TSTP Solution File: ITP002^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP002^2 : TPTP v7.5.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 13:23:28 EDT 2021
% Result : Timeout 296.66s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ITP002^2 : TPTP v7.5.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n014.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 : Thu Mar 18 19:07:56 EDT 2021
% 0.12/0.33 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.38/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.38/0.61 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/ITP001/ITP001^2.ax, trying next directory
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x14925a8>, <kernel.Type object at 0x1492320>) of role type named del_tp
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring del:Type
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x148ff38>, <kernel.Constant object at 0x14923b0>) of role type named bool
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring bool:del
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x14923f8>, <kernel.Constant object at 0x14923b0>) of role type named ind
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring ind:del
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x14925a8>, <kernel.DependentProduct object at 0x1492368>) of role type named arr
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring arr:(del->(del->del))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x1492170>, <kernel.DependentProduct object at 0x1492368>) of role type named mem
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mem:(fofType->(del->Prop))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x14923f8>, <kernel.DependentProduct object at 0x14925a8>) of role type named ap
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring ap:(fofType->(fofType->fofType))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x14921b8>, <kernel.DependentProduct object at 0x14925f0>) of role type named lam
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring lam:(del->((fofType->fofType)->fofType))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x1492200>, <kernel.DependentProduct object at 0x1492368>) of role type named p
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring p:(fofType->Prop)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x14925a8>, <kernel.DependentProduct object at 0x1492248>) of role type named stp_inj_o
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring inj__o:(Prop->fofType)
% 0.38/0.61 FOF formula (forall (X:Prop), (((eq Prop) (p (inj__o X))) X)) of role axiom named stp_inj_surj_o
% 0.38/0.61 A new axiom: (forall (X:Prop), (((eq Prop) (p (inj__o X))) X))
% 0.38/0.61 FOF formula (forall (X:Prop), ((mem (inj__o X)) bool)) of role axiom named stp_inj_mem_o
% 0.38/0.61 A new axiom: (forall (X:Prop), ((mem (inj__o X)) bool))
% 0.38/0.61 FOF formula (forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X))))) of role axiom named stp_iso_mem_o
% 0.38/0.61 A new axiom: (forall (X:fofType), (((mem X) bool)->(((eq fofType) X) (inj__o (p X)))))
% 0.38/0.61 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
% 0.38/0.61 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)))))
% 0.38/0.61 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
% 0.38/0.61 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))))
% 0.38/0.61 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
% 0.38/0.61 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))))))
% 0.38/0.61 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
% 0.38/0.61 A new axiom: (forall (A:del) (F:(fofType->fofType)) (X:fofType), (((mem X) A)->(((eq fofType) ((ap ((lam A) F)) X)) (F X))))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x1472c68>, <kernel.Single object at 0x1472998>) of role type named tp_c_2Ebool_2EF
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring c_2Ebool_2EF:fofType
% 0.38/0.61 FOF formula ((mem c_2Ebool_2EF) bool) of role axiom named mem_c_2Ebool_2EF
% 0.38/0.61 A new axiom: ((mem c_2Ebool_2EF) bool)
% 0.38/0.61 FOF formula ((p c_2Ebool_2EF)->False) of role axiom named ax_false_p
% 0.38/0.61 A new axiom: ((p c_2Ebool_2EF)->False)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x1472dd0>, <kernel.Single object at 0x1472c68>) of role type named tp_c_2Ebool_2ET
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2ET:fofType
% 0.38/0.62 FOF formula ((mem c_2Ebool_2ET) bool) of role axiom named mem_c_2Ebool_2ET
% 0.38/0.62 A new axiom: ((mem c_2Ebool_2ET) bool)
% 0.38/0.62 FOF formula (p c_2Ebool_2ET) of role axiom named ax_true_p
% 0.38/0.62 A new axiom: (p c_2Ebool_2ET)
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1472c68>, <kernel.DependentProduct object at 0x2ba22b3ec0e0>) of role type named tp_ty_2Eoption_2Eoption
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring ty_2Eoption_2Eoption:(del->del)
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1733830>, <kernel.DependentProduct object at 0x2ba22b3ec170>) of role type named tp_c_2Eoption_2ENONE
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2ENONE:(del->fofType)
% 0.38/0.62 FOF formula (forall (A_27a:del), ((mem (c_2Eoption_2ENONE A_27a)) (ty_2Eoption_2Eoption A_27a))) of role axiom named mem_c_2Eoption_2ENONE
% 0.38/0.62 A new axiom: (forall (A_27a:del), ((mem (c_2Eoption_2ENONE A_27a)) (ty_2Eoption_2Eoption A_27a)))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2ba22b3ec170>, <kernel.DependentProduct object at 0x1492b90>) of role type named tp_c_2Eoption_2ETHE
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2ETHE:(del->fofType)
% 0.38/0.62 FOF formula (forall (A_27a:del), ((mem (c_2Eoption_2ETHE A_27a)) ((arr (ty_2Eoption_2Eoption A_27a)) A_27a))) of role axiom named mem_c_2Eoption_2ETHE
% 0.38/0.62 A new axiom: (forall (A_27a:del), ((mem (c_2Eoption_2ETHE A_27a)) ((arr (ty_2Eoption_2Eoption A_27a)) A_27a)))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2ba232ecb4d0>, <kernel.DependentProduct object at 0x1492ab8>) of role type named tp_c_2Eoption_2ESOME
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2ESOME:(del->fofType)
% 0.38/0.62 FOF formula (forall (A_27a:del), ((mem (c_2Eoption_2ESOME A_27a)) ((arr A_27a) (ty_2Eoption_2Eoption A_27a)))) of role axiom named mem_c_2Eoption_2ESOME
% 0.38/0.62 A new axiom: (forall (A_27a:del), ((mem (c_2Eoption_2ESOME A_27a)) ((arr A_27a) (ty_2Eoption_2Eoption A_27a))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2ba232ecb4d0>, <kernel.DependentProduct object at 0x14929e0>) of role type named tp_c_2Eoption_2EIS__SOME
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2EIS__SOME:(del->fofType)
% 0.38/0.62 FOF formula (forall (A_27a:del), ((mem (c_2Eoption_2EIS__SOME A_27a)) ((arr (ty_2Eoption_2Eoption A_27a)) bool))) of role axiom named mem_c_2Eoption_2EIS__SOME
% 0.38/0.62 A new axiom: (forall (A_27a:del), ((mem (c_2Eoption_2EIS__SOME A_27a)) ((arr (ty_2Eoption_2Eoption A_27a)) bool)))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x2ba232ee8e60>, <kernel.Single object at 0x1492bd8>) of role type named tp_c_2Ebool_2E_2F_5C
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2E_2F_5C:fofType
% 0.38/0.62 FOF formula ((mem c_2Ebool_2E_2F_5C) ((arr bool) ((arr bool) bool))) of role axiom named mem_c_2Ebool_2E_2F_5C
% 0.38/0.62 A new axiom: ((mem c_2Ebool_2E_2F_5C) ((arr bool) ((arr bool) bool)))
% 0.38/0.62 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
% 0.38/0.62 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)))))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1492b48>, <kernel.DependentProduct object at 0x1492710>) of role type named tp_c_2Ebool_2ECOND
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Ebool_2ECOND:(del->fofType)
% 0.38/0.62 FOF formula (forall (A_27a:del), ((mem (c_2Ebool_2ECOND A_27a)) ((arr bool) ((arr A_27a) ((arr A_27a) A_27a))))) of role axiom named mem_c_2Ebool_2ECOND
% 0.38/0.62 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2ECOND A_27a)) ((arr bool) ((arr A_27a) ((arr A_27a) A_27a)))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x1492ab8>, <kernel.DependentProduct object at 0x14924d0>) of role type named tp_c_2Eoption_2EOPTION__MAP2
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring c_2Eoption_2EOPTION__MAP2:(del->(del->(del->fofType)))
% 0.38/0.62 FOF formula (forall (A_27a:del) (A_27b:del) (A_27c:del), ((mem (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) ((arr ((arr A_27b) ((arr A_27c) A_27a))) ((arr (ty_2Eoption_2Eoption A_27b)) ((arr (ty_2Eoption_2Eoption A_27c)) (ty_2Eoption_2Eoption A_27a)))))) of role axiom named mem_c_2Eoption_2EOPTION__MAP2
% 0.38/0.62 A new axiom: (forall (A_27a:del) (A_27b:del) (A_27c:del), ((mem (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) ((arr ((arr A_27b) ((arr A_27c) A_27a))) ((arr (ty_2Eoption_2Eoption A_27b)) ((arr (ty_2Eoption_2Eoption A_27c)) (ty_2Eoption_2Eoption A_27a))))))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x14920e0>, <kernel.DependentProduct object at 0x1492710>) of role type named tp_c_2Emin_2E_3D
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Emin_2E_3D:(del->fofType)
% 0.48/0.63 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
% 0.48/0.63 A new axiom: (forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool))))
% 0.48/0.63 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
% 0.48/0.63 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))))))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1492878>, <kernel.DependentProduct object at 0x1492a70>) of role type named tp_c_2Ebool_2E_21
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_2Ebool_2E_21:(del->fofType)
% 0.48/0.63 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
% 0.48/0.63 A new axiom: (forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool)))
% 0.48/0.63 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
% 0.48/0.63 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)))))))
% 0.48/0.63 FOF formula True of role axiom named conj_thm_2Ebool_2ETRUTH
% 0.48/0.63 A new axiom: True
% 0.48/0.63 FOF formula (forall (V0t:fofType), (((mem V0t) bool)->((and ((and ((and ((and ((iff ((and True) (p V0t))) (p V0t))) ((iff ((and (p V0t)) True)) (p V0t)))) ((iff ((and False) (p V0t))) False))) ((iff ((and (p V0t)) False)) False))) ((iff ((and (p V0t)) (p V0t))) (p V0t))))) of role axiom named conj_thm_2Ebool_2EAND__CLAUSES
% 0.48/0.63 A new axiom: (forall (V0t:fofType), (((mem V0t) bool)->((and ((and ((and ((and ((iff ((and True) (p V0t))) (p V0t))) ((iff ((and (p V0t)) True)) (p V0t)))) ((iff ((and False) (p V0t))) False))) ((iff ((and (p V0t)) False)) False))) ((iff ((and (p V0t)) (p V0t))) (p V0t)))))
% 0.48/0.63 FOF formula (forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->((iff (((eq fofType) V0x) V0x)) True))) of role axiom named conj_thm_2Ebool_2EREFL__CLAUSE
% 0.48/0.63 A new axiom: (forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->((iff (((eq fofType) V0x) V0x)) True)))
% 0.48/0.63 FOF formula (forall (A_27a:del) (V0t1:fofType), (((mem V0t1) A_27a)->(forall (V1t2:fofType), (((mem V1t2) A_27a)->((and (((eq fofType) ((ap ((ap ((ap (c_2Ebool_2ECOND A_27a)) c_2Ebool_2ET)) V0t1)) V1t2)) V0t1)) (((eq fofType) ((ap ((ap ((ap (c_2Ebool_2ECOND A_27a)) c_2Ebool_2EF)) V0t1)) V1t2)) V1t2)))))) of role axiom named conj_thm_2Ebool_2ECOND__CLAUSES
% 0.48/0.63 A new axiom: (forall (A_27a:del) (V0t1:fofType), (((mem V0t1) A_27a)->(forall (V1t2:fofType), (((mem V1t2) A_27a)->((and (((eq fofType) ((ap ((ap ((ap (c_2Ebool_2ECOND A_27a)) c_2Ebool_2ET)) V0t1)) V1t2)) V0t1)) (((eq fofType) ((ap ((ap ((ap (c_2Ebool_2ECOND A_27a)) c_2Ebool_2EF)) V0t1)) V1t2)) V1t2))))))
% 0.48/0.63 FOF formula (forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->(forall (V1y:fofType), (((mem V1y) A_27a)->((iff (((eq fofType) ((ap (c_2Eoption_2ESOME A_27a)) V0x)) ((ap (c_2Eoption_2ESOME A_27a)) V1y))) (((eq fofType) V0x) V1y)))))) of role axiom named conj_thm_2Eoption_2ESOME__11
% 0.48/0.63 A new axiom: (forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->(forall (V1y:fofType), (((mem V1y) A_27a)->((iff (((eq fofType) ((ap (c_2Eoption_2ESOME A_27a)) V0x)) ((ap (c_2Eoption_2ESOME A_27a)) V1y))) (((eq fofType) V0x) V1y))))))
% 0.48/0.63 FOF formula (forall (A_27a:del), ((and (forall (V0x:fofType), (((mem V0x) A_27a)->((iff (p ((ap (c_2Eoption_2EIS__SOME A_27a)) ((ap (c_2Eoption_2ESOME A_27a)) V0x)))) True)))) ((iff (p ((ap (c_2Eoption_2EIS__SOME A_27a)) (c_2Eoption_2ENONE A_27a)))) False))) of role axiom named ax_thm_2Eoption_2EIS__SOME__DEF
% 0.48/0.65 A new axiom: (forall (A_27a:del), ((and (forall (V0x:fofType), (((mem V0x) A_27a)->((iff (p ((ap (c_2Eoption_2EIS__SOME A_27a)) ((ap (c_2Eoption_2ESOME A_27a)) V0x)))) True)))) ((iff (p ((ap (c_2Eoption_2EIS__SOME A_27a)) (c_2Eoption_2ENONE A_27a)))) False)))
% 0.48/0.65 FOF formula (forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->(((eq fofType) ((ap (c_2Eoption_2ETHE A_27a)) ((ap (c_2Eoption_2ESOME A_27a)) V0x))) V0x))) of role axiom named ax_thm_2Eoption_2ETHE__DEF
% 0.48/0.65 A new axiom: (forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->(((eq fofType) ((ap (c_2Eoption_2ETHE A_27a)) ((ap (c_2Eoption_2ESOME A_27a)) V0x))) V0x)))
% 0.48/0.65 FOF formula (forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr A_27b) ((arr A_27c) A_27a)))->(forall (V1x:fofType), (((mem V1x) (ty_2Eoption_2Eoption A_27b))->(forall (V2y:fofType), (((mem V2y) (ty_2Eoption_2Eoption A_27c))->(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) V1x)) V2y)) ((ap ((ap ((ap (c_2Ebool_2ECOND (ty_2Eoption_2Eoption A_27a))) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Eoption_2EIS__SOME A_27b)) V1x))) ((ap (c_2Eoption_2EIS__SOME A_27c)) V2y)))) ((ap (c_2Eoption_2ESOME A_27a)) ((ap ((ap V0f) ((ap (c_2Eoption_2ETHE A_27b)) V1x))) ((ap (c_2Eoption_2ETHE A_27c)) V2y))))) (c_2Eoption_2ENONE A_27a))))))))) of role axiom named ax_thm_2Eoption_2EOPTION__MAP2__DEF
% 0.48/0.65 A new axiom: (forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr A_27b) ((arr A_27c) A_27a)))->(forall (V1x:fofType), (((mem V1x) (ty_2Eoption_2Eoption A_27b))->(forall (V2y:fofType), (((mem V2y) (ty_2Eoption_2Eoption A_27c))->(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) V1x)) V2y)) ((ap ((ap ((ap (c_2Ebool_2ECOND (ty_2Eoption_2Eoption A_27a))) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Eoption_2EIS__SOME A_27b)) V1x))) ((ap (c_2Eoption_2EIS__SOME A_27c)) V2y)))) ((ap (c_2Eoption_2ESOME A_27a)) ((ap ((ap V0f) ((ap (c_2Eoption_2ETHE A_27b)) V1x))) ((ap (c_2Eoption_2ETHE A_27c)) V2y))))) (c_2Eoption_2ENONE A_27a)))))))))
% 0.48/0.65 FOF formula (forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr A_27b) ((arr A_27c) A_27a)))->(forall (V1x:fofType), (((mem V1x) A_27b)->(forall (V2y:fofType), (((mem V2y) A_27c)->((and ((and ((and (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) ((ap (c_2Eoption_2ESOME A_27b)) V1x))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) ((ap (c_2Eoption_2ESOME A_27a)) ((ap ((ap V0f) V1x)) V2y)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) ((ap (c_2Eoption_2ESOME A_27b)) V1x))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))))) of role conjecture named conj_thm_2Eoption_2EOPTION__MAP2__THM
% 0.48/0.65 Conjecture to prove = (forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr A_27b) ((arr A_27c) A_27a)))->(forall (V1x:fofType), (((mem V1x) A_27b)->(forall (V2y:fofType), (((mem V2y) A_27c)->((and ((and ((and (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) ((ap (c_2Eoption_2ESOME A_27b)) V1x))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) ((ap (c_2Eoption_2ESOME A_27a)) ((ap ((ap V0f) V1x)) V2y)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) ((ap (c_2Eoption_2ESOME A_27b)) V1x))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))))):Prop
% 0.48/0.65 We need to prove ['(forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr A_27b) ((arr A_27c) A_27a)))->(forall (V1x:fofType), (((mem V1x) A_27b)->(forall (V2y:fofType), (((mem V2y) A_27c)->((and ((and ((and (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) ((ap (c_2Eoption_2ESOME A_27b)) V1x))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) ((ap (c_2Eoption_2ESOME A_27a)) ((ap ((ap V0f) V1x)) V2y)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) ((ap (c_2Eoption_2ESOME A_27b)) V1x))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))))']
% 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_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 ty_2Eoption_2Eoption:(del->del).
% 0.48/0.65 Parameter c_2Eoption_2ENONE:(del->fofType).
% 0.48/0.65 Axiom mem_c_2Eoption_2ENONE:(forall (A_27a:del), ((mem (c_2Eoption_2ENONE A_27a)) (ty_2Eoption_2Eoption A_27a))).
% 0.48/0.65 Parameter c_2Eoption_2ETHE:(del->fofType).
% 0.48/0.65 Axiom mem_c_2Eoption_2ETHE:(forall (A_27a:del), ((mem (c_2Eoption_2ETHE A_27a)) ((arr (ty_2Eoption_2Eoption A_27a)) A_27a))).
% 0.48/0.65 Parameter c_2Eoption_2ESOME:(del->fofType).
% 0.48/0.65 Axiom mem_c_2Eoption_2ESOME:(forall (A_27a:del), ((mem (c_2Eoption_2ESOME A_27a)) ((arr A_27a) (ty_2Eoption_2Eoption A_27a)))).
% 0.48/0.65 Parameter c_2Eoption_2EIS__SOME:(del->fofType).
% 0.48/0.65 Axiom mem_c_2Eoption_2EIS__SOME:(forall (A_27a:del), ((mem (c_2Eoption_2EIS__SOME A_27a)) ((arr (ty_2Eoption_2Eoption A_27a)) bool))).
% 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 c_2Ebool_2ECOND:(del->fofType).
% 0.48/0.65 Axiom mem_c_2Ebool_2ECOND:(forall (A_27a:del), ((mem (c_2Ebool_2ECOND A_27a)) ((arr bool) ((arr A_27a) ((arr A_27a) A_27a))))).
% 0.48/0.65 Parameter c_2Eoption_2EOPTION__MAP2:(del->(del->(del->fofType))).
% 0.48/0.65 Axiom mem_c_2Eoption_2EOPTION__MAP2:(forall (A_27a:del) (A_27b:del) (A_27c:del), ((mem (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) ((arr ((arr A_27b) ((arr A_27c) A_27a))) ((arr (ty_2Eoption_2Eoption A_27b)) ((arr (ty_2Eoption_2Eoption A_27c)) (ty_2Eoption_2Eoption A_27a)))))).
% 3.17/3.38 Parameter c_2Emin_2E_3D:(del->fofType).
% 3.17/3.38 Axiom mem_c_2Emin_2E_3D:(forall (A_27a:del), ((mem (c_2Emin_2E_3D A_27a)) ((arr A_27a) ((arr A_27a) bool)))).
% 3.17/3.38 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)))))).
% 3.17/3.38 Parameter c_2Ebool_2E_21:(del->fofType).
% 3.17/3.38 Axiom mem_c_2Ebool_2E_21:(forall (A_27a:del), ((mem (c_2Ebool_2E_21 A_27a)) ((arr ((arr A_27a) bool)) bool))).
% 3.17/3.38 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))))))).
% 3.17/3.38 Axiom conj_thm_2Ebool_2ETRUTH:True.
% 3.17/3.38 Axiom conj_thm_2Ebool_2EAND__CLAUSES:(forall (V0t:fofType), (((mem V0t) bool)->((and ((and ((and ((and ((iff ((and True) (p V0t))) (p V0t))) ((iff ((and (p V0t)) True)) (p V0t)))) ((iff ((and False) (p V0t))) False))) ((iff ((and (p V0t)) False)) False))) ((iff ((and (p V0t)) (p V0t))) (p V0t))))).
% 3.17/3.38 Axiom conj_thm_2Ebool_2EREFL__CLAUSE:(forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->((iff (((eq fofType) V0x) V0x)) True))).
% 3.17/3.38 Axiom conj_thm_2Ebool_2ECOND__CLAUSES:(forall (A_27a:del) (V0t1:fofType), (((mem V0t1) A_27a)->(forall (V1t2:fofType), (((mem V1t2) A_27a)->((and (((eq fofType) ((ap ((ap ((ap (c_2Ebool_2ECOND A_27a)) c_2Ebool_2ET)) V0t1)) V1t2)) V0t1)) (((eq fofType) ((ap ((ap ((ap (c_2Ebool_2ECOND A_27a)) c_2Ebool_2EF)) V0t1)) V1t2)) V1t2)))))).
% 3.17/3.38 Axiom conj_thm_2Eoption_2ESOME__11:(forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->(forall (V1y:fofType), (((mem V1y) A_27a)->((iff (((eq fofType) ((ap (c_2Eoption_2ESOME A_27a)) V0x)) ((ap (c_2Eoption_2ESOME A_27a)) V1y))) (((eq fofType) V0x) V1y)))))).
% 3.17/3.38 Axiom ax_thm_2Eoption_2EIS__SOME__DEF:(forall (A_27a:del), ((and (forall (V0x:fofType), (((mem V0x) A_27a)->((iff (p ((ap (c_2Eoption_2EIS__SOME A_27a)) ((ap (c_2Eoption_2ESOME A_27a)) V0x)))) True)))) ((iff (p ((ap (c_2Eoption_2EIS__SOME A_27a)) (c_2Eoption_2ENONE A_27a)))) False))).
% 3.17/3.38 Axiom ax_thm_2Eoption_2ETHE__DEF:(forall (A_27a:del) (V0x:fofType), (((mem V0x) A_27a)->(((eq fofType) ((ap (c_2Eoption_2ETHE A_27a)) ((ap (c_2Eoption_2ESOME A_27a)) V0x))) V0x))).
% 3.17/3.38 Axiom ax_thm_2Eoption_2EOPTION__MAP2__DEF:(forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr A_27b) ((arr A_27c) A_27a)))->(forall (V1x:fofType), (((mem V1x) (ty_2Eoption_2Eoption A_27b))->(forall (V2y:fofType), (((mem V2y) (ty_2Eoption_2Eoption A_27c))->(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) V1x)) V2y)) ((ap ((ap ((ap (c_2Ebool_2ECOND (ty_2Eoption_2Eoption A_27a))) ((ap ((ap c_2Ebool_2E_2F_5C) ((ap (c_2Eoption_2EIS__SOME A_27b)) V1x))) ((ap (c_2Eoption_2EIS__SOME A_27c)) V2y)))) ((ap (c_2Eoption_2ESOME A_27a)) ((ap ((ap V0f) ((ap (c_2Eoption_2ETHE A_27b)) V1x))) ((ap (c_2Eoption_2ETHE A_27c)) V2y))))) (c_2Eoption_2ENONE A_27a))))))))).
% 3.17/3.38 Trying to prove (forall (A_27a:del) (A_27b:del) (A_27c:del) (V0f:fofType), (((mem V0f) ((arr A_27b) ((arr A_27c) A_27a)))->(forall (V1x:fofType), (((mem V1x) A_27b)->(forall (V2y:fofType), (((mem V2y) A_27c)->((and ((and ((and (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) ((ap (c_2Eoption_2ESOME A_27b)) V1x))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) ((ap (c_2Eoption_2ESOME A_27a)) ((ap ((ap V0f) V1x)) V2y)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) ((ap (c_2Eoption_2ESOME A_27b)) V1x))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a)))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))))
% 3.17/3.38 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 3.17/3.38 Found (eq_ref0 b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 3.17/3.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 4.14/4.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 4.14/4.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 4.14/4.31 Found eq_ref00:=(eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))):(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 4.14/4.31 Found (eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 4.14/4.31 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 4.14/4.31 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 4.14/4.31 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 4.14/4.31 Found x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 4.14/4.31 Found (fun (x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))))=> x20) as proof of (P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 4.14/4.31 Found (fun (x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))))=> x20) as proof of (P0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 4.14/4.31 Found eq_ref00:=(eq_ref0 (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):(((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))
% 4.14/4.31 Found (eq_ref0 (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of (((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) b)
% 4.14/4.31 Found ((eq_ref Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of (((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) b)
% 4.14/4.31 Found ((eq_ref Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of (((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) b)
% 14.39/14.57 Found ((eq_ref Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of (((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) b)
% 14.39/14.57 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 14.39/14.57 Found (eq_ref0 b) as proof of (((eq fofType) b) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 14.39/14.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 14.39/14.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 14.39/14.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 14.39/14.57 Found eq_ref00:=(eq_ref0 (c_2Eoption_2ENONE A_27a)):(((eq fofType) (c_2Eoption_2ENONE A_27a)) (c_2Eoption_2ENONE A_27a))
% 14.39/14.57 Found (eq_ref0 (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 14.39/14.57 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 14.39/14.57 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 14.39/14.57 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 14.39/14.57 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 14.39/14.57 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 14.39/14.57 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 14.39/14.57 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 14.39/14.57 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 14.39/14.57 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 28.69/28.86 Found eq_ref00:=(eq_ref0 (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))):(((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a)))
% 28.69/28.86 Found (eq_ref0 (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) as proof of (((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) b)
% 28.69/28.86 Found ((eq_ref Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) as proof of (((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) b)
% 28.69/28.86 Found ((eq_ref Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) as proof of (((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) b)
% 28.69/28.86 Found ((eq_ref Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) as proof of (((eq Prop) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) (c_2Eoption_2ENONE A_27a))) b)
% 28.69/28.86 Found x2:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 28.69/28.86 Instantiate: b:=((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)):fofType
% 28.69/28.86 Found x2 as proof of (P0 b)
% 28.69/28.86 Found eq_ref00:=(eq_ref0 (c_2Eoption_2ENONE A_27a)):(((eq fofType) (c_2Eoption_2ENONE A_27a)) (c_2Eoption_2ENONE A_27a))
% 28.69/28.86 Found (eq_ref0 (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 28.69/28.86 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 28.69/28.86 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 28.69/28.86 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 28.69/28.86 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 28.69/28.86 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 28.69/28.86 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 34.51/34.69 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.51/34.69 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.51/34.69 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.51/34.69 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 34.51/34.69 Found (eq_ref0 b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 34.51/34.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 34.51/34.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 34.51/34.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 34.51/34.69 Found eq_ref00:=(eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))):(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y)))
% 34.51/34.69 Found (eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) b)
% 34.51/34.69 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) b)
% 34.51/34.69 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) b)
% 34.51/34.69 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))) b)
% 34.51/34.69 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 34.81/35.04 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 34.81/35.04 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 34.81/35.04 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.81/35.04 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.81/35.04 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.81/35.04 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.81/35.04 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.81/35.04 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 34.81/35.04 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 34.81/35.04 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 44.05/44.24 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 44.05/44.24 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 44.05/44.24 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 44.05/44.24 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 44.05/44.24 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 44.05/44.24 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 44.05/44.24 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 44.05/44.24 Found x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y)))
% 44.05/44.24 Found (fun (x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))))=> x20) as proof of (P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y)))
% 44.05/44.24 Found (fun (x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y))))=> x20) as proof of (P0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) ((ap (c_2Eoption_2ESOME A_27c)) V2y)))
% 44.05/44.24 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 82.11/82.29 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 82.11/82.29 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 82.11/82.29 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 82.11/82.29 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 82.11/82.29 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 82.11/82.29 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 82.11/82.29 Found (eq_ref0 b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 82.11/82.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 82.11/82.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 82.11/82.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 82.11/82.29 Found eq_ref00:=(eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))):(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 82.11/82.29 Found (eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 82.11/82.29 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 82.11/82.29 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 82.11/82.29 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 105.84/106.03 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 105.84/106.03 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 105.84/106.03 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 105.84/106.03 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 105.84/106.03 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 105.84/106.03 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 105.84/106.03 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 105.84/106.03 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 105.84/106.04 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 105.84/106.04 Found eq_ref00:=(eq_ref0 (c_2Eoption_2ENONE A_27a)):(((eq fofType) (c_2Eoption_2ENONE A_27a)) (c_2Eoption_2ENONE A_27a))
% 105.84/106.04 Found (eq_ref0 (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 107.17/107.35 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 107.17/107.35 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 107.17/107.35 Found ((eq_ref fofType) (c_2Eoption_2ENONE A_27a)) as proof of (((eq fofType) (c_2Eoption_2ENONE A_27a)) b)
% 107.17/107.35 Found x2:(P0 b)
% 107.17/107.35 Instantiate: b:=((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)):fofType
% 107.17/107.35 Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 107.17/107.35 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))))
% 107.17/107.35 Found (fun (P0:(fofType->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 107.17/107.35 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 107.17/107.35 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 107.17/107.35 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 107.17/107.35 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.17/107.35 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.17/107.35 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.17/107.35 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 107.17/107.35 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 107.82/108.00 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 107.82/108.00 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.82/108.00 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.82/108.00 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.82/108.00 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.82/108.00 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.82/108.00 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 107.82/108.00 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 107.82/108.00 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 107.82/108.00 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.14/108.33 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.14/108.33 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.14/108.33 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.14/108.33 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.14/108.33 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.14/108.33 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.14/108.33 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.14/108.33 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.14/108.33 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.99/109.17 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.99/109.17 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.99/109.17 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 108.99/109.17 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.99/109.17 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.99/109.17 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.99/109.17 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.99/109.17 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.99/109.17 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 108.99/109.17 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.18/109.40 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.18/109.40 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.18/109.40 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 109.18/109.40 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 109.18/109.40 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 109.18/109.40 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.18/109.40 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.18/109.40 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.18/109.40 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.18/109.40 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.47/109.70 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.47/109.70 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.47/109.70 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.47/109.70 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 109.47/109.70 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 109.47/109.70 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 109.47/109.70 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 109.47/109.70 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 109.47/109.70 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 120.28/120.52 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 120.28/120.52 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 120.28/120.52 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 120.28/120.52 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 120.28/120.52 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 120.28/120.52 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 120.28/120.52 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 120.28/120.52 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 120.28/120.52 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 120.28/120.52 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 129.10/129.29 Found stp_inj_surj_o0:=(stp_inj_surj_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):(((eq Prop) (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))
% 129.10/129.29 Instantiate: b:=(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)):Prop
% 129.10/129.29 Found stp_inj_surj_o0 as proof of (((eq Prop) (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) b)
% 129.10/129.29 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 129.10/129.29 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (c_2Eoption_2ENONE A_27a))
% 129.10/129.29 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (c_2Eoption_2ENONE A_27a))
% 129.10/129.29 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (c_2Eoption_2ENONE A_27a))
% 129.10/129.29 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (c_2Eoption_2ENONE A_27a))
% 129.10/129.29 Found eq_ref00:=(eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))):(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 129.10/129.29 Found (eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b0)
% 129.10/129.29 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b0)
% 129.10/129.29 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b0)
% 129.10/129.29 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b0)
% 129.10/129.29 Found x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 129.10/129.29 Found (fun (x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))))=> x20) as proof of (P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 129.10/129.29 Found (fun (x20:(P ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))))=> x20) as proof of (P0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 129.10/129.29 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 129.10/129.29 Found (eq_ref0 b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 129.10/129.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 139.47/139.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 139.47/139.69 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (c_2Eoption_2ENONE A_27a))
% 139.47/139.69 Found eq_ref00:=(eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))):(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 139.47/139.69 Found (eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 139.47/139.69 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 139.47/139.69 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 139.47/139.69 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 139.47/139.69 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 139.47/139.69 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 139.47/139.69 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 139.47/139.69 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 139.47/139.69 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 139.47/139.69 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 140.02/140.20 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 140.02/140.20 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 140.02/140.20 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 140.02/140.20 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 140.02/140.20 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 140.02/140.20 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 140.02/140.20 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 140.02/140.20 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 140.02/140.20 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 140.52/140.75 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 140.52/140.75 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 140.52/140.75 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 140.52/140.75 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 140.52/140.75 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 140.52/140.75 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 140.52/140.75 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 140.52/140.75 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 140.52/140.75 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 140.52/140.75 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.17/141.36 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.17/141.36 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.17/141.36 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.17/141.36 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.17/141.36 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.17/141.36 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.17/141.36 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.17/141.36 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.17/141.36 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.17/141.36 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.51/141.70 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.51/141.70 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.51/141.70 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.51/141.70 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.51/141.70 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.51/141.70 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.51/141.70 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 141.51/141.70 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.51/141.70 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.51/141.70 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 141.82/142.02 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 141.82/142.02 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 141.82/142.02 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 141.82/142.02 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 141.82/142.02 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 141.82/142.02 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 141.82/142.02 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 141.82/142.02 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 141.82/142.02 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 206.17/206.37 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 206.17/206.37 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 206.17/206.37 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 206.17/206.37 Found x2:(P (c_2Eoption_2ENONE A_27a))
% 206.17/206.37 Instantiate: b:=(c_2Eoption_2ENONE A_27a):fofType
% 206.17/206.37 Found x2 as proof of (P0 b)
% 206.17/206.37 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 206.17/206.37 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 206.17/206.37 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 206.17/206.37 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))):((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 206.17/206.37 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 206.17/206.37 Found (stp_inj_mem_o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))) bool)
% 206.17/206.37 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 296.66/296.93 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 296.66/296.93 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 296.66/296.93 Found eq_ref00:=(eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))):(((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c)))
% 296.66/296.93 Found (eq_ref0 ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 296.66/296.93 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 296.66/296.93 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 296.66/296.93 Found ((eq_ref fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) as proof of (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) b)
% 296.66/296.93 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 296.66/296.93 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 296.66/296.93 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 296.66/296.93 Found eq_ref00:=(eq_ref0 a):(((eq del) a) a)
% 296.66/296.93 Found (eq_ref0 a) as proof of (((eq del) a) A_27a)
% 299.28/299.47 Found ((eq_ref del) a) as proof of (((eq del) a) A_27a)
% 299.28/299.47 Found ((eq_ref del) a) as proof of (((eq del) a) A_27a)
% 299.28/299.47 Found ((eq_ref del) a) as proof of (((eq del) a) A_27a)
% 299.28/299.47 Found stp_inj_mem_o0:=(stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))):((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 299.28/299.47 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 299.28/299.47 Found (stp_inj_mem_o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))) as proof of ((mem (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))) bool)
% 299.28/299.48 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))):((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 299.28/299.48 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 299.28/299.48 Found (stp_inj_mem_o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))) as proof of ((mem (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))) bool)
% 299.28/299.48 Found stp_inj_mem_o0:=(stp_inj_mem_o (p (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))))):((mem (inj__o (p (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))))) bool)
% 299.28/299.48 Found (stp_inj_mem_o (p (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))))) bool)
% 299.28/299.48 Found (stp_inj_mem_o (p (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a))))))))) as proof of ((mem (inj__o (p (inj__o (p (inj__o (p (inj__o (((eq fofType) ((ap ((ap ((ap (((c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) (c_2Eoption_2ENONE A_27b))) (c_2Eoption_2ENONE A_27c))) (c_2Eoption_2ENONE A_27a)))))))))) bool)
% 299.28/299.48 Found stp_inj_mem_o0:=(stp
%------------------------------------------------------------------------------