x3 x22) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x3 x22) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x3 x22) as proof of (cNUMBER Xn)
% 224.04/224.61 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 224.04/224.61 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found x120:=(x12 x110):(cNUMBER Xn0)
% 224.04/224.61 Found (x12 x110) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x12 x110) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 224.04/224.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 224.04/224.61 Instantiate: Xn0:=(cS Xx):fofType
% 224.04/224.61 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 224.04/224.61 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 224.04/224.61 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 224.04/224.61 Found x50:(cNUMBER Xn0)
% 224.04/224.61 Instantiate: Xn0:=(cS Xx):fofType
% 224.04/224.61 Found x50 as proof of (cNUMBER (cS Xx))
% 224.04/224.61 Found (fun (x6:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 224.04/224.61 Found x50:(cNUMBER Xn0)
% 224.04/224.61 Instantiate: Xn0:=(cS Xx):fofType
% 224.04/224.61 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 224.04/224.61 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 224.04/224.61 Found x50:=(x5 x40):(cNUMBER Xn0)
% 224.04/224.61 Found (x5 x40) as proof of (cNUMBER Xn0)
% 224.04/224.61 Found (x5 x40) as proof of (cNUMBER Xn0)
% 224.04/224.61 Found x50:=(x5 x41):(cNUMBER Xn0)
% 224.04/224.61 Instantiate: Xn0:=Xn:fofType
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found x50:=(x5 x41):(cNUMBER Xn0)
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 224.04/224.61 Found x30:(cNUMBER Xn0)
% 224.04/224.61 Instantiate: Xn0:=Xn:fofType
% 224.04/224.61 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 224.04/224.61 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 224.04/224.61 Found x11:(cEVEN c0)
% 224.04/224.61 Instantiate: Xn0:=c0:fofType
% 224.04/224.61 Found x11 as proof of (cEVEN Xn0)
% 224.04/224.61 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found x9:(cODD (cS c0))
% 224.04/224.61 Instantiate: Xn0:=(cS c0):fofType
% 224.04/224.61 Found x9 as proof of (cODD Xn0)
% 224.04/224.61 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 224.04/224.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 227.47/227.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 227.47/227.98 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 227.47/227.98 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 227.47/227.98 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 227.47/227.98 Found x70:=(x7 x60):(cNUMBER Xn0)
% 227.47/227.98 Instantiate: Xn0:=(cS Xx):fofType
% 227.47/227.98 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found x9:(cODD (cS c0))
% 227.47/227.98 Instantiate: Xn0:=(cS c0):fofType
% 227.47/227.98 Found x9 as proof of (cODD Xn0)
% 227.47/227.98 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.47/227.98 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.47/227.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.47/227.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.47/227.98 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 227.47/227.98 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 227.47/227.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 227.47/227.98 Instantiate: Xn0:=(cS Xx):fofType
% 227.47/227.98 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found x70:(cNUMBER Xn0)
% 227.47/227.98 Instantiate: Xn0:=(cS Xx):fofType
% 227.47/227.98 Found x70 as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found x50:=(x5 x40):(cNUMBER Xn0)
% 227.47/227.98 Instantiate: Xn0:=c0:fofType
% 227.47/227.98 Found (x5 x40) as proof of (cNUMBER c0)
% 227.47/227.98 Found (x5 x40) as proof of (cNUMBER c0)
% 227.47/227.98 Found x30:(cNUMBER Xn0)
% 227.47/227.98 Instantiate: Xn0:=(cS Xx):fofType
% 227.47/227.98 Found x30 as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found x50:=(x5 x40):(cNUMBER Xn0)
% 227.47/227.98 Found (x5 x40) as proof of (cNUMBER c0)
% 227.47/227.98 Found (x5 x40) as proof of (cNUMBER c0)
% 227.47/227.98 Found (x5 x40) as proof of (cNUMBER c0)
% 227.47/227.98 Found x50:(cNUMBER Xn0)
% 227.47/227.98 Found x50 as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 227.47/227.98 Found x8:(cNUMBER Xx)
% 227.47/227.98 Instantiate: Xn0:=Xx:fofType
% 227.47/227.98 Found x8 as proof of (cNUMBER Xn0)
% 227.47/227.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 227.47/227.98 Instantiate: Xn0:=c0:fofType
% 227.47/227.98 Found (x3 x20) as proof of (cNUMBER c0)
% 227.47/227.98 Found (x3 x20) as proof of (cNUMBER c0)
% 227.47/227.98 Found x50:=(x5 x40):(cNUMBER Xn0)
% 227.47/227.98 Instantiate: Xn0:=Xn:fofType
% 227.47/227.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 227.47/227.98 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 227.47/227.98 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 227.47/227.98 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 227.47/227.98 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 227.47/227.98 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 227.47/227.98 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 227.47/227.98 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 234.38/234.89 Found x9:(cODD (cS c0))
% 234.38/234.89 Instantiate: Xn0:=(cS c0):fofType
% 234.38/234.89 Found x9 as proof of (cODD Xn0)
% 234.38/234.89 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 234.38/234.89 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 234.38/234.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 234.38/234.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 234.38/234.89 Found x60:=(x6 x50):(cNUMBER Xn0)
% 234.38/234.89 Instantiate: Xn0:=(cS Xx):fofType
% 234.38/234.89 Found (x6 x50) as proof of (cNUMBER (cS Xx))
% 234.38/234.89 Found (x6 x50) as proof of (cNUMBER (cS Xx))
% 234.38/234.89 Found x50:(cNUMBER Xn0)
% 234.38/234.89 Instantiate: Xn0:=(cS Xx):fofType
% 234.38/234.89 Found x50 as proof of (cNUMBER (cS Xx))
% 234.38/234.89 Found x30:=(x3 x20):(cNUMBER Xn0)
% 234.38/234.89 Found (x3 x20) as proof of (cNUMBER Xn0)
% 234.38/234.89 Found (x3 x20) as proof of (cNUMBER Xn0)
% 234.38/234.89 Found x6:(cNUMBER Xx)
% 234.38/234.89 Instantiate: Xn0:=Xx:fofType
% 234.38/234.89 Found x6 as proof of (cNUMBER Xn0)
% 234.38/234.89 Found x50:(cNUMBER Xn0)
% 234.38/234.89 Instantiate: Xn0:=Xn:fofType
% 234.38/234.89 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 234.38/234.89 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 234.38/234.89 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 234.38/234.89 Found x70:=(x7 x60):(cNUMBER Xn0)
% 234.38/234.89 Instantiate: Xn0:=c0:fofType
% 234.38/234.89 Found (x7 x60) as proof of (cNUMBER c0)
% 234.38/234.89 Found (x7 x60) as proof of (cNUMBER c0)
% 234.38/234.89 Found x90:=(x9 x80):(cNUMBER Xn0)
% 234.38/234.89 Found (x9 x80) as proof of (cNUMBER Xn)
% 234.38/234.89 Found (x9 x80) as proof of (cNUMBER Xn)
% 234.38/234.89 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 234.38/234.89 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 234.38/234.89 Found x30:(cNUMBER Xn0)
% 234.38/234.89 Instantiate: Xn0:=Xn:fofType
% 234.38/234.89 Found (fun (x7:cIND)=> x30) as proof of (cNUMBER Xn)
% 234.38/234.89 Found (fun (x7:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 234.38/234.89 Found x50:(cNUMBER Xn00)
% 234.38/234.89 Instantiate: Xn00:=Xn:fofType
% 234.38/234.89 Found (fun (x7:cIND)=> x50) as proof of (cNUMBER Xn)
% 234.38/234.89 Found (fun (x7:cIND)=> x50) as proof of (cIND->(cNUMBER Xn))
% 234.38/234.89 Found x30:(cNUMBER Xn0)
% 234.38/234.89 Instantiate: Xn0:=Xn:fofType
% 234.38/234.89 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 234.38/234.89 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 234.38/234.89 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 234.38/234.89 Found x30:(cNUMBER Xn0)
% 234.38/234.89 Instantiate: Xn0:=Xn:fofType
% 234.38/234.89 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 234.38/234.89 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 234.38/234.89 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 234.38/234.89 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 234.38/234.89 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 235.22/235.76 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 235.22/235.76 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 235.22/235.76 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 235.22/235.76 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30))) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 235.22/235.76 Found x50:=(x5 x40):(cNUMBER Xn0)
% 235.22/235.76 Instantiate: Xn0:=(cS Xx):fofType
% 235.22/235.76 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 235.22/235.76 Found (fun (x8:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 235.22/235.76 Found x30:=(x3 x21):(cNUMBER Xn0)
% 235.22/235.76 Instantiate: Xn0:=Xn:fofType
% 235.22/235.76 Found (x3 x21) as proof of (cNUMBER Xn)
% 235.22/235.76 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 235.22/235.76 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 235.22/235.76 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 235.22/235.76 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 235.22/235.76 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 235.22/235.76 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 238.27/238.80 Found x70:(cNUMBER Xn0)
% 238.27/238.80 Instantiate: Xn0:=(cS Xx):fofType
% 238.27/238.80 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 238.27/238.80 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 238.27/238.80 Found x50:=(x5 x40):(cNUMBER Xn0)
% 238.27/238.80 Found (x5 x40) as proof of (cNUMBER Xn0)
% 238.27/238.80 Found (x5 x40) as proof of (cNUMBER Xn0)
% 238.27/238.80 Found x30:(cNUMBER Xn0)
% 238.27/238.80 Found x30 as proof of (cNUMBER (cS Xx))
% 238.27/238.80 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 238.27/238.80 Found x30:(cNUMBER Xn0)
% 238.27/238.80 Instantiate: Xn0:=c0:fofType
% 238.27/238.80 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER c0)
% 238.27/238.80 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER c0))
% 238.27/238.80 Found x50:(cNUMBER Xn0)
% 238.27/238.80 Instantiate: Xn0:=(cS Xx):fofType
% 238.27/238.80 Found x50 as proof of (cNUMBER (cS Xx))
% 238.27/238.80 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 238.27/238.80 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 238.27/238.80 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.27/238.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 238.27/238.80 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 238.27/238.80 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.27/238.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 238.27/238.80 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 238.27/238.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 238.27/238.80 Instantiate: Xn0:=(cS Xx):fofType
% 238.27/238.80 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 238.27/238.80 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 238.27/238.80 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 238.27/238.80 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 238.27/238.80 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.27/238.80 Found (x7 x60) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (x7 x60) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 238.27/238.80 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 240.98/241.52 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found (x5 x41) as proof of (cNUMBER Xn)
% 240.98/241.52 Found (x5 x41) as proof of (cNUMBER Xn)
% 240.98/241.52 Found (x5 x41) as proof of (cNUMBER Xn)
% 240.98/241.52 Found x30:(cNUMBER Xn0)
% 240.98/241.52 Instantiate: Xn0:=c0:fofType
% 240.98/241.52 Found x30 as proof of (cNUMBER c0)
% 240.98/241.52 Found x70:=(x7 x60):(cNUMBER Xn0)
% 240.98/241.52 Instantiate: Xn0:=c0:fofType
% 240.98/241.52 Found (x7 x60) as proof of (cNUMBER c0)
% 240.98/241.52 Found (x7 x60) as proof of (cNUMBER c0)
% 240.98/241.52 Found x9:(cODD (cS c0))
% 240.98/241.52 Instantiate: Xn0:=(cS c0):fofType
% 240.98/241.52 Found x9 as proof of (cODD Xn0)
% 240.98/241.52 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found x70:(cNUMBER Xn0)
% 240.98/241.52 Found x70 as proof of (cNUMBER (cS Xx))
% 240.98/241.52 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 240.98/241.52 Found x70:=(x7 x60):(cNUMBER Xn0)
% 240.98/241.52 Found (x7 x60) as proof of (cNUMBER c0)
% 240.98/241.52 Found (x7 x60) as proof of (cNUMBER c0)
% 240.98/241.52 Found (x7 x60) as proof of (cNUMBER c0)
% 240.98/241.52 Found x30:(cNUMBER Xn0)
% 240.98/241.52 Instantiate: Xn0:=Xn:fofType
% 240.98/241.52 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 240.98/241.52 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 240.98/241.52 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 240.98/241.52 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 240.98/241.52 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 240.98/241.52 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 240.98/241.52 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 240.98/241.52 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 240.98/241.52 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 240.98/241.52 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.98/241.52 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 242.85/243.38 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 242.85/243.38 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 242.85/243.38 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 242.85/243.38 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 242.85/243.38 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 242.85/243.38 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 242.85/243.38 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 242.85/243.38 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 242.85/243.38 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 242.85/243.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 242.85/243.38 Instantiate: Xn0:=(cS Xx):fofType
% 242.85/243.38 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 242.85/243.38 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 242.85/243.38 Found x30:=(x3 x21):(cNUMBER Xn0)
% 242.85/243.38 Instantiate: Xn0:=Xn:fofType
% 242.85/243.38 Found (x3 x21) as proof of (cNUMBER Xn)
% 242.85/243.38 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 242.85/243.38 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 242.85/243.38 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 242.85/243.38 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 242.85/243.38 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 242.85/243.38 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 244.51/245.04 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 244.51/245.04 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cIND->(cNUMBER Xn))
% 244.51/245.04 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 244.51/245.04 Found x50:=(x5 x40):(cNUMBER Xn0)
% 244.51/245.04 Instantiate: Xn0:=c0:fofType
% 244.51/245.04 Found (x5 x40) as proof of (cNUMBER c0)
% 244.51/245.04 Found (x5 x40) as proof of (cNUMBER c0)
% 244.51/245.04 Found x110:((or (cEVEN Xn0)) (cODD Xn0))
% 244.51/245.04 Found x110 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 244.51/245.04 Found (x12 x110) as proof of (cNUMBER Xn)
% 244.51/245.04 Found (x12 x110) as proof of (cNUMBER Xn)
% 244.51/245.04 Found (x12 x110) as proof of (cNUMBER Xn)
% 244.51/245.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 244.51/245.04 Instantiate: Xn0:=c0:fofType
% 244.51/245.04 Found (x3 x20) as proof of (cNUMBER c0)
% 244.51/245.04 Found (x3 x20) as proof of (cNUMBER c0)
% 244.51/245.04 Found x8:(cODD (cS c0))
% 244.51/245.04 Instantiate: Xn0:=(cS c0):fofType
% 244.51/245.04 Found x8 as proof of (cODD Xn0)
% 244.51/245.04 Found (or_intror00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 244.51/245.04 Found ((or_intror0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 244.51/245.04 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 244.51/245.04 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 244.51/245.04 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)) as proof of (cNUMBER Xn0)
% 244.51/245.04 Found (fun (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (cNUMBER Xn0)
% 244.51/245.04 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 244.51/245.04 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 245.00/245.53 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 245.00/245.53 Found ((and_rect4 (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 245.00/245.53 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 245.00/245.53 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 245.00/245.53 Found x50:=(x5 x40):(cNUMBER Xn0)
% 245.00/245.53 Instantiate: Xn0:=Xn:fofType
% 245.00/245.53 Found (x5 x40) as proof of (cNUMBER Xn)
% 245.00/245.53 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 245.00/245.53 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.00/245.53 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 245.00/245.53 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 245.00/245.53 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 245.00/245.53 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 245.00/245.53 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 245.00/245.53 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 245.00/245.53 Found x30:(cNUMBER Xn0)
% 245.00/245.53 Instantiate: Xn0:=c0:fofType
% 245.00/245.53 Found x30 as proof of (cNUMBER c0)
% 245.00/245.53 Found x30:(cNUMBER Xn0)
% 245.00/245.53 Instantiate: Xn0:=(cS Xx):fofType
% 245.00/245.53 Found x30 as proof of (cNUMBER (cS Xx))
% 245.00/245.53 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 245.00/245.53 Found x60:=(x6 x50):(cNUMBER Xn0)
% 245.00/245.53 Instantiate: Xn0:=(cS Xx):fofType
% 245.00/245.53 Found (x6 x50) as proof of (cNUMBER (cS Xx))
% 245.00/245.53 Found (fun (x6:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x6 x50)) as proof of (cNUMBER (cS Xx))
% 247.10/247.63 Found (fun (x6:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x6 x50)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER (cS Xx)))
% 247.10/247.63 Found x70:=(x7 x60):(cNUMBER Xn0)
% 247.10/247.63 Instantiate: Xn0:=(cS Xx):fofType
% 247.10/247.63 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 247.10/247.63 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 247.10/247.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 247.10/247.63 Found (x3 x20) as proof of (cNUMBER Xn0)
% 247.10/247.63 Found (x3 x20) as proof of (cNUMBER Xn0)
% 247.10/247.63 Found x50:(cNUMBER Xn0)
% 247.10/247.63 Instantiate: Xn0:=(cS Xx):fofType
% 247.10/247.63 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 247.10/247.63 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 247.10/247.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 247.10/247.63 Instantiate: Xn0:=(cS Xx):fofType
% 247.10/247.63 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 247.10/247.63 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 247.10/247.63 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 247.10/247.63 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.10/247.63 Found (x5 x40) as proof of (cNUMBER c0)
% 247.10/247.63 Found (x5 x40) as proof of (cNUMBER c0)
% 247.10/247.63 Found (x5 x40) as proof of (cNUMBER c0)
% 247.10/247.63 Found x9:(cODD (cS c0))
% 247.10/247.63 Instantiate: Xn0:=(cS c0):fofType
% 247.10/247.63 Found (fun (x9:(cODD (cS c0)))=> x9) as proof of (cODD Xn0)
% 247.10/247.63 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9) as proof of ((cODD (cS c0))->(cODD Xn0))
% 247.10/247.63 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 247.10/247.63 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)) as proof of (cODD Xn0)
% 247.10/247.63 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)) as proof of (cODD Xn0)
% 247.10/247.63 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)) as proof of (cODD Xn0)
% 247.10/247.63 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)) as proof of (cODD Xn0)
% 247.10/247.63 Found (or_intror00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.10/247.63 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.10/247.63 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.12/247.68 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.12/247.68 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 247.12/247.68 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 247.12/247.68 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 247.12/247.68 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 247.12/247.68 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 247.12/247.68 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 247.12/247.68 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 247.12/247.68 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 247.12/247.68 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 247.12/247.68 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 247.12/247.68 Found (or_comm_i00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.12/247.68 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.12/247.68 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.26/247.80 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.26/247.80 Found x30:(cNUMBER Xn0)
% 247.26/247.80 Instantiate: Xn0:=Xn:fofType
% 247.26/247.80 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 247.26/247.80 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 247.26/247.80 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 247.26/247.80 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))))
% 247.26/247.80 Found x30:(cNUMBER Xn0)
% 247.26/247.80 Instantiate: Xn0:=Xn:fofType
% 247.26/247.80 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 247.26/247.80 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 247.26/247.80 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 247.26/247.80 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))))
% 247.26/247.80 Found ((or_ind00 (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 247.26/247.80 Found (((or_ind0 (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 249.42/249.96 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 249.42/249.96 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x2 x30))) (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 249.42/249.96 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x2 x30))) (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 249.42/249.96 Found x30:=(x3 x20):(cNUMBER Xn0)
% 249.42/249.96 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found x70:=(x7 x60):(cNUMBER Xn0)
% 249.42/249.96 Instantiate: Xn0:=(cS Xx):fofType
% 249.42/249.96 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found x70:(cNUMBER Xn0)
% 249.42/249.96 Instantiate: Xn0:=(cS Xx):fofType
% 249.42/249.96 Found x70 as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found x30:(cNUMBER Xn0)
% 249.42/249.96 Found x30 as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 249.42/249.96 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 249.42/249.96 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 249.42/249.96 Found (x3 x20) as proof of (cNUMBER c0)
% 249.42/249.96 Found (x3 x20) as proof of (cNUMBER c0)
% 249.42/249.96 Found (x3 x20) as proof of (cNUMBER c0)
% 249.53/250.12 Found x30:=(x3 x21):(cNUMBER Xn0)
% 249.53/250.12 Instantiate: Xn0:=Xn:fofType
% 249.53/250.12 Found (x3 x21) as proof of (cNUMBER Xn)
% 249.53/250.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 249.53/250.12 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 249.53/250.12 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 249.53/250.12 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 249.53/250.12 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 249.53/250.12 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 249.53/250.12 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 249.53/250.12 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cIND->(cNUMBER Xn))
% 249.53/250.12 Found x50:=(x5 x40):(cNUMBER Xn0)
% 249.53/250.12 Instantiate: Xn0:=Xn:fofType
% 249.53/250.12 Found (x5 x40) as proof of (cNUMBER Xn)
% 249.53/250.12 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 249.53/250.12 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 249.53/250.12 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 249.53/250.12 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 249.53/250.12 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 249.60/250.17 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 249.60/250.17 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 249.60/250.17 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 249.60/250.17 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 249.60/250.17 Found x50:=(x5 x40):(cNUMBER Xn0)
% 249.60/250.17 Instantiate: Xn0:=Xn:fofType
% 249.60/250.17 Found (x5 x40) as proof of (cNUMBER Xn)
% 249.60/250.17 Found (x5 x40) as proof of (cNUMBER Xn)
% 249.60/250.17 Found x70:=(x7 x60):(cNUMBER Xn00)
% 249.60/250.17 Instantiate: Xn00:=Xn:fofType
% 249.60/250.17 Found (x7 x60) as proof of (cNUMBER Xn)
% 249.60/250.17 Found (x7 x60) as proof of (cNUMBER Xn)
% 249.60/250.17 Found x50:(cNUMBER Xn0)
% 249.60/250.17 Instantiate: Xn0:=Xn:fofType
% 249.60/250.17 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 249.60/250.17 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 249.60/250.17 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 249.60/250.17 Found x50:(cNUMBER Xn0)
% 249.60/250.17 Instantiate: Xn0:=Xn:fofType
% 249.60/250.17 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 249.60/250.17 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 249.60/250.17 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 249.60/250.17 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 249.60/250.17 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 249.60/250.17 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x40)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 252.24/252.80 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 252.24/252.80 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 252.24/252.80 Found x50:=(x5 x40):(cNUMBER Xn0)
% 252.24/252.80 Instantiate: Xn0:=c0:fofType
% 252.24/252.80 Found (x5 x40) as proof of (cNUMBER c0)
% 252.24/252.80 Found (x5 x40) as proof of (cNUMBER c0)
% 252.24/252.80 Found x90:=(x9 x80):(cNUMBER Xn0)
% 252.24/252.80 Found (x9 x80) as proof of (cNUMBER Xn)
% 252.24/252.80 Found (x9 x80) as proof of (cNUMBER Xn)
% 252.24/252.80 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 252.24/252.80 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 252.24/252.80 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 252.24/252.80 Found x30:=(x3 x21):(cNUMBER Xn0)
% 252.24/252.80 Instantiate: Xn0:=Xn:fofType
% 252.24/252.80 Found (x3 x21) as proof of (cNUMBER Xn)
% 252.24/252.80 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 252.24/252.80 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 252.24/252.80 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 252.24/252.80 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 252.24/252.80 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 252.24/252.80 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 252.24/252.80 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 252.75/253.32 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 252.75/253.32 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 252.75/253.32 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 252.75/253.32 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 252.75/253.32 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 252.75/253.32 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 252.75/253.32 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.75/253.32 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.75/253.32 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.75/253.32 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.75/253.32 Found (x5 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 252.75/253.32 Found (x5 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 252.75/253.32 Found x50:(cNUMBER Xn00)
% 252.75/253.32 Instantiate: Xn00:=Xn:fofType
% 252.75/253.32 Found (fun (x7:cIND)=> x50) as proof of (cNUMBER Xn)
% 252.75/253.32 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:cIND)=> x50) as proof of (cIND->(cNUMBER Xn))
% 252.75/253.32 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:cIND)=> x50) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 254.62/255.21 Found x30:(cNUMBER Xn0)
% 254.62/255.21 Instantiate: Xn0:=Xn:fofType
% 254.62/255.21 Found (fun (x7:cIND)=> x30) as proof of (cNUMBER Xn)
% 254.62/255.21 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:cIND)=> x30) as proof of (cIND->(cNUMBER Xn))
% 254.62/255.21 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:cIND)=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->(cNUMBER Xn)))
% 254.62/255.21 Found x50:(cNUMBER Xn0)
% 254.62/255.21 Found x50 as proof of (cNUMBER (cS Xx))
% 254.62/255.21 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 254.62/255.21 Found x50:=(x5 x40):(cNUMBER Xn0)
% 254.62/255.21 Found (x5 x40) as proof of (cNUMBER c0)
% 254.62/255.21 Found (x5 x40) as proof of (cNUMBER c0)
% 254.62/255.21 Found (x5 x40) as proof of (cNUMBER c0)
% 254.62/255.21 Found x50:(cNUMBER Xn0)
% 254.62/255.21 Instantiate: Xn0:=c0:fofType
% 254.62/255.21 Found x50 as proof of (cNUMBER c0)
% 254.62/255.21 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 254.62/255.21 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 254.62/255.21 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 254.62/255.21 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 254.62/255.21 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 254.62/255.21 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 254.62/255.21 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 254.62/255.21 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 254.62/255.21 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 254.62/255.21 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 254.62/255.21 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 256.02/256.57 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 256.02/256.57 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 256.02/256.57 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 256.02/256.57 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 256.02/256.57 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 256.02/256.57 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 256.02/256.57 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 256.02/256.57 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.02/256.57 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.02/256.57 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.02/256.57 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.02/256.57 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 256.02/256.57 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 256.02/256.57 Found x9:(cODD (cS c0))
% 256.02/256.57 Instantiate: Xn0:=(cS c0):fofType
% 256.02/256.57 Found x9 as proof of (cODD Xn0)
% 256.02/256.57 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.02/256.57 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.02/256.57 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.02/256.57 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.86/257.39 Found x11:(cEVEN c0)
% 256.86/257.39 Instantiate: Xn0:=c0:fofType
% 256.86/257.39 Found x11 as proof of (cEVEN Xn0)
% 256.86/257.39 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.86/257.39 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.86/257.39 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.86/257.39 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.86/257.39 Found x30:(cNUMBER Xn0)
% 256.86/257.39 Found x30 as proof of (cNUMBER (cS Xx))
% 256.86/257.39 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 256.86/257.39 Found x30:=(x3 x21):(cNUMBER Xn0)
% 256.86/257.39 Instantiate: Xn0:=Xn:fofType
% 256.86/257.39 Found (x3 x21) as proof of (cNUMBER Xn)
% 256.86/257.39 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 256.86/257.39 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 256.86/257.39 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 256.86/257.39 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 256.86/257.39 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 256.86/257.39 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 256.86/257.39 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 256.86/257.39 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cIND->(cNUMBER Xn))
% 256.86/257.39 Found x30:(cNUMBER Xn0)
% 256.86/257.39 Instantiate: Xn0:=c0:fofType
% 256.86/257.39 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER c0)
% 256.86/257.39 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER c0))
% 258.95/259.50 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER c0)))
% 258.95/259.50 Found x50:=(x5 x40):(cNUMBER Xn0)
% 258.95/259.50 Instantiate: Xn0:=(cS Xx):fofType
% 258.95/259.50 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 258.95/259.50 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 258.95/259.50 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found (x9 x80) as proof of (cNUMBER Xn)
% 258.95/259.50 Found (x9 x80) as proof of (cNUMBER Xn)
% 258.95/259.50 Found (x9 x80) as proof of (cNUMBER Xn)
% 258.95/259.50 Found x70:=(x7 x60):(cNUMBER Xn0)
% 258.95/259.50 Instantiate: Xn0:=c0:fofType
% 258.95/259.50 Found (x7 x60) as proof of (cNUMBER c0)
% 258.95/259.50 Found (x7 x60) as proof of (cNUMBER c0)
% 258.95/259.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 258.95/259.50 Instantiate: Xn0:=(cS Xx):fofType
% 258.95/259.50 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 258.95/259.50 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 258.95/259.50 Found x9:(cODD (cS c0))
% 258.95/259.50 Instantiate: Xn0:=(cS c0):fofType
% 258.95/259.50 Found x9 as proof of (cODD Xn0)
% 258.95/259.50 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found x11:(cEVEN c0)
% 258.95/259.50 Instantiate: Xn0:=c0:fofType
% 258.95/259.50 Found x11 as proof of (cEVEN Xn0)
% 258.95/259.50 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.95/259.50 Found x30:=(x3 x21):(cNUMBER Xn0)
% 258.95/259.50 Instantiate: Xn0:=Xn:fofType
% 258.95/259.50 Found (x3 x21) as proof of (cNUMBER Xn)
% 258.95/259.50 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 258.95/259.50 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 258.95/259.50 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 258.95/259.50 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 258.95/259.50 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 258.95/259.50 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 263.00/263.53 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.53 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 263.00/263.53 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 263.00/263.53 Found x70:(cNUMBER Xn0)
% 263.00/263.53 Instantiate: Xn0:=c0:fofType
% 263.00/263.53 Found x70 as proof of (cNUMBER c0)
% 263.00/263.53 Found x30:(cNUMBER Xn0)
% 263.00/263.53 Instantiate: Xn0:=(cS Xx):fofType
% 263.00/263.53 Found x30 as proof of (cNUMBER (cS Xx))
% 263.00/263.53 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 263.00/263.53 Found x50:=(x5 x40):(cNUMBER Xn0)
% 263.00/263.53 Instantiate: Xn0:=(cS Xx):fofType
% 263.00/263.53 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 263.00/263.53 Found (fun (x8:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 263.00/263.53 Found x70:=(x7 x60):(cNUMBER Xn00)
% 263.00/263.53 Instantiate: Xn00:=Xn:fofType
% 263.00/263.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 263.00/263.53 Found x30:=(x3 x20):(cNUMBER Xn0)
% 263.00/263.53 Instantiate: Xn0:=Xn:fofType
% 263.00/263.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 263.00/263.53 Found x30:=(x3 x20):(cNUMBER Xn0)
% 263.00/263.53 Instantiate: Xn0:=c0:fofType
% 263.00/263.53 Found (x3 x20) as proof of (cNUMBER c0)
% 263.00/263.53 Found (x3 x20) as proof of (cNUMBER c0)
% 263.00/263.53 Found x30:=(x3 x20):(cNUMBER Xn0)
% 263.00/263.53 Instantiate: Xn0:=(cS Xx):fofType
% 263.00/263.53 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 263.00/263.53 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 263.00/263.53 Found x9:(cODD (cS c0))
% 263.00/263.53 Instantiate: Xn0:=(cS c0):fofType
% 263.00/263.53 Found x9 as proof of (cODD Xn0)
% 263.00/263.53 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.53 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.53 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.53 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.53 Found x50:(cNUMBER Xn0)
% 263.00/263.53 Instantiate: Xn0:=(cS Xx):fofType
% 263.00/263.53 Found x50 as proof of (cNUMBER (cS Xx))
% 263.00/263.53 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 263.00/263.53 Found x70:=(x7 x60):(cNUMBER Xn0)
% 263.00/263.53 Instantiate: Xn0:=Xn:fofType
% 263.00/263.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 263.00/263.53 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 263.00/263.53 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 263.00/263.53 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 263.00/263.53 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 264.36/264.92 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 264.36/264.92 Found x110:((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.92 Found x110 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.92 Found (x12 x110) as proof of (cNUMBER Xn)
% 264.36/264.92 Found (x12 x110) as proof of (cNUMBER Xn)
% 264.36/264.92 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 264.36/264.92 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 264.36/264.92 Found x70:=(x7 x60):(cNUMBER Xn0)
% 264.36/264.92 Instantiate: Xn0:=(cS Xx):fofType
% 264.36/264.92 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 264.36/264.92 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 264.36/264.92 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 264.36/264.92 Found x50:=(x5 x40):(cNUMBER Xn0)
% 264.36/264.92 Instantiate: Xn0:=c0:fofType
% 264.36/264.92 Found (x5 x40) as proof of (cNUMBER c0)
% 264.36/264.92 Found (x5 x40) as proof of (cNUMBER c0)
% 264.36/264.92 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 264.36/264.92 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 264.36/264.92 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 264.36/264.92 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 264.36/264.92 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 264.36/264.92 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 264.36/264.92 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.92 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.92 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.92 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.92 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 264.36/264.93 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 264.36/264.93 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.93 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.93 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.36/264.93 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found x30:=(x3 x20):(cNUMBER Xn0)
% 266.99/267.55 Found (x3 x20) as proof of (cNUMBER Xn0)
% 266.99/267.55 Found (x3 x20) as proof of (cNUMBER Xn0)
% 266.99/267.55 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found (x5 x40) as proof of (cNUMBER c0)
% 266.99/267.55 Found (x5 x40) as proof of (cNUMBER c0)
% 266.99/267.55 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER c0)
% 266.99/267.55 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER c0))
% 266.99/267.55 Found x30:=(x3 x20):(cNUMBER Xn0)
% 266.99/267.55 Instantiate: Xn0:=(cS Xx):fofType
% 266.99/267.55 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 266.99/267.55 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 266.99/267.55 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 266.99/267.55 Found x9:(cODD (cS c0))
% 266.99/267.55 Instantiate: Xn0:=(cS c0):fofType
% 266.99/267.55 Found x9 as proof of (cODD Xn0)
% 266.99/267.55 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found x30:(cNUMBER Xn0)
% 266.99/267.55 Instantiate: Xn0:=(cS Xx):fofType
% 266.99/267.55 Found x30 as proof of (cNUMBER (cS Xx))
% 266.99/267.55 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 266.99/267.55 Found x30:=(x3 x20):(cNUMBER Xn0)
% 266.99/267.55 Found (x3 x20) as proof of (cNUMBER Xn0)
% 266.99/267.55 Found (x3 x20) as proof of (cNUMBER Xn0)
% 266.99/267.55 Found x30:(cNUMBER Xn0)
% 266.99/267.55 Instantiate: Xn0:=c0:fofType
% 266.99/267.55 Found x30 as proof of (cNUMBER c0)
% 266.99/267.55 Found x30:(cNUMBER Xn0)
% 266.99/267.55 Instantiate: Xn0:=c0:fofType
% 266.99/267.55 Found x30 as proof of (cNUMBER c0)
% 266.99/267.55 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found x31:(cNUMBER Xn0)
% 266.99/267.55 Instantiate: Xn0:=Xn:fofType
% 266.99/267.55 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 266.99/267.55 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 266.99/267.55 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x31) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 266.99/267.55 Found x6:(cNUMBER Xx)
% 266.99/267.55 Instantiate: Xn0:=Xx:fofType
% 266.99/267.55 Found x6 as proof of (cNUMBER Xn0)
% 266.99/267.55 Found x9:(cODD (cS c0))
% 266.99/267.55 Instantiate: Xn0:=(cS c0):fofType
% 266.99/267.55 Found x9 as proof of (cODD Xn0)
% 266.99/267.55 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found x70:=(x7 x60):(cNUMBER Xn0)
% 266.99/267.55 Instantiate: Xn0:=(cS Xx):fofType
% 266.99/267.55 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 266.99/267.55 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 266.99/267.55 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.55 Instantiate: Xn00:=Xn:fofType
% 266.99/267.55 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.55 Found x50:=(x5 x40):(cNUMBER Xn0)
% 266.99/267.55 Instantiate: Xn0:=Xn:fofType
% 266.99/267.55 Found (x5 x40) as proof of (cNUMBER Xn)
% 266.99/267.55 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 266.99/267.55 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 271.25/271.82 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 271.25/271.82 Instantiate: Xn0:=Xn:fofType
% 271.25/271.82 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 271.25/271.82 Found x70:(cNUMBER Xn0)
% 271.25/271.82 Found x70 as proof of (cNUMBER (cS Xx))
% 271.25/271.82 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 271.25/271.82 Found x70:=(x7 x60):(cNUMBER Xn00)
% 271.25/271.82 Instantiate: Xn00:=Xn:fofType
% 271.25/271.82 Found (x7 x60) as proof of (cNUMBER Xn)
% 271.25/271.82 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 271.25/271.82 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 271.25/271.82 Found x70:=(x7 x60):(cNUMBER Xn0)
% 271.25/271.82 Found (x7 x60) as proof of (cNUMBER c0)
% 271.25/271.82 Found (x7 x60) as proof of (cNUMBER c0)
% 271.25/271.82 Found (x7 x60) as proof of (cNUMBER c0)
% 271.25/271.82 Found x50:=(x5 x40):(cNUMBER Xn0)
% 271.25/271.82 Instantiate: Xn0:=c0:fofType
% 271.25/271.82 Found (x5 x40) as proof of (cNUMBER c0)
% 271.25/271.82 Found (x5 x40) as proof of (cNUMBER c0)
% 271.25/271.82 Found x70:=(x7 x60):(cNUMBER Xn0)
% 271.25/271.82 Instantiate: Xn0:=c0:fofType
% 271.25/271.82 Found (x7 x60) as proof of (cNUMBER c0)
% 271.25/271.82 Found (x7 x60) as proof of (cNUMBER c0)
% 271.25/271.82 Found x70:=(x7 x60):(cNUMBER Xn0)
% 271.25/271.82 Instantiate: Xn0:=(cS Xx):fofType
% 271.25/271.82 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 271.25/271.82 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 271.25/271.82 Found x50:(cNUMBER Xn0)
% 271.25/271.82 Instantiate: Xn0:=Xn:fofType
% 271.25/271.82 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 271.25/271.82 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 271.25/271.82 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 271.25/271.82 Found x50:(cNUMBER Xn0)
% 271.25/271.82 Instantiate: Xn0:=Xn:fofType
% 271.25/271.82 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 271.25/271.82 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 271.25/271.82 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 271.25/271.82 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 271.25/271.82 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 271.25/271.82 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x40)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 271.25/271.82 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 271.25/271.82 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 272.54/273.12 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50))) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 272.54/273.12 Found x50:=(x5 x41):(cNUMBER Xn0)
% 272.54/273.12 Instantiate: Xn0:=Xn:fofType
% 272.54/273.12 Found (x5 x41) as proof of (cNUMBER Xn)
% 272.54/273.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 272.54/273.12 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 272.54/273.12 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 272.54/273.12 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 272.54/273.12 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 272.54/273.12 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 272.54/273.12 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 272.54/273.12 Found x50:(cNUMBER Xn0)
% 272.54/273.12 Found x50 as proof of (cNUMBER (cS Xx))
% 272.54/273.12 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 272.54/273.12 Found x50:=(x5 x40):(cNUMBER Xn00)
% 272.54/273.12 Instantiate: Xn00:=Xn:fofType
% 272.54/273.12 Found (x5 x40) as proof of (cNUMBER Xn)
% 272.54/273.12 Found (x5 x40) as proof of (cNUMBER Xn)
% 272.54/273.12 Found x30:=(x3 x20):(cNUMBER Xn0)
% 272.54/273.12 Instantiate: Xn0:=Xn:fofType
% 272.54/273.12 Found (x3 x20) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (x3 x20) as proof of (cNUMBER Xn)
% 278.31/278.88 Found x50:(cNUMBER Xn0)
% 278.31/278.88 Instantiate: Xn0:=c0:fofType
% 278.31/278.88 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER c0)
% 278.31/278.88 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER c0))
% 278.31/278.88 Found x70:=(x7 x60):(cNUMBER Xn0)
% 278.31/278.88 Found (x7 x60) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (x7 x60) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 278.31/278.88 Found x70:=(x7 x60):(cNUMBER Xn0)
% 278.31/278.88 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found x30:=(x3 x20):(cNUMBER Xn0)
% 278.31/278.88 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found x70:(cNUMBER Xn0)
% 278.31/278.88 Found x70 as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found x50:=(x5 x40):(cNUMBER Xn0)
% 278.31/278.88 Instantiate: Xn0:=(cS Xx):fofType
% 278.31/278.88 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (fun (x8:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (fun (x8:(cNUMBER Xx))=> (x5 x40)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 278.31/278.88 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found (x9 x80) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (x9 x80) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 278.31/278.88 Found x70:=(x7 x60):(cNUMBER Xn0)
% 278.31/278.88 Instantiate: Xn0:=(cS Xx):fofType
% 278.31/278.88 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found (x7 x60) as proof of (cNUMBER c0)
% 278.31/278.88 Found (x7 x60) as proof of (cNUMBER c0)
% 278.31/278.88 Found (x7 x60) as proof of (cNUMBER c0)
% 278.31/278.88 Found x9:(cODD (cS c0))
% 278.31/278.88 Instantiate: Xn0:=(cS c0):fofType
% 278.31/278.88 Found x9 as proof of (cODD Xn0)
% 278.31/278.88 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found x50:(cNUMBER Xn0)
% 278.31/278.88 Instantiate: Xn0:=c0:fofType
% 278.31/278.88 Found x50 as proof of (cNUMBER c0)
% 278.31/278.88 Found x30:(cNUMBER Xn0)
% 278.31/278.88 Found x30 as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found (x3 x20) as proof of (cNUMBER c0)
% 278.31/278.88 Found (x3 x20) as proof of (cNUMBER c0)
% 278.31/278.88 Found (x3 x20) as proof of (cNUMBER c0)
% 278.31/278.88 Found x70:(cNUMBER Xn0)
% 278.31/278.88 Instantiate: Xn0:=(cS Xx):fofType
% 278.31/278.88 Found x70 as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 278.31/278.88 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Instantiate: Xn0:=Xn:fofType
% 278.31/278.88 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.31/278.88 Found x6:(cNUMBER Xx)
% 278.31/278.88 Instantiate: Xn0:=Xx:fofType
% 278.31/278.88 Found x6 as proof of (cNUMBER Xn0)
% 278.31/278.88 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 278.31/278.88 Instantiate: Xn00:=Xn:fofType
% 278.31/278.88 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.88 Found x30:=(x3 x20):(cNUMBER Xn0)
% 278.31/278.88 Instantiate: Xn0:=Xn:fofType
% 278.31/278.88 Found (x3 x20) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 278.31/278.88 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 280.38/280.92 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 280.38/280.92 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 280.38/280.92 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 280.38/280.92 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 280.38/280.92 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 280.38/280.92 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 280.38/280.92 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.38/280.93 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.38/280.93 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.38/280.93 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.38/280.93 Found (x5 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 280.38/280.93 Found (x5 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 280.38/280.93 Found x50:(cNUMBER Xn0)
% 280.38/280.93 Found x50 as proof of (cNUMBER (cS Xx))
% 280.38/280.93 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 280.38/280.93 Found x70:=(x7 x60):(cNUMBER Xn00)
% 280.38/280.93 Instantiate: Xn00:=Xn:fofType
% 280.38/280.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 280.38/280.93 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 280.38/280.93 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 280.38/280.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 280.38/280.93 Found (x5 x40) as proof of (cNUMBER c0)
% 280.38/280.93 Found (x5 x40) as proof of (cNUMBER c0)
% 280.38/280.93 Found (x5 x40) as proof of (cNUMBER c0)
% 280.38/280.93 Found x50:(cNUMBER Xn0)
% 280.38/280.93 Instantiate: Xn0:=c0:fofType
% 280.38/280.93 Found x50 as proof of (cNUMBER c0)
% 280.38/280.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 280.38/280.93 Instantiate: Xn0:=(cS Xx):fofType
% 280.38/280.93 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 280.38/280.93 Found (fun (x8:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 281.99/282.56 Found x30:=(x3 x20):(cNUMBER Xn0)
% 281.99/282.56 Instantiate: Xn0:=(cS Xx):fofType
% 281.99/282.56 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 281.99/282.56 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 281.99/282.56 Found x70:=(x7 x60):(cNUMBER Xn0)
% 281.99/282.56 Instantiate: Xn0:=Xn:fofType
% 281.99/282.56 Found (x7 x60) as proof of (cNUMBER Xn)
% 281.99/282.56 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 281.99/282.56 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 281.99/282.56 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 281.99/282.56 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 281.99/282.56 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 281.99/282.56 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 281.99/282.56 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 281.99/282.56 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 281.99/282.56 Found x30:(cNUMBER Xn0)
% 281.99/282.56 Instantiate: Xn0:=c0:fofType
% 281.99/282.56 Found x30 as proof of (cNUMBER c0)
% 281.99/282.56 Found x8:(cODD (cS c0))
% 281.99/282.56 Instantiate: Xn0:=(cS c0):fofType
% 281.99/282.56 Found x8 as proof of (cODD Xn0)
% 281.99/282.56 Found (or_intror00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 281.99/282.56 Found ((or_intror0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 281.99/282.56 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 281.99/282.56 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 281.99/282.56 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)) as proof of (cNUMBER Xn0)
% 281.99/282.56 Found (fun (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (cNUMBER Xn0)
% 281.99/282.56 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 281.99/282.56 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 281.99/282.56 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 281.99/282.56 Found ((and_rect4 (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 281.99/282.56 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 283.53/284.08 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 283.53/284.08 Found x50:=(x5 x40):(cNUMBER Xn0)
% 283.53/284.08 Instantiate: Xn0:=c0:fofType
% 283.53/284.08 Found (x5 x40) as proof of (cNUMBER c0)
% 283.53/284.08 Found (x5 x40) as proof of (cNUMBER c0)
% 283.53/284.08 Found x8:(cNUMBER Xx)
% 283.53/284.08 Instantiate: Xn0:=Xx:fofType
% 283.53/284.08 Found x8 as proof of (cNUMBER Xn0)
% 283.53/284.08 Found (x2 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.08 Found (x2 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.08 Found x50:(cNUMBER Xn0)
% 283.53/284.08 Instantiate: Xn0:=c0:fofType
% 283.53/284.08 Found x50 as proof of (cNUMBER c0)
% 283.53/284.08 Found x50:(cNUMBER Xn0)
% 283.53/284.08 Instantiate: Xn0:=(cS Xx):fofType
% 283.53/284.08 Found x50 as proof of (cNUMBER (cS Xx))
% 283.53/284.08 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 283.53/284.08 Found x31:(cNUMBER Xn0)
% 283.53/284.08 Instantiate: Xn0:=Xn:fofType
% 283.53/284.08 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 283.53/284.08 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 283.53/284.08 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 283.53/284.08 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.53/284.08 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.53/284.08 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.53/284.08 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.53/284.08 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 283.53/284.08 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.08 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.08 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.08 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.08 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.53/284.09 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 283.53/284.09 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.09 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.09 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.09 Found (fun (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.10 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cIND->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.53/284.10 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->(cIND->((or (cEVEN Xn0)) (cODD Xn0))))
% 283.53/284.10 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.11 Found ((and_rect2 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.11 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.11 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.53/284.13 Found (x3 (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 283.53/284.13 Found (x3 (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 283.62/284.17 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 283.62/284.17 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.62/284.17 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.62/284.17 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.62/284.17 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.62/284.17 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 283.62/284.17 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.62/284.17 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.62/284.17 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.62/284.17 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.62/284.17 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 283.62/284.17 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 283.62/284.17 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.62/284.17 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.62/284.17 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.62/284.17 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 283.64/284.18 Found (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 283.64/284.18 Found (fun (x5:cIND)=> (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of (cNUMBER Xn0)
% 283.64/284.18 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of (cIND->(cNUMBER Xn0))
% 283.64/284.18 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->(cIND->(cNUMBER Xn0)))
% 283.64/284.19 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 283.64/284.19 Found ((and_rect2 (cNUMBER Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 283.64/284.19 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 285.34/285.89 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->(cIND->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) cIND) P) x4) x0)) (cNUMBER Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:cIND)=> (x3 (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 285.34/285.89 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 285.34/285.89 Instantiate: Xn00:=Xn:fofType
% 285.34/285.89 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.34/285.89 Found x30:=(x3 x20):(cNUMBER Xn0)
% 285.34/285.89 Instantiate: Xn0:=c0:fofType
% 285.34/285.89 Found (x3 x20) as proof of (cNUMBER c0)
% 285.34/285.89 Found (x3 x20) as proof of (cNUMBER c0)
% 285.34/285.89 Found x50:=(x5 x40):(cNUMBER Xn0)
% 285.34/285.89 Instantiate: Xn0:=(cS Xx):fofType
% 285.34/285.89 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 285.34/285.89 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 285.34/285.89 Found x70:=(x7 x60):(cNUMBER Xn0)
% 285.34/285.89 Instantiate: Xn0:=(cS Xx):fofType
% 285.34/285.89 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 285.34/285.89 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 285.34/285.89 Found x9:(cODD (cS c0))
% 285.34/285.89 Instantiate: Xn0:=(cS c0):fofType
% 285.34/285.89 Found x9 as proof of (cODD Xn0)
% 285.34/285.89 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.34/285.89 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.34/285.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.34/285.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.34/285.89 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 285.34/285.89 Found (fun (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 285.34/285.89 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 285.78/286.34 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 285.78/286.34 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 285.78/286.34 Found ((and_rect4 (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 285.78/286.34 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 285.78/286.34 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 285.78/286.34 Found x50:=(x5 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 285.78/286.34 Found (x5 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 285.78/286.34 Found (x5 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 285.78/286.34 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 285.78/286.34 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 285.78/286.34 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0)))) as proof of (cODD Xn0)
% 285.78/286.34 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0)))) as proof of (cODD Xn0)
% 285.78/286.34 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0)))) as proof of (cODD Xn0)
% 285.78/286.34 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0)))) as proof of (cODD Xn0)
% 285.78/286.34 Found (or_intror00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.78/286.34 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.81/286.38 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.81/286.38 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.81/286.38 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 285.81/286.38 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 285.81/286.38 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 285.81/286.38 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 285.81/286.38 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 285.81/286.38 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 285.81/286.38 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 285.81/286.38 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 285.81/286.38 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 285.81/286.38 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 285.81/286.38 Found (or_comm_i00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.81/286.38 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 288.03/288.61 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 288.03/288.61 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 288.03/288.61 Found x4:(cNUMBER Xx)
% 288.03/288.61 Instantiate: Xn0:=Xx:fofType
% 288.03/288.61 Found x4 as proof of (cNUMBER Xn0)
% 288.03/288.61 Found (x5 x4) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 288.03/288.61 Found (x5 x4) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 288.03/288.61 Found x50:=(x5 x40):(cNUMBER Xn0)
% 288.03/288.61 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 288.03/288.61 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 288.03/288.61 Found (fun (x8:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 288.03/288.61 Found x50:(cNUMBER Xn0)
% 288.03/288.61 Instantiate: Xn0:=Xn:fofType
% 288.03/288.61 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 288.03/288.61 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 288.03/288.61 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 288.03/288.61 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))))
% 288.03/288.61 Found x50:(cNUMBER Xn0)
% 288.03/288.61 Instantiate: Xn0:=Xn:fofType
% 288.03/288.61 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 288.03/288.61 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 288.03/288.61 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 288.03/288.61 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))))
% 288.03/288.61 Found ((or_ind00 (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 288.03/288.61 Found (((or_ind0 (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 288.03/288.61 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x40)) (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 288.03/288.61 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x4 x50))) (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 288.03/288.61 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x4 x50))) (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 290.68/291.27 Found x70:(cNUMBER Xn0)
% 290.68/291.27 Instantiate: Xn0:=(cS Xx):fofType
% 290.68/291.27 Found x70 as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found (fun (x8:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found x30:(cNUMBER Xn0)
% 290.68/291.27 Instantiate: Xn0:=(cS Xx):fofType
% 290.68/291.27 Found x30 as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 290.68/291.27 Instantiate: Xn0:=(cS Xx):fofType
% 290.68/291.27 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found x30:(cNUMBER Xn0)
% 290.68/291.27 Instantiate: Xn0:=(cS Xx):fofType
% 290.68/291.27 Found x30 as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found x50:=(x5 x40):(cNUMBER Xn0)
% 290.68/291.27 Instantiate: Xn0:=Xn:fofType
% 290.68/291.27 Found (x5 x40) as proof of (cNUMBER Xn)
% 290.68/291.27 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 290.68/291.27 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 290.68/291.27 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 290.68/291.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 290.68/291.27 Found (x3 x20) as proof of (cNUMBER Xn0)
% 290.68/291.27 Found (x3 x20) as proof of (cNUMBER Xn0)
% 290.68/291.27 Found x30:(cNUMBER Xn0)
% 290.68/291.27 Instantiate: Xn0:=(cS Xx):fofType
% 290.68/291.27 Found x30 as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found (fun (x8:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found x50:=(x5 x40):(cNUMBER Xn0)
% 290.68/291.27 Instantiate: Xn0:=(cS Xx):fofType
% 290.68/291.27 Found (x5 x40) as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found (fun (x8:(cNUMBER Xx))=> (x5 x40)) as proof of (cNUMBER (cS Xx))
% 290.68/291.27 Found x70:=(x7 x60):(cNUMBER Xn0)
% 290.68/291.27 Instantiate: Xn0:=Xn:fofType
% 290.68/291.27 Found (x7 x60) as proof of (cNUMBER Xn)
% 290.68/291.27 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 290.68/291.27 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 290.68/291.27 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 290.68/291.27 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 290.68/291.27 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 290.68/291.27 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 290.68/291.27 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 290.68/291.27 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 290.68/291.27 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 292.82/293.41 Found x50:(cNUMBER Xn0)
% 292.82/293.41 Found x50 as proof of (cNUMBER (cS Xx))
% 292.82/293.41 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 292.82/293.41 Found x70:(cNUMBER Xn0)
% 292.82/293.41 Instantiate: Xn0:=c0:fofType
% 292.82/293.41 Found x70 as proof of (cNUMBER c0)
% 292.82/293.41 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 292.82/293.41 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.82/293.41 Found (x5 x40) as proof of (cNUMBER c0)
% 292.82/293.41 Found (x5 x40) as proof of (cNUMBER c0)
% 292.82/293.41 Found (x5 x40) as proof of (cNUMBER c0)
% 292.82/293.41 Found x70:=(x7 x60):(cNUMBER Xn0)
% 292.82/293.41 Instantiate: Xn0:=c0:fofType
% 292.82/293.41 Found (x7 x60) as proof of (cNUMBER c0)
% 292.82/293.41 Found (x7 x60) as proof of (cNUMBER c0)
% 292.82/293.41 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 292.82/293.41 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.82/293.41 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.82/293.41 Found x50:(cNUMBER Xn0)
% 292.82/293.41 Instantiate: Xn0:=(cS Xx):fofType
% 292.82/293.41 Found x50 as proof of (cNUMBER (cS Xx))
% 292.82/293.41 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 292.82/293.41 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 292.82/293.41 Instantiate: Xn0:=Xn:fofType
% 292.82/293.41 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 292.82/293.41 Found x50:=(x5 x41):(cNUMBER Xn0)
% 292.82/293.41 Instantiate: Xn0:=Xn:fofType
% 292.82/293.41 Found (x5 x41) as proof of (cNUMBER Xn)
% 292.82/293.41 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 292.82/293.41 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 292.82/293.41 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 292.82/293.41 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 292.82/293.41 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 292.82/293.41 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 292.82/293.41 Found (((fun (P:Type) (x6:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 296.43/296.98 Found x50:=(x5 x40):(cNUMBER Xn0)
% 296.43/296.98 Instantiate: Xn0:=c0:fofType
% 296.43/296.98 Found (x5 x40) as proof of (cNUMBER c0)
% 296.43/296.98 Found (x5 x40) as proof of (cNUMBER c0)
% 296.43/296.98 Found x70:=(x7 x60):(cNUMBER Xn0)
% 296.43/296.98 Instantiate: Xn0:=(cS Xx):fofType
% 296.43/296.98 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 296.43/296.98 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 296.43/296.98 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 296.43/296.98 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 296.43/296.98 Instantiate: Xn00:=Xn:fofType
% 296.43/296.98 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.43/296.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 296.43/296.98 Instantiate: Xn0:=Xn:fofType
% 296.43/296.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 296.43/296.98 Found (fun (x7:cIND)=> (x3 x20)) as proof of (cNUMBER Xn)
% 296.43/296.98 Found (fun (x7:cIND)=> (x3 x20)) as proof of (cIND->(cNUMBER Xn))
% 296.43/296.98 Found x50:=(x5 x40):(cNUMBER Xn00)
% 296.43/296.98 Instantiate: Xn00:=Xn:fofType
% 296.43/296.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 296.43/296.98 Found (fun (x7:cIND)=> (x5 x40)) as proof of (cNUMBER Xn)
% 296.43/296.98 Found (fun (x7:cIND)=> (x5 x40)) as proof of (cIND->(cNUMBER Xn))
% 296.43/296.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 296.43/296.98 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.43/296.98 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 296.43/296.98 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 296.43/296.98 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 296.43/296.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 296.43/296.98 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 296.43/296.98 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 296.43/296.98 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 296.43/296.98 Found x6:(cNUMBER Xx)
% 296.43/296.98 Instantiate: Xn0:=Xx:fofType
% 296.43/296.98 Found x6 as proof of (cNUMBER Xn0)
% 296.43/296.98 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 296.43/296.98 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 296.43/296.98 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 296.43/296.98 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 296.43/296.98 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 296.43/296.98 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 296.43/296.98 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.43/296.98 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.43/296.98 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.43/296.98 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.43/296.98 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 296.97/297.56 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 296.97/297.56 Found x60:=(x6 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 296.97/297.56 Found (x6 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 296.97/297.56 Found (x6 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 296.97/297.56 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 296.97/297.56 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 296.97/297.56 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))) as proof of (cODD Xn0)
% 296.97/297.56 Found ((and_rect4 (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))) as proof of (cODD Xn0)
% 296.97/297.56 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))) as proof of (cODD Xn0)
% 296.97/297.56 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))))) as proof of (cODD Xn0)
% 296.97/297.56 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0))
% 296.97/297.56 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0)))
% 296.97/297.56 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))))) as proof of (cODD Xn0)
% 296.97/297.57 Found ((and_rect3 (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))))) as proof of (cODD Xn0)
% 296.97/297.57 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))))) as proof of (cODD Xn0)
% 296.97/297.57 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))))) as proof of (cODD Xn0)
% 296.97/297.57 Found (or_intror00 (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.97/297.57 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 297.27/297.88 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 297.27/297.88 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 297.27/297.88 Found x50:(cNUMBER Xn0)
% 297.27/297.88 Instantiate: Xn0:=c0:fofType
% 297.27/297.88 Found x50 as proof of (cNUMBER c0)
% 297.27/297.88 Found x30:=(x3 x20):(cNUMBER Xn0)
% 297.27/297.88 Found (x3 x20) as proof of (cNUMBER Xn0)
% 297.27/297.88 Found (x3 x20) as proof of (cNUMBER Xn0)
% 297.27/297.88 Found x30:=(x3 x21):(cNUMBER Xn0)
% 297.27/297.88 Instantiate: Xn0:=Xn:fofType
% 297.27/297.88 Found (x3 x21) as proof of (cNUMBER Xn)
% 297.27/297.88 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 297.27/297.88 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 297.27/297.88 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 297.27/297.88 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 297.27/297.88 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 297.27/297.88 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 297.27/297.88 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 298.92/299.47 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 298.92/299.47 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 298.92/299.47 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 298.92/299.47 Found x50:(cNUMBER Xn0)
% 298.92/299.47 Found x50 as proof of (cNUMBER (cS Xx))
% 298.92/299.47 Found (fun (x8:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 298.92/299.47 Found x30:=(x3 x20):(cNUMBER Xn0)
% 298.92/299.47 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 298.92/299.47 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 298.92/299.47 Found (fun (x8:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 298.92/299.47 Found x9:(cODD (cS c0))
% 298.92/299.47 Instantiate: Xn0:=(cS c0):fofType
% 298.92/299.47 Found x9 as proof of (cODD Xn0)
% 298.92/299.47 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found x11:(cEVEN c0)
% 298.92/299.47 Instantiate: Xn0:=c0:fofType
% 298.92/299.47 Found x11 as proof of (cEVEN Xn0)
% 298.92/299.47 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found x60:=(x6 x50):(cNUMBER Xn0)
% 298.92/299.47 Found (x6 x50) as proof of (cNUMBER (cS Xx))
% 298.92/299.47 Found (x6 x50) as proof of (cNUMBER (cS Xx))
% 298.92/299.47 Found (x6 x50) as proof of (cNUMBER (cS Xx))
% 298.92/299.47 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 298.92/299.47 Instantiate: Xn00:=Xn:fofType
% 298.92/299.47 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.92/299.47 Found x50:(cNUMBER Xn0)
% 298.92/299.47 Instantiate: Xn0:=c0:fofType
% 298.92/299.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER c0)
% 299.53/300.11 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER c0))
% 299.53/300.11 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER c0)))
% 299.53/300.11 Found x70:=(x7 x60):(cNUMBER Xn0)
% 299.53/300.11 Instantiate: Xn0:=(cS Xx):fofType
% 299.53/300.11 Found (x7 x60) as proof of (cNUMBER (cS Xx))
% 299.53/300.11 Found (fun (x8:(cNUMBER Xx))=> (x7 x60)) as proof of (cNUMBER (cS Xx))
% 299.53/300.11 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 299.53/300.11 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 299.53/300.11 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 299.53/300.11 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 299.53/300.11 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 299.53/300.11 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 299.53/300.11 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.53/300.11 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.53/300.11 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.53/300.11 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.53/300.11 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0)))
% 299.53/300.11 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0))))
% 299.53/300.12 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.53/300.12 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.53/300.12 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.53/300.12 Found (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.58/300.13 Found (or_comm_i00 (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.58/300.13 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.58/300.13 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.58/300.13 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType
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