TSTP Solution File: ITP019^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP019^2 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% DateTime : Sun Mar 21 13:23:49 EDT 2021
% Result : Timeout 289.36s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ITP019^2 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.10/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 19 01:56:58 EDT 2021
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.47/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.47/0.62 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/ITP001/ITP001^2.ax, trying next directory
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2adf73c2ecb0>, <kernel.Type object at 0x2adf73c2eb48>) of role type named del_tp
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring del:Type
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x1660ef0>, <kernel.Constant object at 0x2adf73c2ebd8>) of role type named bool
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring bool:del
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2adf73c2ea70>, <kernel.Constant object at 0x2adf73c2ebd8>) of role type named ind
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring ind:del
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2adf73c2ecb0>, <kernel.DependentProduct object at 0x2adf73c2e9e0>) of role type named arr
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring arr:(del->(del->del))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2adf73c2ea28>, <kernel.DependentProduct object at 0x2adf73c2e9e0>) of role type named mem
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring mem:(fofType->(del->Prop))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2adf73c2ea70>, <kernel.DependentProduct object at 0x2adf73c2ecb0>) of role type named ap
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring ap:(fofType->(fofType->fofType))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2adf73c2e8c0>, <kernel.DependentProduct object at 0x2adf73c2e7e8>) of role type named lam
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring lam:(del->((fofType->fofType)->fofType))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2adf73c2eab8>, <kernel.DependentProduct object at 0x2adf73c2e9e0>) of role type named p
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring p:(fofType->Prop)
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x2adf73c2ecb0>, <kernel.DependentProduct object at 0x2adf73c2e950>) of role type named stp_inj_o
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring inj__o:(Prop->fofType)
% 0.47/0.62 FOF formula (forall (X:Prop), (((eq Prop) (p (inj__o X))) X)) of role axiom named stp_inj_surj_o
% 0.47/0.62 A new axiom: (forall (X:Prop), (((eq Prop) (p (inj__o X))) X))
% 0.47/0.62 FOF formula (forall (X:Prop), ((mem (inj__o X)) bool)) of role axiom named stp_inj_mem_o
% 0.47/0.62 A new axiom: (forall (X:Prop), ((mem (inj__o X)) bool))
% 0.47/0.62 FOF formula (forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X))))) of role axiom named stp_iso_mem_o
% 0.47/0.62 A new axiom: (forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X)))))
% 0.47/0.62 FOF formula (forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (X:fofType), (((mem X) A)->((mem ((ap F) X)) B))))) of role axiom named ap_tp
% 0.47/0.62 A new axiom: (forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (X:fofType), (((mem X) A)->((mem ((ap F) X)) B)))))
% 0.47/0.62 FOF formula (forall (A:del) (B:del) (F:(fofType->fofType)), ((forall (X:fofType), (((mem X) A)->((mem (F X)) B)))->((mem ((lam A) F)) ((arr A) B)))) of role axiom named lam_tp
% 0.47/0.62 A new axiom: (forall (A:del) (B:del) (F:(fofType->fofType)), ((forall (X:fofType), (((mem X) A)->((mem (F X)) B)))->((mem ((lam A) F)) ((arr A) B))))
% 0.47/0.62 FOF formula (forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (G:fofType), (((mem G) ((arr A) B))->((forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap G) X))))->(((eq fofType) F) G)))))) of role axiom named funcext
% 0.47/0.62 A new axiom: (forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (G:fofType), (((mem G) ((arr A) B))->((forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap G) X))))->(((eq fofType) F) G))))))
% 0.47/0.62 FOF formula (forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X)))) of role axiom named beta
% 0.47/0.62 A new axiom: (forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X))))
% 0.47/0.62 FOF formula (<kernel.Constant object at 0x165c5a8>, <kernel.Single object at 0x165cbd8>) of role type named tp_c_2Ebool_2E_7E
% 0.47/0.62 Using role type
% 0.47/0.62 Declaring c_2Ebool_2E_7E:fofType
% 0.47/0.62 FOF formula ((mem c_2Ebool_2E_7E) ((arr bool) bool)) of role axiom named mem_c_2Ebool_2E_7E
% 0.47/0.62 A new axiom: ((mem c_2Ebool_2E_7E) ((arr bool) bool))
% 0.47/0.62 FOF formula (forall (Q:fofType), (((mem Q) bool)->((iff (p ((ap c_2Ebool_2E_7E) Q))) ((p Q)->False)))) of role axiom named ax_neg_p
% 0.47/0.63 A new axiom: (forall (Q:fofType), (((mem Q) bool)->((iff (p ((ap c_2Ebool_2E_7E) Q))) ((p Q)->False))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x165cc20>, <kernel.Single object at 0x2adf7b6ff098>) of role type named tp_c_2Ebool_2EF
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Ebool_2EF:fofType
% 0.47/0.63 FOF formula ((mem c_2Ebool_2EF) bool) of role axiom named mem_c_2Ebool_2EF
% 0.47/0.63 A new axiom: ((mem c_2Ebool_2EF) bool)
% 0.47/0.63 FOF formula ((p c_2Ebool_2EF)->False) of role axiom named ax_false_p
% 0.47/0.63 A new axiom: ((p c_2Ebool_2EF)->False)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6ff098>, <kernel.Single object at 0x2adf7b6ffd88>) of role type named tp_c_2Ebool_2ET
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Ebool_2ET:fofType
% 0.47/0.63 FOF formula ((mem c_2Ebool_2ET) bool) of role axiom named mem_c_2Ebool_2ET
% 0.47/0.63 A new axiom: ((mem c_2Ebool_2ET) bool)
% 0.47/0.63 FOF formula (p c_2Ebool_2ET) of role axiom named ax_true_p
% 0.47/0.63 A new axiom: (p c_2Ebool_2ET)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6ff098>, <kernel.Single object at 0x2adf7b6ffb48>) of role type named tp_c_2Emin_2E_3D_3D_3E
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Emin_2E_3D_3D_3E:fofType
% 0.47/0.63 FOF formula ((mem c_2Emin_2E_3D_3D_3E) ((arr bool) ((arr bool) bool))) of role axiom named mem_c_2Emin_2E_3D_3D_3E
% 0.47/0.63 A new axiom: ((mem c_2Emin_2E_3D_3D_3E) ((arr bool) ((arr bool) bool)))
% 0.47/0.63 FOF formula (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Emin_2E_3D_3D_3E) Q)) R))) ((p Q)->(p R))))))) of role axiom named ax_imp_p
% 0.47/0.63 A new axiom: (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Emin_2E_3D_3D_3E) Q)) R))) ((p Q)->(p R)))))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6dda28>, <kernel.Single object at 0x2adf7b6ffd88>) of role type named tp_c_2Ebool_2E_2F_5C
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring c_2Ebool_2E_2F_5C:fofType
% 0.47/0.63 FOF formula ((mem c_2Ebool_2E_2F_5C) ((arr bool) ((arr bool) bool))) of role axiom named mem_c_2Ebool_2E_2F_5C
% 0.47/0.63 A new axiom: ((mem c_2Ebool_2E_2F_5C) ((arr bool) ((arr bool) bool)))
% 0.47/0.63 FOF formula (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_2F_5C) Q)) R))) ((and (p Q)) (p R))))))) of role axiom named ax_and_p
% 0.47/0.63 A new axiom: (forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_2F_5C) Q)) R))) ((and (p Q)) (p R)))))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6e43f8>, <kernel.Constant object at 0x2adf7b6ffb48>) of role type named tp_ty_2Enum_2Enum
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring ty_2Enum_2Enum:del
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6ff098>, <kernel.Type object at 0x2adf7b6fc9e0>) of role type named stp_ty_2Enum_2Enum
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring tp__ty_2Enum_2Enum:Type
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6ffc20>, <kernel.DependentProduct object at 0x2adf73c2ecf8>) of role type named stp_inj_ty_2Enum_2Enum
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring inj__ty_2Enum_2Enum:(tp__ty_2Enum_2Enum->fofType)
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6ff488>, <kernel.DependentProduct object at 0x2adf73c2eb90>) of role type named stp_surj_ty_2Enum_2Enum
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring surj__ty_2Enum_2Enum:(fofType->tp__ty_2Enum_2Enum)
% 0.47/0.63 FOF formula (forall (X:tp__ty_2Enum_2Enum), (((eq tp__ty_2Enum_2Enum) (surj__ty_2Enum_2Enum (inj__ty_2Enum_2Enum X))) X)) of role axiom named stp_inj_surj_ty_2Enum_2Enum
% 0.47/0.63 A new axiom: (forall (X:tp__ty_2Enum_2Enum), (((eq tp__ty_2Enum_2Enum) (surj__ty_2Enum_2Enum (inj__ty_2Enum_2Enum X))) X))
% 0.47/0.63 FOF formula (forall (X:tp__ty_2Enum_2Enum), ((mem (inj__ty_2Enum_2Enum X)) ty_2Enum_2Enum)) of role axiom named stp_inj_mem_ty_2Enum_2Enum
% 0.47/0.63 A new axiom: (forall (X:tp__ty_2Enum_2Enum), ((mem (inj__ty_2Enum_2Enum X)) ty_2Enum_2Enum))
% 0.47/0.63 FOF formula (forall (X:fofType), (((mem X) ty_2Enum_2Enum)->(((eq fofType) X) (inj__ty_2Enum_2Enum (surj__ty_2Enum_2Enum X))))) of role axiom named stp_iso_mem_ty_2Enum_2Enum
% 0.47/0.63 A new axiom: (forall (X:fofType), (((mem X) ty_2Enum_2Enum)->(((eq fofType) X) (inj__ty_2Enum_2Enum (surj__ty_2Enum_2Enum X)))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6fca70>, <kernel.Single object at 0x2adf7b6fcc68>) of role type named tp_c_2Enum_2E0
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Enum_2E0:fofType
% 0.48/0.63 FOF formula ((mem c_2Enum_2E0) ty_2Enum_2Enum) of role axiom named mem_c_2Enum_2E0
% 0.48/0.63 A new axiom: ((mem c_2Enum_2E0) ty_2Enum_2Enum)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6fcc68>, <kernel.Constant object at 0x2adf73c2efc8>) of role type named stp_fo_c_2Enum_2E0
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring fo__c_2Enum_2E0:tp__ty_2Enum_2Enum
% 0.48/0.63 FOF formula (((eq fofType) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)) c_2Enum_2E0) of role axiom named stp_eq_fo_c_2Enum_2E0
% 0.48/0.63 A new axiom: (((eq fofType) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)) c_2Enum_2E0)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6fcab8>, <kernel.Constant object at 0x2adf73c2eb48>) of role type named tp_ty_2Erealax_2Ereal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring ty_2Erealax_2Ereal:del
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf7b6fcab8>, <kernel.Type object at 0x2adf73c2eb90>) of role type named stp_ty_2Erealax_2Ereal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring tp__ty_2Erealax_2Ereal:Type
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf73c2edd0>, <kernel.DependentProduct object at 0x2adf73c2e098>) of role type named stp_inj_ty_2Erealax_2Ereal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring inj__ty_2Erealax_2Ereal:(tp__ty_2Erealax_2Ereal->fofType)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf73c2ed40>, <kernel.DependentProduct object at 0x2adf73c2ed88>) of role type named stp_surj_ty_2Erealax_2Ereal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring surj__ty_2Erealax_2Ereal:(fofType->tp__ty_2Erealax_2Ereal)
% 0.48/0.63 FOF formula (forall (X:tp__ty_2Erealax_2Ereal), (((eq tp__ty_2Erealax_2Ereal) (surj__ty_2Erealax_2Ereal (inj__ty_2Erealax_2Ereal X))) X)) of role axiom named stp_inj_surj_ty_2Erealax_2Ereal
% 0.48/0.63 A new axiom: (forall (X:tp__ty_2Erealax_2Ereal), (((eq tp__ty_2Erealax_2Ereal) (surj__ty_2Erealax_2Ereal (inj__ty_2Erealax_2Ereal X))) X))
% 0.48/0.63 FOF formula (forall (X:tp__ty_2Erealax_2Ereal), ((mem (inj__ty_2Erealax_2Ereal X)) ty_2Erealax_2Ereal)) of role axiom named stp_inj_mem_ty_2Erealax_2Ereal
% 0.48/0.63 A new axiom: (forall (X:tp__ty_2Erealax_2Ereal), ((mem (inj__ty_2Erealax_2Ereal X)) ty_2Erealax_2Ereal))
% 0.48/0.63 FOF formula (forall (X:fofType), (((mem X) ty_2Erealax_2Ereal)->(((eq fofType) X) (inj__ty_2Erealax_2Ereal (surj__ty_2Erealax_2Ereal X))))) of role axiom named stp_iso_mem_ty_2Erealax_2Ereal
% 0.48/0.63 A new axiom: (forall (X:fofType), (((mem X) ty_2Erealax_2Ereal)->(((eq fofType) X) (inj__ty_2Erealax_2Ereal (surj__ty_2Erealax_2Ereal X)))))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf73c2eea8>, <kernel.DependentProduct object at 0x2adf73c2e488>) of role type named tp_ty_2Epair_2Eprod
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring ty_2Epair_2Eprod:(del->(del->del))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf73c2ea70>, <kernel.Type object at 0x2adf73c2ef38>) of role type named stp_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:Type
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf73c2ee60>, <kernel.DependentProduct object at 0x2adf73c2edd0>) of role type named stp_inj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal->fofType)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2adf73c2e0e0>, <kernel.DependentProduct object at 0x2adf73c2e7e8>) of role type named stp_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:(fofType->tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)
% 0.48/0.63 FOF formula (forall (X:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X))) X)) of role axiom named stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 0.48/0.63 A new axiom: (forall (X:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X))) X))
% 0.48/0.64 FOF formula (forall (X:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X)) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))) of role axiom named stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 0.48/0.64 A new axiom: (forall (X:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X)) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal)))
% 0.48/0.64 FOF formula (forall (X:fofType), (((mem X) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))->(((eq fofType) X) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X))))) of role axiom named stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 0.48/0.64 A new axiom: (forall (X:fofType), (((mem X) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))->(((eq fofType) X) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X)))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2adf73c2e7e8>, <kernel.Single object at 0x2adf73c2ea70>) of role type named tp_c_2Ecomplex_2Ecomplex__of__num
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_2Ecomplex_2Ecomplex__of__num:fofType
% 0.48/0.64 FOF formula ((mem c_2Ecomplex_2Ecomplex__of__num) ((arr ty_2Enum_2Enum) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))) of role axiom named mem_c_2Ecomplex_2Ecomplex__of__num
% 0.48/0.64 A new axiom: ((mem c_2Ecomplex_2Ecomplex__of__num) ((arr ty_2Enum_2Enum) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal)))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2adf73c2eb00>, <kernel.Single object at 0x2adf73c2e050>) of role type named tp_c_2Ecomplex_2Ecomplex__inv
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_2Ecomplex_2Ecomplex__inv:fofType
% 0.48/0.64 FOF formula ((mem c_2Ecomplex_2Ecomplex__inv) ((arr ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal)) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))) of role axiom named mem_c_2Ecomplex_2Ecomplex__inv
% 0.48/0.64 A new axiom: ((mem c_2Ecomplex_2Ecomplex__inv) ((arr ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal)) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal)))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2adf73c2ea70>, <kernel.DependentProduct object at 0x2adf73c2eb00>) of role type named tp_c_2Emin_2E_3D
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_2Emin_2E_3D:(del->fofType)
% 0.48/0.64 FOF formula (forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool)))) of role axiom named mem_c_2Emin_2E_3D
% 0.48/0.64 A new axiom: (forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool))))
% 0.48/0.64 FOF formula (forall (A:del) (X:fofType), (((mem X) A)->(forall (Y:fofType), (((mem Y) A)->((iff (p ((ap ((ap (c_2Emin_2E_3D A)) X)) Y))) (((eq fofType) X) Y)))))) of role axiom named ax_eq_p
% 0.48/0.64 A new axiom: (forall (A:del) (X:fofType), (((mem X) A)->(forall (Y:fofType), (((mem Y) A)->((iff (p ((ap ((ap (c_2Emin_2E_3D A)) X)) Y))) (((eq fofType) X) Y))))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2adf73c2e1b8>, <kernel.DependentProduct object at 0x2adf73c2e638>) of role type named tp_c_2Ebool_2E_21
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_2Ebool_2E_21:(del->fofType)
% 0.48/0.64 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool))) of role axiom named mem_c_2Ebool_2E_21
% 0.48/0.64 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool)))
% 0.48/0.64 FOF formula (forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_21 A)) Q))) (forall (X:fofType), (((mem X) A)->(p ((ap Q) X))))))) of role axiom named ax_all_p
% 0.48/0.64 A new axiom: (forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_21 A)) Q))) (forall (X:fofType), (((mem X) A)->(p ((ap Q) X)))))))
% 0.48/0.64 FOF formula True of role axiom named conj_thm_2Ebool_2ETRUTH
% 0.48/0.65 A new axiom: True
% 0.48/0.65 FOF formula (forall (A_27a:del) (V0t:fofType), (((mem V0t) bool)->((iff (forall (V1x:fofType), (((mem V1x) A_27a)->(p V0t)))) (p V0t)))) of role axiom named conj_thm_2Ebool_2EFORALL__SIMP
% 0.48/0.65 A new axiom: (forall (A_27a:del) (V0t:fofType), (((mem V0t) bool)->((iff (forall (V1x:fofType), (((mem V1x) A_27a)->(p V0t)))) (p V0t))))
% 0.48/0.65 FOF formula (forall (V0t:fofType), (((mem V0t) bool)->((and ((and ((and ((and ((iff (True->(p V0t))) (p V0t))) ((iff ((p V0t)->True)) True))) ((iff (False->(p V0t))) True))) ((iff ((p V0t)->(p V0t))) True))) ((iff ((p V0t)->False)) ((p V0t)->False))))) of role axiom named conj_thm_2Ebool_2EIMP__CLAUSES
% 0.48/0.65 A new axiom: (forall (V0t:fofType), (((mem V0t) bool)->((and ((and ((and ((and ((iff (True->(p V0t))) (p V0t))) ((iff ((p V0t)->True)) True))) ((iff (False->(p V0t))) True))) ((iff ((p V0t)->(p V0t))) True))) ((iff ((p V0t)->False)) ((p V0t)->False)))))
% 0.48/0.65 FOF formula (forall (V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((iff (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))) (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) of role axiom named conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0
% 0.48/0.65 A new axiom: (forall (V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((iff (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))) (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))))
% 0.48/0.65 FOF formula (forall (V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((not (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))->(not (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))))) of role conjecture named conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ
% 0.48/0.65 Conjecture to prove = (forall (V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((not (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))->(not (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))))):Prop
% 0.48/0.65 Parameter tp__ty_2Erealax_2Ereal_DUMMY:tp__ty_2Erealax_2Ereal.
% 0.48/0.65 Parameter tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal_DUMMY:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal.
% 0.48/0.65 We need to prove ['(forall (V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((not (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))->(not (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))']
% 0.48/0.65 Parameter del:Type.
% 0.48/0.65 Parameter bool:del.
% 0.48/0.65 Parameter ind:del.
% 0.48/0.65 Parameter arr:(del->(del->del)).
% 0.48/0.65 Parameter fofType:Type.
% 0.48/0.65 Parameter mem:(fofType->(del->Prop)).
% 0.48/0.65 Parameter ap:(fofType->(fofType->fofType)).
% 0.48/0.65 Parameter lam:(del->((fofType->fofType)->fofType)).
% 0.48/0.65 Parameter p:(fofType->Prop).
% 0.48/0.65 Parameter inj__o:(Prop->fofType).
% 0.48/0.65 Axiom stp_inj_surj_o:(forall (X:Prop), (((eq Prop) (p (inj__o X))) X)).
% 0.48/0.65 Axiom stp_inj_mem_o:(forall (X:Prop), ((mem (inj__o X)) bool)).
% 0.48/0.65 Axiom stp_iso_mem_o:(forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X))))).
% 0.48/0.65 Axiom ap_tp:(forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (X:fofType), (((mem X) A)->((mem ((ap F) X)) B))))).
% 0.48/0.65 Axiom lam_tp:(forall (A:del) (B:del) (F:(fofType->fofType)), ((forall (X:fofType), (((mem X) A)->((mem (F X)) B)))->((mem ((lam A) F)) ((arr A) B)))).
% 0.48/0.65 Axiom funcext:(forall (A:del) (B:del) (F:fofType), (((mem F) ((arr A) B))->(forall (G:fofType), (((mem G) ((arr A) B))->((forall (X:fofType), (((mem X) A)->(((eq fofType) ((ap F) X)) ((ap G) X))))->(((eq fofType) F) G)))))).
% 0.48/0.65 Axiom beta:(forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X)))).
% 0.48/0.65 Parameter c_2Ebool_2E_7E:fofType.
% 0.48/0.65 Axiom mem_c_2Ebool_2E_7E:((mem c_2Ebool_2E_7E) ((arr bool) bool)).
% 0.48/0.65 Axiom ax_neg_p:(forall (Q:fofType), (((mem Q) bool)->((iff (p ((ap c_2Ebool_2E_7E) Q))) ((p Q)->False)))).
% 0.48/0.65 Parameter c_2Ebool_2EF:fofType.
% 0.48/0.65 Axiom mem_c_2Ebool_2EF:((mem c_2Ebool_2EF) bool).
% 0.48/0.65 Axiom ax_false_p:((p c_2Ebool_2EF)->False).
% 0.48/0.65 Parameter c_2Ebool_2ET:fofType.
% 0.48/0.65 Axiom mem_c_2Ebool_2ET:((mem c_2Ebool_2ET) bool).
% 0.48/0.65 Axiom ax_true_p:(p c_2Ebool_2ET).
% 0.48/0.65 Parameter c_2Emin_2E_3D_3D_3E:fofType.
% 0.48/0.65 Axiom mem_c_2Emin_2E_3D_3D_3E:((mem c_2Emin_2E_3D_3D_3E) ((arr bool) ((arr bool) bool))).
% 0.48/0.65 Axiom ax_imp_p:(forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Emin_2E_3D_3D_3E) Q)) R))) ((p Q)->(p R))))))).
% 0.48/0.65 Parameter c_2Ebool_2E_2F_5C:fofType.
% 0.48/0.65 Axiom mem_c_2Ebool_2E_2F_5C:((mem c_2Ebool_2E_2F_5C) ((arr bool) ((arr bool) bool))).
% 0.48/0.65 Axiom ax_and_p:(forall (Q:fofType), (((mem Q) bool)->(forall (R:fofType), (((mem R) bool)->((iff (p ((ap ((ap c_2Ebool_2E_2F_5C) Q)) R))) ((and (p Q)) (p R))))))).
% 0.48/0.65 Parameter ty_2Enum_2Enum:del.
% 0.48/0.65 Parameter tp__ty_2Enum_2Enum:Type.
% 0.48/0.65 Parameter inj__ty_2Enum_2Enum:(tp__ty_2Enum_2Enum->fofType).
% 0.48/0.65 Parameter surj__ty_2Enum_2Enum:(fofType->tp__ty_2Enum_2Enum).
% 0.48/0.65 Axiom stp_inj_surj_ty_2Enum_2Enum:(forall (X:tp__ty_2Enum_2Enum), (((eq tp__ty_2Enum_2Enum) (surj__ty_2Enum_2Enum (inj__ty_2Enum_2Enum X))) X)).
% 0.48/0.65 Axiom stp_inj_mem_ty_2Enum_2Enum:(forall (X:tp__ty_2Enum_2Enum), ((mem (inj__ty_2Enum_2Enum X)) ty_2Enum_2Enum)).
% 0.48/0.65 Axiom stp_iso_mem_ty_2Enum_2Enum:(forall (X:fofType), (((mem X) ty_2Enum_2Enum)->(((eq fofType) X) (inj__ty_2Enum_2Enum (surj__ty_2Enum_2Enum X))))).
% 0.48/0.65 Parameter c_2Enum_2E0:fofType.
% 0.48/0.65 Axiom mem_c_2Enum_2E0:((mem c_2Enum_2E0) ty_2Enum_2Enum).
% 0.48/0.65 Parameter fo__c_2Enum_2E0:tp__ty_2Enum_2Enum.
% 0.48/0.65 Axiom stp_eq_fo_c_2Enum_2E0:(((eq fofType) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)) c_2Enum_2E0).
% 0.48/0.65 Parameter ty_2Erealax_2Ereal:del.
% 0.48/0.65 Parameter tp__ty_2Erealax_2Ereal:Type.
% 0.48/0.65 Parameter inj__ty_2Erealax_2Ereal:(tp__ty_2Erealax_2Ereal->fofType).
% 0.48/0.65 Parameter surj__ty_2Erealax_2Ereal:(fofType->tp__ty_2Erealax_2Ereal).
% 0.48/0.65 Axiom stp_inj_surj_ty_2Erealax_2Ereal:(forall (X:tp__ty_2Erealax_2Ereal), (((eq tp__ty_2Erealax_2Ereal) (surj__ty_2Erealax_2Ereal (inj__ty_2Erealax_2Ereal X))) X)).
% 0.48/0.65 Axiom stp_inj_mem_ty_2Erealax_2Ereal:(forall (X:tp__ty_2Erealax_2Ereal), ((mem (inj__ty_2Erealax_2Ereal X)) ty_2Erealax_2Ereal)).
% 0.48/0.66 Axiom stp_iso_mem_ty_2Erealax_2Ereal:(forall (X:fofType), (((mem X) ty_2Erealax_2Ereal)->(((eq fofType) X) (inj__ty_2Erealax_2Ereal (surj__ty_2Erealax_2Ereal X))))).
% 0.48/0.66 Parameter ty_2Epair_2Eprod:(del->(del->del)).
% 0.48/0.66 Parameter tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:Type.
% 0.48/0.66 Parameter inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal->fofType).
% 0.48/0.66 Parameter surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:(fofType->tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal).
% 0.48/0.66 Axiom stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:(forall (X:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X))) X)).
% 0.48/0.66 Axiom stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:(forall (X:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X)) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))).
% 0.48/0.66 Axiom stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal:(forall (X:fofType), (((mem X) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))->(((eq fofType) X) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal X))))).
% 0.48/0.66 Parameter c_2Ecomplex_2Ecomplex__of__num:fofType.
% 0.48/0.66 Axiom mem_c_2Ecomplex_2Ecomplex__of__num:((mem c_2Ecomplex_2Ecomplex__of__num) ((arr ty_2Enum_2Enum) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))).
% 0.48/0.66 Parameter c_2Ecomplex_2Ecomplex__inv:fofType.
% 0.48/0.66 Axiom mem_c_2Ecomplex_2Ecomplex__inv:((mem c_2Ecomplex_2Ecomplex__inv) ((arr ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal)) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))).
% 0.48/0.66 Parameter c_2Emin_2E_3D:(del->fofType).
% 0.48/0.66 Axiom mem_c_2Emin_2E_3D:(forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool)))).
% 0.48/0.66 Axiom ax_eq_p:(forall (A:del) (X:fofType), (((mem X) A)->(forall (Y:fofType), (((mem Y) A)->((iff (p ((ap ((ap (c_2Emin_2E_3D A)) X)) Y))) (((eq fofType) X) Y)))))).
% 0.48/0.66 Parameter c_2Ebool_2E_21:(del->fofType).
% 0.48/0.66 Axiom mem_c_2Ebool_2E_21:(forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool))).
% 0.48/0.66 Axiom ax_all_p:(forall (A:del) (Q:fofType), (((mem Q) ((arr A) bool))->((iff (p ((ap (c_2Ebool_2E_21 A)) Q))) (forall (X:fofType), (((mem X) A)->(p ((ap Q) X))))))).
% 0.48/0.66 Axiom conj_thm_2Ebool_2ETRUTH:True.
% 0.48/0.66 Axiom conj_thm_2Ebool_2EFORALL__SIMP:(forall (A_27a:del) (V0t:fofType), (((mem V0t) bool)->((iff (forall (V1x:fofType), (((mem V1x) A_27a)->(p V0t)))) (p V0t)))).
% 0.48/0.66 Axiom conj_thm_2Ebool_2EIMP__CLAUSES:(forall (V0t:fofType), (((mem V0t) bool)->((and ((and ((and ((and ((iff (True->(p V0t))) (p V0t))) ((iff ((p V0t)->True)) True))) ((iff (False->(p V0t))) True))) ((iff ((p V0t)->(p V0t))) True))) ((iff ((p V0t)->False)) ((p V0t)->False))))).
% 0.48/0.66 Axiom conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0:(forall (V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((iff (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))) (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))).
% 0.48/0.66 Trying to prove (forall (V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal), ((not (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))->(not (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))
% 5.52/5.68 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 5.52/5.68 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 5.52/5.68 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 5.52/5.68 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 5.52/5.68 Found (eq_ref00 P) as proof of (P0 V0z)
% 5.52/5.68 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 5.52/5.68 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 5.52/5.68 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 5.52/5.68 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 5.52/5.68 Found (eq_ref00 P) as proof of (P0 V0z)
% 5.52/5.68 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 5.52/5.68 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 5.52/5.68 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 5.52/5.68 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 5.52/5.68 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 5.52/5.68 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 5.52/5.68 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 5.52/5.68 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 5.52/5.68 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 5.52/5.68 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 5.52/5.68 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 5.52/5.68 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 5.52/5.68 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 13.08/13.24 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 13.08/13.24 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 13.08/13.24 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 13.08/13.24 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 13.08/13.24 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 13.08/13.24 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 13.08/13.24 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 13.08/13.24 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 13.08/13.24 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 13.08/13.24 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 13.08/13.24 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 13.08/13.24 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 13.08/13.24 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 13.08/13.24 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 13.08/13.24 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 16.68/16.88 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 16.68/16.88 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 16.68/16.88 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 16.68/16.88 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 16.68/16.88 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 16.68/16.88 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 16.68/16.88 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 16.68/16.88 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 16.68/16.88 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 16.68/16.88 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 16.68/16.88 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 16.68/16.88 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 18.64/18.80 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 18.64/18.80 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 18.64/18.80 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 18.64/18.80 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 18.64/18.80 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 18.64/18.80 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 18.64/18.80 Found x1:(P V0z)
% 18.64/18.80 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 18.64/18.80 Found x1 as proof of (P0 b)
% 18.64/18.80 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 18.64/18.80 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 18.64/18.80 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 19.93/20.10 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 19.93/20.10 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 19.93/20.10 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 19.93/20.10 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 19.93/20.10 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 19.93/20.10 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 19.93/20.10 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 19.93/20.10 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 19.93/20.10 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 19.93/20.10 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 24.34/24.52 Found x10:(P V0z)
% 24.34/24.52 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 24.34/24.52 Found x10 as proof of (P0 b)
% 24.34/24.52 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 24.34/24.52 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 24.34/24.52 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 24.34/24.52 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 24.34/24.52 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 24.34/24.52 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 24.34/24.52 Found x1:(P V0z)
% 24.34/24.52 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 24.34/24.52 Found x1 as proof of (P0 b)
% 24.34/24.52 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 24.34/24.52 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 24.34/24.52 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 24.34/24.52 Found x1:(P V0z)
% 24.34/24.52 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 24.34/24.52 Found x1 as proof of (P0 b)
% 24.34/24.52 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 24.34/24.52 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 24.34/24.52 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 24.34/24.52 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 29.99/30.22 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 29.99/30.22 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 29.99/30.22 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 29.99/30.22 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 29.99/30.22 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 29.99/30.22 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 29.99/30.22 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 29.99/30.22 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 29.99/30.22 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 29.99/30.22 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 29.99/30.22 Found (eq_ref0 b) as proof of (P b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 29.99/30.22 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 29.99/30.22 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 29.99/30.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 35.67/35.89 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 35.67/35.89 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 35.67/35.89 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 35.67/35.89 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 35.67/35.89 Found x1 as proof of (P0 b)
% 35.67/35.89 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 35.67/35.89 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 35.67/35.89 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 35.67/35.89 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 35.67/35.89 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 35.67/35.89 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 35.67/35.89 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 35.67/35.89 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 35.67/35.89 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 35.67/35.89 Found (eq_ref0 b) as proof of (P b)
% 35.67/35.89 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 35.67/35.89 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 35.67/35.89 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 35.67/35.89 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 35.67/35.89 Found (eq_ref00 P) as proof of (P0 V0z)
% 35.67/35.89 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 35.67/35.89 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 35.67/35.89 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 35.67/35.89 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 35.67/35.89 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 36.82/37.04 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 36.82/37.04 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 36.82/37.04 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 36.82/37.04 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 36.82/37.04 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 36.82/37.04 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 36.82/37.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 36.82/37.04 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 36.82/37.04 Found (eq_ref00 P) as proof of (P0 V0z)
% 36.82/37.04 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 37.58/37.76 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 37.58/37.76 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 37.58/37.76 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 37.58/37.76 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 37.58/37.76 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 37.58/37.76 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 37.58/37.76 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 37.58/37.76 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 37.58/37.76 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 37.58/37.76 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 37.58/37.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 41.01/41.18 Found x1:(P V0z)
% 41.01/41.18 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 41.01/41.18 Found x1 as proof of (P0 b)
% 41.01/41.18 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 41.01/41.18 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 41.01/41.18 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) b)
% 41.01/41.18 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 41.01/41.18 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 41.01/41.18 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) b)
% 41.01/41.18 Found x1:(P V0z)
% 41.01/41.18 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 41.01/41.18 Found x1 as proof of (P0 b)
% 41.01/41.18 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 41.01/41.18 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 47.75/47.95 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 47.75/47.95 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 47.75/47.95 Found x1 as proof of (P0 b)
% 47.75/47.95 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 47.75/47.95 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 47.75/47.95 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 47.75/47.95 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 47.75/47.95 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 47.75/47.95 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 47.75/47.95 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 47.75/47.95 Found x1 as proof of (P0 b)
% 47.75/47.95 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 47.75/47.95 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 47.75/47.95 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 47.75/47.95 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 47.75/47.95 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 47.75/47.95 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 47.75/47.95 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 47.75/47.95 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 47.75/47.95 Found (eq_ref0 a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))
% 47.75/47.95 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))
% 47.75/47.95 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))
% 47.75/47.95 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))
% 47.75/47.95 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 52.05/52.25 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 52.05/52.25 Found x1:(P V0z)
% 52.05/52.25 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 52.05/52.25 Found x1 as proof of (P0 b)
% 52.05/52.25 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 52.05/52.25 Found (stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) b)
% 52.05/52.25 Found (stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) b)
% 52.05/52.25 Found (stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) b)
% 52.05/52.25 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 52.05/52.25 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 52.05/52.25 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 55.75/55.92 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 55.75/55.92 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 55.75/55.92 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 55.75/55.92 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 55.75/55.92 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 55.75/55.92 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 55.75/55.92 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 55.75/55.92 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 55.75/55.92 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 55.75/55.92 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))):((P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))->(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))
% 55.75/55.92 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) as proof of (P0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 55.75/55.92 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) as proof of (P0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 56.85/57.06 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 56.85/57.06 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 56.85/57.06 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 56.85/57.06 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 56.85/57.06 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 56.85/57.06 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 56.85/57.06 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 56.85/57.06 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 56.85/57.06 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 56.85/57.06 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 56.85/57.06 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 56.85/57.06 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 56.85/57.06 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 57.82/58.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 57.82/58.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 57.82/58.04 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 57.82/58.04 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 57.82/58.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 57.82/58.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 57.82/58.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 57.82/58.04 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 57.82/58.04 Found (eq_ref0 a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 57.82/58.04 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 57.82/58.04 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 57.82/58.04 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 57.82/58.04 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 57.82/58.04 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 57.82/58.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 57.82/58.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 57.82/58.04 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 57.82/58.04 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 57.82/58.04 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 58.25/58.44 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 58.25/58.44 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 58.25/58.44 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 58.25/58.44 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 58.25/58.44 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 58.25/58.44 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 58.25/58.44 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 58.25/58.44 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 58.25/58.44 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 58.25/58.44 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 58.25/58.44 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 58.25/58.44 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 61.27/61.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 61.27/61.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 61.27/61.46 Found (eq_ref0 a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 61.27/61.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 61.27/61.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 61.27/61.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 61.27/61.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 61.27/61.46 Found (eq_ref0 a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 61.27/61.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 61.27/61.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 61.27/61.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 61.27/61.46 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 61.27/61.46 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 61.27/61.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 61.27/61.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 61.27/61.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 61.27/61.46 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 61.27/61.46 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 61.27/61.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 71.12/71.33 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 71.12/71.33 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 71.12/71.33 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 71.12/71.33 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 71.12/71.33 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 71.12/71.33 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 71.12/71.33 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 71.12/71.33 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 71.12/71.33 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 71.12/71.33 Found (eq_ref00 P) as proof of (P0 V0z)
% 71.12/71.33 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 71.12/71.33 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 71.12/71.33 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 71.12/71.33 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 71.12/71.33 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 77.10/77.35 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 77.10/77.35 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))) V0z)
% 77.10/77.35 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 77.10/77.35 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))) b)
% 77.10/77.35 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 77.10/77.35 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 77.10/77.35 Found x1 as proof of (P0 b)
% 77.10/77.35 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 77.10/77.35 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 77.10/77.35 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 77.10/77.35 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 77.10/77.35 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 77.10/77.35 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 77.10/77.35 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 77.10/77.35 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 77.10/77.35 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 77.10/77.35 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 77.10/77.35 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 77.10/77.35 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 77.10/77.35 Found x1:(P V0z)
% 77.10/77.35 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 77.10/77.35 Found x1 as proof of (P0 b)
% 77.10/77.35 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))))
% 79.03/79.28 Found (stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))) b)
% 79.03/79.28 Found (stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))) b)
% 79.03/79.28 Found (stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))) b)
% 79.03/79.28 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))) V0z)
% 79.03/79.28 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 79.03/79.28 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))) b)
% 84.01/84.24 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 84.01/84.24 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 84.01/84.24 Found x1 as proof of (P0 b)
% 84.01/84.24 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))) V0z)
% 84.01/84.24 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 84.01/84.24 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))) b)
% 84.01/84.24 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 84.01/84.24 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 84.01/84.24 Found x1 as proof of (P0 b)
% 84.01/84.24 Found x1:(P V0z)
% 84.01/84.24 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 84.01/84.24 Found x1 as proof of (P0 b)
% 84.01/84.24 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 84.01/84.24 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 84.01/84.24 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 84.01/84.24 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 84.01/84.24 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 84.01/84.24 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 84.01/84.24 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 87.31/87.50 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 87.31/87.50 Found (eq_ref00 P) as proof of (P0 V0z)
% 87.31/87.50 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 87.31/87.50 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 87.31/87.50 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 87.31/87.50 Found eq_ref000:=(eq_ref00 P0):((P0 V0z)->(P0 V0z))
% 87.31/87.50 Found (eq_ref00 P0) as proof of (P V0z)
% 87.31/87.50 Found ((eq_ref0 V0z) P0) as proof of (P V0z)
% 87.31/87.50 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P0) as proof of (P V0z)
% 87.31/87.50 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P0) as proof of (P V0z)
% 87.31/87.50 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 87.31/87.50 Found (eq_ref00 P) as proof of (P0 V0z)
% 87.31/87.50 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 87.31/87.50 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 87.31/87.50 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 87.31/87.50 Found x1:(P V0z)
% 87.31/87.50 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 87.31/87.50 Found x1 as proof of (P0 b)
% 87.31/87.50 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))))
% 87.31/87.50 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 87.31/87.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 87.94/88.21 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 87.94/88.21 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 87.94/88.21 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 87.94/88.21 Found (eq_ref00 P) as proof of (P0 V0z)
% 87.94/88.21 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 87.94/88.21 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 87.94/88.21 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 87.94/88.21 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 87.94/88.21 Found (eq_ref00 P) as proof of (P0 V0z)
% 87.94/88.21 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 87.94/88.21 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 87.94/88.21 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 87.94/88.21 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 92.21/92.40 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 92.21/92.40 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) b)
% 92.21/92.40 Found x10:(P V0z)
% 92.21/92.40 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 92.21/92.40 Found x10 as proof of (P0 b)
% 92.21/92.40 Found x1:(P V0z)
% 92.21/92.40 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 92.21/92.40 Found x1 as proof of (P0 b)
% 92.21/92.40 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 92.21/92.40 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 92.21/92.40 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) b)
% 92.21/92.40 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 92.21/92.40 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 92.21/92.40 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 92.21/92.40 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 92.21/92.40 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 92.21/92.40 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P b))):((P b)->(P b))
% 92.21/92.40 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P b))) as proof of (P0 b)
% 92.21/92.40 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P b))) as proof of (P0 b)
% 92.21/92.40 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 103.20/103.43 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 103.20/103.43 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 103.20/103.43 Found x1:(P V0z)
% 103.20/103.43 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 103.20/103.43 Found x1 as proof of (P0 b)
% 103.20/103.43 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 103.20/103.43 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))
% 103.20/103.43 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))
% 103.20/103.43 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))
% 103.20/103.43 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))
% 103.20/103.43 Found x1:(P V0z)
% 103.20/103.43 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 103.20/103.43 Found x1 as proof of (P0 b)
% 103.20/103.43 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))))
% 103.20/103.43 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 105.00/105.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 105.00/105.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 105.00/105.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 105.00/105.25 Found x1:(P V0z)
% 105.00/105.25 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 105.00/105.25 Found x1 as proof of (P0 b)
% 105.00/105.25 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 105.00/105.25 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 105.00/105.25 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 120.48/120.73 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 120.48/120.73 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 120.48/120.73 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 120.48/120.73 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 120.48/120.73 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 120.48/120.73 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 120.48/120.73 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 120.48/120.73 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 120.48/120.73 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 120.48/120.73 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 120.48/120.73 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 120.48/120.73 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 120.48/120.73 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 120.48/120.73 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 122.41/122.69 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 122.41/122.69 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 122.41/122.69 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 122.41/122.69 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 122.41/122.69 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 122.41/122.69 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 122.41/122.69 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 122.41/122.69 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 122.41/122.69 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 122.41/122.69 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 123.28/123.50 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 123.28/123.50 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 123.28/123.50 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 123.28/123.50 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 123.28/123.50 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 123.28/123.50 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 136.18/136.51 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 136.18/136.51 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 136.18/136.51 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 136.18/136.51 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 136.18/136.51 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 136.18/136.51 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 136.18/136.51 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 136.18/136.51 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 136.18/136.51 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 136.18/136.51 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 136.18/136.51 Found (eq_ref0 b) as proof of (P b)
% 136.18/136.51 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 136.18/136.51 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 136.18/136.51 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 136.18/136.51 Found x1:(P V0z)
% 136.18/136.51 Found x1 as proof of (P0 V0z)
% 136.18/136.51 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 136.18/136.51 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 136.18/136.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 136.18/136.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 136.18/136.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 136.18/136.51 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 136.18/136.51 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 141.50/141.76 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 141.50/141.76 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 141.50/141.76 Found stp_eq_fo_c_2Enum_2E00:=(stp_eq_fo_c_2Enum_2E0 (fun (x1:fofType)=> (P V0z))):((P V0z)->(P V0z))
% 141.50/141.76 Found (stp_eq_fo_c_2Enum_2E0 (fun (x1:fofType)=> (P V0z))) as proof of (P0 V0z)
% 141.50/141.76 Found (stp_eq_fo_c_2Enum_2E0 (fun (x1:fofType)=> (P V0z))) as proof of (P0 V0z)
% 141.50/141.76 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 141.50/141.76 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 141.50/141.76 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 141.50/141.76 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 141.50/141.76 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 148.20/148.46 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 148.20/148.46 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 148.20/148.46 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 148.20/148.46 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 148.20/148.46 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 148.20/148.46 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 148.20/148.46 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 148.20/148.46 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 148.20/148.46 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 148.20/148.46 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 148.20/148.46 Found (eq_ref0 b) as proof of (P b)
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 148.20/148.46 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (P b)
% 149.97/150.25 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 149.97/150.25 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 149.97/150.25 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 149.97/150.25 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 149.97/150.25 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 149.97/150.25 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 149.97/150.25 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 149.97/150.25 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 149.97/150.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.36/155.60 Found x1:(P V0z)
% 155.36/155.60 Found x1 as proof of (P0 V0z)
% 155.36/155.60 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 155.36/155.60 Found (eq_ref00 P) as proof of (P0 V0z)
% 155.36/155.60 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 155.36/155.60 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 155.36/155.60 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 155.36/155.60 Found x1:(P V0z)
% 155.36/155.60 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 155.36/155.60 Found x1 as proof of (P0 b)
% 155.36/155.60 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))))
% 155.36/155.60 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 155.36/155.60 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))) b)
% 155.36/155.60 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 155.36/155.60 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.36/155.60 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.36/155.60 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.36/155.60 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.95/156.20 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 155.95/156.20 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.95/156.20 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 155.95/156.20 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.95/156.20 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 155.95/156.20 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 155.95/156.20 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 155.95/156.20 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 155.95/156.20 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 156.68/157.00 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 156.68/157.00 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 156.68/157.00 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 156.68/157.00 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 156.68/157.00 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 156.68/157.00 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 156.68/157.00 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 156.68/157.00 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 156.68/157.00 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 158.44/158.77 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 158.44/158.77 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 158.44/158.77 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 158.44/158.77 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 158.44/158.77 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 158.44/158.77 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 158.44/158.77 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 158.44/158.77 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 158.44/158.77 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 158.44/158.77 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 158.44/158.77 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 159.27/159.54 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 159.27/159.54 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 159.27/159.54 Found x1:(P V0z)
% 159.27/159.54 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 159.27/159.54 Found x1 as proof of (P0 b)
% 159.27/159.54 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))))))))
% 159.27/159.54 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) b)
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) b)
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) b)
% 159.27/159.54 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))))) b)
% 170.57/170.83 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 170.57/170.83 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b0)
% 170.57/170.83 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b0)
% 170.57/170.83 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b0)
% 170.57/170.83 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b0)
% 170.57/170.83 Found eq_ref00:=(eq_ref0 b0):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b0) b0)
% 170.57/170.83 Found (eq_ref0 b0) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b0) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 170.57/170.83 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b0) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b0) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 170.57/170.83 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b0) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b0) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 170.57/170.83 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b0) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b0) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 170.57/170.83 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 170.57/170.83 Instantiate: a:=((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)):fofType
% 170.57/170.83 Found x1 as proof of (P0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal a))
% 170.57/170.83 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 170.57/170.83 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 170.57/170.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 170.57/170.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 170.57/170.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 170.57/170.83 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 170.57/170.83 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 170.57/170.83 Found x1:(P V0z)
% 170.57/170.83 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 170.57/170.83 Found x1 as proof of (P0 b)
% 170.57/170.83 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))
% 172.84/173.18 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 172.84/173.18 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 172.84/173.18 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 172.84/173.18 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 172.84/173.18 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 172.84/173.18 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 172.84/173.18 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 172.84/173.18 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 172.84/173.18 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 172.84/173.18 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 172.84/173.18 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 172.84/173.18 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 175.27/175.58 Found x1:(P V0z)
% 175.27/175.58 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 175.27/175.58 Found x1 as proof of (P0 b)
% 175.27/175.58 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 175.27/175.58 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 175.27/175.58 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) b)
% 175.27/175.58 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 175.27/175.58 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 175.27/175.58 Found x1 as proof of (P0 b)
% 175.27/175.58 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 175.27/175.58 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 175.27/175.58 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 175.27/175.58 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 175.27/175.58 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 175.27/175.58 Found stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 175.27/175.58 Found (stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 175.27/175.58 Found (stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 180.76/181.01 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 180.76/181.01 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 180.76/181.01 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 180.76/181.01 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 180.76/181.01 Found x1 as proof of (P0 b)
% 180.76/181.01 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 180.76/181.01 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 180.76/181.01 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 180.76/181.01 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 181.77/182.09 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 181.77/182.09 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 181.77/182.09 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 181.77/182.09 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 181.77/182.09 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 181.77/182.09 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 181.77/182.09 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 181.77/182.09 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 181.77/182.09 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 181.77/182.09 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 181.77/182.09 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 181.77/182.09 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 181.77/182.09 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 181.77/182.09 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 182.67/182.96 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 182.67/182.96 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 182.67/182.96 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 182.67/182.96 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 182.67/182.96 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 182.67/182.96 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 182.67/182.96 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 182.67/182.96 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 182.67/182.96 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 182.67/182.96 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 182.67/182.96 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 184.95/185.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 184.95/185.22 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 184.95/185.22 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 184.95/185.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 184.95/185.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 184.95/185.22 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 184.95/185.22 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 184.95/185.22 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 184.95/185.22 Found x10:(P V0z)
% 184.95/185.22 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 184.95/185.22 Found x10 as proof of (P0 b)
% 184.95/185.22 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))))
% 184.95/185.22 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 186.98/187.28 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 186.98/187.28 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 186.98/187.28 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 186.98/187.28 Found x1:(P V0z)
% 186.98/187.28 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 186.98/187.28 Found x1 as proof of (P0 b)
% 186.98/187.28 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))))
% 186.98/187.28 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 186.98/187.28 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 186.98/187.28 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 186.98/187.28 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 189.06/189.34 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 189.06/189.34 Instantiate: a:=((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)):fofType
% 189.06/189.34 Found x1 as proof of (P0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal a))
% 189.06/189.34 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 189.06/189.34 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 189.06/189.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 189.06/189.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 189.06/189.34 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 189.06/189.34 Found x1:(P V0z)
% 189.06/189.34 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 189.06/189.34 Found x1 as proof of (P0 b)
% 189.06/189.34 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))))))
% 189.06/189.34 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) b)
% 189.06/189.34 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) b)
% 189.06/189.34 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) b)
% 189.06/189.34 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) b)
% 195.12/195.36 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 195.12/195.36 Instantiate: a:=((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)):fofType
% 195.12/195.36 Found x1 as proof of (P0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal a))
% 195.12/195.36 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 195.12/195.36 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 195.12/195.36 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 195.12/195.36 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 195.12/195.36 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))
% 195.12/195.36 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 195.12/195.36 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 195.12/195.36 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))) b)
% 195.12/195.36 Found x1:(P V0z)
% 195.12/195.36 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 195.12/195.36 Found x1 as proof of (P0 b)
% 195.12/195.36 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 195.12/195.36 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 195.12/195.36 Found x1 as proof of (P0 b)
% 195.12/195.36 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 195.12/195.36 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 195.12/195.36 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 195.12/195.36 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 196.83/197.15 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 196.83/197.15 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 196.83/197.15 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 196.83/197.15 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 196.83/197.15 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 196.83/197.15 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 196.83/197.15 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 196.83/197.15 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 196.83/197.15 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 196.83/197.15 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 196.83/197.15 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 196.83/197.15 Found stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))):((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 196.83/197.15 Found (stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) as proof of ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 207.83/208.16 Found (stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) as proof of ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 207.83/208.16 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 207.83/208.16 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))
% 207.83/208.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))
% 207.83/208.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))
% 207.83/208.16 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))))
% 207.83/208.16 Found x1:(P V0z)
% 207.83/208.16 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 207.83/208.16 Found x1 as proof of (P0 b)
% 207.83/208.16 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))
% 207.83/208.16 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 209.22/209.52 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 209.22/209.52 Found x1:(P V0z)
% 209.22/209.52 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 209.22/209.52 Found x1 as proof of (P0 b)
% 209.22/209.52 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))))
% 209.22/209.52 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 209.22/209.52 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 212.54/212.84 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 212.54/212.84 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))) b)
% 212.54/212.84 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 212.54/212.84 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 212.54/212.84 Found x1 as proof of (P0 b)
% 212.54/212.84 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 212.54/212.84 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 212.54/212.84 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 217.15/217.49 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 217.15/217.49 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 217.15/217.49 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 217.15/217.49 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 217.15/217.49 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 217.15/217.49 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))
% 217.15/217.49 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 217.15/217.49 Found x1 as proof of (P0 b)
% 217.15/217.49 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 217.15/217.49 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 219.44/219.72 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 219.44/219.72 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 219.44/219.72 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) b)
% 219.44/219.72 Found x1:(P V0z)
% 219.44/219.72 Instantiate: b:=V0z:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 219.44/219.72 Found x1 as proof of (P0 b)
% 219.44/219.72 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))))))))
% 219.44/219.72 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) b)
% 219.44/219.72 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) b)
% 219.44/219.72 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) b)
% 219.44/219.72 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))))) b)
% 232.62/232.98 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 232.62/232.98 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 232.62/232.98 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 232.62/232.98 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 232.62/232.98 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 232.62/232.98 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 232.62/232.98 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 232.62/232.98 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 232.62/232.98 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 232.62/232.98 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 232.62/232.98 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 232.62/232.98 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 234.23/234.56 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 234.23/234.56 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 234.23/234.56 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 234.23/234.56 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 234.23/234.56 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 234.23/234.56 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 234.23/234.56 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 234.23/234.56 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 234.23/234.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 234.23/234.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 234.23/234.56 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 234.23/234.56 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 234.23/234.56 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 234.23/234.56 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 234.23/234.56 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 235.90/236.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 235.90/236.25 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 235.90/236.25 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 235.90/236.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 235.90/236.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 235.90/236.25 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 235.90/236.25 Found stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))):((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 235.90/236.25 Found (stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) as proof of ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 235.90/236.25 Found (stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) as proof of ((mem (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) ((ty_2Epair_2Eprod ty_2Erealax_2Ereal) ty_2Erealax_2Ereal))
% 235.90/236.25 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 235.90/236.25 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 235.90/236.25 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 235.90/236.25 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))
% 256.61/256.92 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 256.61/256.92 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))
% 256.61/256.92 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 256.61/256.92 Found (eq_ref0 a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 256.61/256.92 Found x00:=(x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))):((P V0z)->(P V0z))
% 256.61/256.92 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 256.61/256.92 Found (x0 (fun (x1:tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)=> (P V0z))) as proof of (P0 V0z)
% 256.61/256.92 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 256.61/256.92 Found (eq_ref0 a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 256.61/256.92 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 256.61/256.92 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 256.61/256.92 Found (eq_ref00 P) as proof of (P0 V0z)
% 256.61/256.92 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 256.61/256.92 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 256.61/256.92 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 256.61/256.92 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 263.90/264.29 Found (eq_ref00 P) as proof of (P0 V0z)
% 263.90/264.29 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 263.90/264.29 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 263.90/264.29 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 263.90/264.29 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 263.90/264.29 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 263.90/264.29 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) b)
% 263.90/264.29 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 263.90/264.29 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 263.90/264.29 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 263.90/264.29 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 263.90/264.29 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 263.90/264.29 Found x0:(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 263.90/264.29 Found x0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 263.90/264.29 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 263.90/264.29 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal0 as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 263.90/264.29 Found eq_ref000:=(eq_ref00 P):((P V0z)->(P V0z))
% 263.90/264.29 Found (eq_ref00 P) as proof of (P0 V0z)
% 283.68/284.01 Found ((eq_ref0 V0z) P) as proof of (P0 V0z)
% 283.68/284.01 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 283.68/284.01 Found (((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) P) as proof of (P0 V0z)
% 283.68/284.01 Found eq_ref00:=(eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 283.68/284.01 Found (eq_ref0 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 283.68/284.01 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 283.68/284.01 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 283.68/284.01 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0)))) b)
% 283.68/284.01 Found eq_ref00:=(eq_ref0 b):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) b)
% 283.68/284.01 Found (eq_ref0 b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 283.68/284.01 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 283.68/284.01 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 283.68/284.01 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) b) V0z)
% 283.68/284.01 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 283.68/284.01 Found (eq_ref0 a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 283.68/284.01 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 283.68/284.01 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 283.68/284.01 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 283.68/284.01 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 283.68/284.01 Found (eq_ref0 a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))
% 289.36/289.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))
% 289.36/289.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))
% 289.36/289.70 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__inv) (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))))))
% 289.36/289.70 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 289.36/289.70 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 289.36/289.70 Found x1 as proof of (P0 b)
% 289.36/289.70 Found eq_ref00:=(eq_ref0 V0z):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) V0z)
% 289.36/289.70 Found (eq_ref0 V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 289.36/289.70 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 289.36/289.70 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 289.36/289.70 Found ((eq_ref tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) as proof of (((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) V0z) b)
% 289.36/289.70 Found x1:(P (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))))
% 289.36/289.70 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ((ap c_2Ecomplex_2Ecomplex__of__num) (inj__ty_2Enum_2Enum fo__c_2Enum_2E0))):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 289.36/289.70 Found x1 as proof of (P0 b)
% 289.36/289.70 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1:=(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))):(((eq tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z))))) (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)))
% 289.36/289.70 Instantiate: b:=(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal V0z)):tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal
% 289.36/289.70 Found stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal1 as p
%------------------------------------------------------------------------------