include('Axioms/HL4001^2.ax').
thf(tp_c_2Ebool_2E_3F,type,(c_2Ebool_2E_3F:(del>$i))).
thf(mem_c_2Ebool_2E_3F,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2E_3F@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(ax_ex_p,axiom,( ! [A:del] : ( ! [Q:$i] : ((mem@Q@(arr@A@bool)) => ((p@(ap@(c_2Ebool_2E_3F@A)@Q)) <=> (? [X:$i] : ((mem@X@A) & (p@(ap@Q@X))))))))).
thf(tp_ty_2Enum_2Enum,type,( ty_2Enum_2Enum:del )).
thf(stp_ty_2Enum_2Enum,type,(tp__ty_2Enum_2Enum : $tType)).
thf(stp_inj_ty_2Enum_2Enum,type,(inj__ty_2Enum_2Enum : (tp__ty_2Enum_2Enum > $i))).
thf(stp_surj_ty_2Enum_2Enum,type,(surj__ty_2Enum_2Enum : ($i > tp__ty_2Enum_2Enum))).
thf(stp_inj_surj_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X)) = X))).
thf(stp_inj_mem_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : (mem @ (inj__ty_2Enum_2Enum @ X) @ ty_2Enum_2Enum))).
thf(stp_iso_mem_ty_2Enum_2Enum,axiom,( ! [X:$i] : ((mem @ X @ ty_2Enum_2Enum) => (X = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Earithmetic_2EDIV,type,(c_2Earithmetic_2EDIV:$i)).
thf(mem_c_2Earithmetic_2EDIV,axiom,(mem@c_2Earithmetic_2EDIV@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EDIV,type,(fo__c_2Earithmetic_2EDIV:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EDIV,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EDIV @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EDIV @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_ty_2Efcp_2Ecart,type,( ty_2Efcp_2Ecart: del > del >del )).
thf(tp_ty_2Ebinary__ieee_2Efloat,type,( ty_2Ebinary__ieee_2Efloat: del > del >del )).
thf(tp_c_2Ebinary__ieee_2Efloat__Significand,type,(c_2Ebinary__ieee_2Efloat__Significand:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__Significand,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Exponent,type,(c_2Ebinary__ieee_2Efloat__Exponent:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__Exponent,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Efcp_2Ecart@bool@A_27w)))))).
thf(tp_c_2Ebool_2EARB,type,(c_2Ebool_2EARB:(del>$i))).
thf(mem_c_2Ebool_2EARB,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2EARB@A_27a)@A_27a))).
thf(tp_c_2Ebinary__ieee_2Efloat__Significand__fupd,type,(c_2Ebinary__ieee_2Efloat__Significand__fupd:(del>(del>(del>$i))))).
thf(mem_c_2Ebinary__ieee_2Efloat__Significand__fupd,axiom,( ! [A_27t:del] : ( ! [A_27u:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@(arr@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27u@A_27w)))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Exponent__fupd,type,(c_2Ebinary__ieee_2Efloat__Exponent__fupd:(del>(del>(del>$i))))).
thf(mem_c_2Ebinary__ieee_2Efloat__Exponent__fupd,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : ( ! [A_27x:del] : (mem@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@(arr@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27x)))))))).
thf(tp_ty_2Eone_2Eone,type,( ty_2Eone_2Eone:del )).
thf(stp_ty_2Eone_2Eone,type,(tp__ty_2Eone_2Eone : $tType)).
thf(stp_inj_ty_2Eone_2Eone,type,(inj__ty_2Eone_2Eone : (tp__ty_2Eone_2Eone > $i))).
thf(stp_surj_ty_2Eone_2Eone,type,(surj__ty_2Eone_2Eone : ($i > tp__ty_2Eone_2Eone))).
thf(stp_inj_surj_ty_2Eone_2Eone,axiom,( ! [X:tp__ty_2Eone_2Eone] : ((surj__ty_2Eone_2Eone @ (inj__ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_ty_2Eone_2Eone,axiom,( ! [X:tp__ty_2Eone_2Eone] : (mem @ (inj__ty_2Eone_2Eone @ X) @ ty_2Eone_2Eone))).
thf(stp_iso_mem_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ ty_2Eone_2Eone) => (X = (inj__ty_2Eone_2Eone @ (surj__ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)))).
thf(stp_iso_mem_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)) => (X = (inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Sign__fupd,type,(c_2Ebinary__ieee_2Efloat__Sign__fupd:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__Sign__fupd,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@(arr@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__negate,type,(c_2Ebinary__ieee_2Efloat__negate:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__negate,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__negate@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_ty_2Elist_2Elist,type,( ty_2Elist_2Elist: del >del )).
thf(tp_c_2Elist_2ENIL,type,(c_2Elist_2ENIL:(del>$i))).
thf(mem_c_2Elist_2ENIL,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ENIL@A_27a)@(ty_2Elist_2Elist@A_27a)))).
thf(tp_c_2Elist_2ECONS,type,(c_2Elist_2ECONS:(del>$i))).
thf(mem_c_2Elist_2ECONS,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ECONS@A_27a)@(arr@A_27a@(arr@(ty_2Elist_2Elist@A_27a)@(ty_2Elist_2Elist@A_27a)))))).
thf(tp_ty_2Ebinary__ieee_2Eflags,type,( ty_2Ebinary__ieee_2Eflags:del )).
thf(stp_ty_2Ebinary__ieee_2Eflags,type,(tp__ty_2Ebinary__ieee_2Eflags : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Eflags,type,(inj__ty_2Ebinary__ieee_2Eflags : (tp__ty_2Ebinary__ieee_2Eflags > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Eflags,type,(surj__ty_2Ebinary__ieee_2Eflags : ($i > tp__ty_2Ebinary__ieee_2Eflags))).
thf(stp_inj_surj_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Eflags] : ((surj__ty_2Ebinary__ieee_2Eflags @ (inj__ty_2Ebinary__ieee_2Eflags @ X)) = X))).
thf(stp_inj_mem_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Eflags] : (mem @ (inj__ty_2Ebinary__ieee_2Eflags @ X) @ ty_2Ebinary__ieee_2Eflags))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Eflags) => (X = (inj__ty_2Ebinary__ieee_2Eflags @ (surj__ty_2Ebinary__ieee_2Eflags @ X)))))).
thf(tp_c_2Ebinary__ieee_2Echeck__for__signalling,type,(c_2Ebinary__ieee_2Echeck__for__signalling:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Echeck__for__signalling,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ebinary__ieee_2Echeck__for__signalling@A_27a@A_27b)@(arr@(ty_2Elist_2Elist@(ty_2Ebinary__ieee_2Efloat@A_27a@A_27b))@ty_2Ebinary__ieee_2Eflags))))).
thf(tp_c_2Ebinary__ieee_2Eclear__flags,type,(c_2Ebinary__ieee_2Eclear__flags:$i)).
thf(mem_c_2Ebinary__ieee_2Eclear__flags,axiom,(mem@c_2Ebinary__ieee_2Eclear__flags@ty_2Ebinary__ieee_2Eflags)).
thf(stp_fo_c_2Ebinary__ieee_2Eclear__flags,type,(fo__c_2Ebinary__ieee_2Eclear__flags:tp__ty_2Ebinary__ieee_2Eflags)).
thf(stp_eq_fo_c_2Ebinary__ieee_2Eclear__flags,axiom,((inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Eclear__flags) = c_2Ebinary__ieee_2Eclear__flags)).
thf(tp_ty_2Epair_2Eprod,type,( ty_2Epair_2Eprod: del > del >del )).
thf(tp_ty_2Erealax_2Ereal,type,( ty_2Erealax_2Ereal:del )).
thf(stp_ty_2Erealax_2Ereal,type,(tp__ty_2Erealax_2Ereal : $tType)).
thf(stp_inj_ty_2Erealax_2Ereal,type,(inj__ty_2Erealax_2Ereal : (tp__ty_2Erealax_2Ereal > $i))).
thf(stp_surj_ty_2Erealax_2Ereal,type,(surj__ty_2Erealax_2Ereal : ($i > tp__ty_2Erealax_2Ereal))).
thf(stp_inj_surj_ty_2Erealax_2Ereal,axiom,( ! [X:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (inj__ty_2Erealax_2Ereal @ X)) = X))).
thf(stp_inj_mem_ty_2Erealax_2Ereal,axiom,( ! [X:tp__ty_2Erealax_2Ereal] : (mem @ (inj__ty_2Erealax_2Ereal @ X) @ ty_2Erealax_2Ereal))).
thf(stp_iso_mem_ty_2Erealax_2Ereal,axiom,( ! [X:$i] : ((mem @ X @ ty_2Erealax_2Ereal) => (X = (inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X)))))).
thf(tp_ty_2Ebinary__ieee_2Erounding,type,( ty_2Ebinary__ieee_2Erounding:del )).
thf(stp_ty_2Ebinary__ieee_2Erounding,type,(tp__ty_2Ebinary__ieee_2Erounding : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Erounding,type,(inj__ty_2Ebinary__ieee_2Erounding : (tp__ty_2Ebinary__ieee_2Erounding > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Erounding,type,(surj__ty_2Ebinary__ieee_2Erounding : ($i > tp__ty_2Ebinary__ieee_2Erounding))).
thf(stp_inj_surj_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Erounding] : ((surj__ty_2Ebinary__ieee_2Erounding @ (inj__ty_2Ebinary__ieee_2Erounding @ X)) = X))).
thf(stp_inj_mem_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Erounding] : (mem @ (inj__ty_2Ebinary__ieee_2Erounding @ X) @ ty_2Ebinary__ieee_2Erounding))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Erounding) => (X = (inj__ty_2Ebinary__ieee_2Erounding @ (surj__ty_2Ebinary__ieee_2Erounding @ X)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__round__with__flags,type,(c_2Ebinary__ieee_2Efloat__round__with__flags:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__round__with__flags,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__round__with__flags@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@bool@(arr@ty_2Erealax_2Ereal@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Sign,type,(c_2Ebinary__ieee_2Efloat__Sign:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__Sign,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)))))).
thf(tp_c_2Ebinary__ieee_2Edividezero__flags,type,(c_2Ebinary__ieee_2Edividezero__flags:$i)).
thf(mem_c_2Ebinary__ieee_2Edividezero__flags,axiom,(mem@c_2Ebinary__ieee_2Edividezero__flags@ty_2Ebinary__ieee_2Eflags)).
thf(stp_fo_c_2Ebinary__ieee_2Edividezero__flags,type,(fo__c_2Ebinary__ieee_2Edividezero__flags:tp__ty_2Ebinary__ieee_2Eflags)).
thf(stp_eq_fo_c_2Ebinary__ieee_2Edividezero__flags,axiom,((inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Edividezero__flags) = c_2Ebinary__ieee_2Edividezero__flags)).
thf(tp_ty_2Ebinary__ieee_2Efp__op,type,( ty_2Ebinary__ieee_2Efp__op: del > del >del )).
thf(tp_c_2Ebinary__ieee_2EFP__Div,type,(c_2Ebinary__ieee_2EFP__Div:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2EFP__Div,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2EFP__Div@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efp__op@A_27t@A_27w)))))))).
thf(tp_c_2Ebinary__ieee_2Einvalidop__flags,type,(c_2Ebinary__ieee_2Einvalidop__flags:$i)).
thf(mem_c_2Ebinary__ieee_2Einvalidop__flags,axiom,(mem@c_2Ebinary__ieee_2Einvalidop__flags@ty_2Ebinary__ieee_2Eflags)).
thf(stp_fo_c_2Ebinary__ieee_2Einvalidop__flags,type,(fo__c_2Ebinary__ieee_2Einvalidop__flags:tp__ty_2Ebinary__ieee_2Eflags)).
thf(stp_eq_fo_c_2Ebinary__ieee_2Einvalidop__flags,axiom,((inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Einvalidop__flags) = c_2Ebinary__ieee_2Einvalidop__flags)).
thf(tp_ty_2Ebinary__ieee_2Efloat__value,type,( ty_2Ebinary__ieee_2Efloat__value:del )).
thf(stp_ty_2Ebinary__ieee_2Efloat__value,type,(tp__ty_2Ebinary__ieee_2Efloat__value : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Efloat__value,type,(inj__ty_2Ebinary__ieee_2Efloat__value : (tp__ty_2Ebinary__ieee_2Efloat__value > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Efloat__value,type,(surj__ty_2Ebinary__ieee_2Efloat__value : ($i > tp__ty_2Ebinary__ieee_2Efloat__value))).
thf(stp_inj_surj_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Efloat__value] : ((surj__ty_2Ebinary__ieee_2Efloat__value @ (inj__ty_2Ebinary__ieee_2Efloat__value @ X)) = X))).
thf(stp_inj_mem_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Efloat__value] : (mem @ (inj__ty_2Ebinary__ieee_2Efloat__value @ X) @ ty_2Ebinary__ieee_2Efloat__value))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Efloat__value) => (X = (inj__ty_2Ebinary__ieee_2Efloat__value @ (surj__ty_2Ebinary__ieee_2Efloat__value @ X)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__value__CASE,type,(c_2Ebinary__ieee_2Efloat__value__CASE:(del>$i))).
thf(mem_c_2Ebinary__ieee_2Efloat__value__CASE,axiom,( ! [A_27a:del] : (mem@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(arr@ty_2Ebinary__ieee_2Efloat__value@(arr@(arr@ty_2Erealax_2Ereal@A_27a)@(arr@A_27a@(arr@A_27a@A_27a))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__div,type,(c_2Ebinary__ieee_2Efloat__div:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__div,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__div@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))))).
thf(tp_c_2Erealax_2Ereal__neg,type,(c_2Erealax_2Ereal__neg:$i)).
thf(mem_c_2Erealax_2Ereal__neg,axiom,(mem@c_2Erealax_2Ereal__neg@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Erealax_2Ereal__neg,type,(fo__c_2Erealax_2Ereal__neg:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Erealax_2Ereal__neg,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Erealax_2Ereal__neg @ X0)) = (ap @ c_2Erealax_2Ereal__neg @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_ty_2Ebool_2Eitself,type,( ty_2Ebool_2Eitself: del >del )).
thf(tp_c_2Ebinary__ieee_2Efloat__minus__min,type,(c_2Ebinary__ieee_2Efloat__minus__min:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__minus__min,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__minus__min@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ewords_2EINT__MAX,type,(c_2Ewords_2EINT__MAX:(del>$i))).
thf(mem_c_2Ewords_2EINT__MAX,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2EINT__MAX@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Ereal_2Epow,type,(c_2Ereal_2Epow:$i)).
thf(mem_c_2Ereal_2Epow,axiom,(mem@c_2Ereal_2Epow@(arr@ty_2Erealax_2Ereal@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Epow,type,(fo__c_2Ereal_2Epow:(tp__ty_2Erealax_2Ereal > (tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Epow,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Epow @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Epow @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ereal_2E_2F,type,(c_2Ereal_2E_2F:$i)).
thf(mem_c_2Ereal_2E_2F,axiom,(mem@c_2Ereal_2E_2F@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2E_2F,type,(fo__c_2Ereal_2E_2F:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2E_2F,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2E_2F @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2E_2F @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__min,type,(c_2Ebinary__ieee_2Efloat__plus__min:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__plus__min,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__plus__min@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__minus__zero,type,(c_2Ebinary__ieee_2Efloat__minus__zero:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__minus__zero,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__minus__zero@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ereal_2Ereal__of__num,type,(c_2Ereal_2Ereal__of__num:$i)).
thf(mem_c_2Ereal_2Ereal__of__num,axiom,(mem@c_2Ereal_2Ereal__of__num@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Ereal_2Ereal__of__num,type,(fo__c_2Ereal_2Ereal__of__num:(tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Ereal_2Ereal__of__num @ X0)) = (ap @ c_2Ereal_2Ereal__of__num @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ebinary__ieee_2EFloat,type,(c_2Ebinary__ieee_2EFloat:$i)).
thf(mem_c_2Ebinary__ieee_2EFloat,axiom,(mem@c_2Ebinary__ieee_2EFloat@(arr@ty_2Erealax_2Ereal@ty_2Ebinary__ieee_2Efloat__value))).
thf(stp_fo_c_2Ebinary__ieee_2EFloat,type,(fo__c_2Ebinary__ieee_2EFloat:(tp__ty_2Erealax_2Ereal > tp__ty_2Ebinary__ieee_2Efloat__value))).
thf(stp_eq_fo_c_2Ebinary__ieee_2EFloat,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Ebinary__ieee_2Efloat__value @ (fo__c_2Ebinary__ieee_2EFloat @ X0)) = (ap @ c_2Ebinary__ieee_2EFloat @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__zero,type,(c_2Ebinary__ieee_2Efloat__plus__zero:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__plus__zero,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__plus__zero@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2ENaN,type,(c_2Ebinary__ieee_2ENaN:$i)).
thf(mem_c_2Ebinary__ieee_2ENaN,axiom,(mem@c_2Ebinary__ieee_2ENaN@ty_2Ebinary__ieee_2Efloat__value)).
thf(stp_fo_c_2Ebinary__ieee_2ENaN,type,(fo__c_2Ebinary__ieee_2ENaN:tp__ty_2Ebinary__ieee_2Efloat__value)).
thf(stp_eq_fo_c_2Ebinary__ieee_2ENaN,axiom,((inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2ENaN) = c_2Ebinary__ieee_2ENaN)).
thf(tp_c_2Ebinary__ieee_2Efloat__some__qnan,type,(c_2Ebinary__ieee_2Efloat__some__qnan:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__some__qnan,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__some__qnan@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efp__op@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__minus__infinity,type,(c_2Ebinary__ieee_2Efloat__minus__infinity:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__minus__infinity,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__minus__infinity@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2EInfinity,type,(c_2Ebinary__ieee_2EInfinity:$i)).
thf(mem_c_2Ebinary__ieee_2EInfinity,axiom,(mem@c_2Ebinary__ieee_2EInfinity@ty_2Ebinary__ieee_2Efloat__value)).
thf(stp_fo_c_2Ebinary__ieee_2EInfinity,type,(fo__c_2Ebinary__ieee_2EInfinity:tp__ty_2Ebinary__ieee_2Efloat__value)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EInfinity,axiom,((inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2EInfinity) = c_2Ebinary__ieee_2EInfinity)).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__infinity,type,(c_2Ebinary__ieee_2Efloat__plus__infinity:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__plus__infinity,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__value,type,(c_2Ebinary__ieee_2Efloat__value:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__value,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@ty_2Ebinary__ieee_2Efloat__value))))).
thf(tp_c_2Ebool_2ELET,type,(c_2Ebool_2ELET:(del>(del>$i)))).
thf(mem_c_2Ebool_2ELET,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ebool_2ELET@A_27a@A_27b)@(arr@(arr@A_27a@A_27b)@(arr@A_27a@A_27b)))))).
thf(tp_c_2Ecombin_2EI,type,(c_2Ecombin_2EI:(del>$i))).
thf(mem_c_2Ecombin_2EI,axiom,( ! [A_27a:del] : (mem@(c_2Ecombin_2EI@A_27a)@(arr@A_27a@A_27a)))).
thf(tp_c_2Ecombin_2EK,type,(c_2Ecombin_2EK:(del>(del>$i)))).
thf(mem_c_2Ecombin_2EK,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ecombin_2EK@A_27a@A_27b)@(arr@A_27a@(arr@A_27b@A_27a)))))).
thf(tp_c_2Ecombin_2Eo,type,(c_2Ecombin_2Eo:(del>(del>(del>$i))))).
thf(mem_c_2Ecombin_2Eo,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : (mem@(c_2Ecombin_2Eo@A_27a@A_27b@A_27c)@(arr@(arr@A_27c@A_27b)@(arr@(arr@A_27a@A_27c)@(arr@A_27a@A_27b)))))))).
thf(tp_c_2Earithmetic_2E_3E_3D,type,(c_2Earithmetic_2E_3E_3D:$i)).
thf(mem_c_2Earithmetic_2E_3E_3D,axiom,(mem@c_2Earithmetic_2E_3E_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Earithmetic_2E_3E,type,(c_2Earithmetic_2E_3E:$i)).
thf(mem_c_2Earithmetic_2E_3E,axiom,(mem@c_2Earithmetic_2E_3E@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Eprim__rec_2EPRE,type,(c_2Eprim__rec_2EPRE:$i)).
thf(mem_c_2Eprim__rec_2EPRE,axiom,(mem@c_2Eprim__rec_2EPRE@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eprim__rec_2EPRE,type,(fo__c_2Eprim__rec_2EPRE:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eprim__rec_2EPRE @ X0)) = (ap @ c_2Eprim__rec_2EPRE @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2EEXP,type,(c_2Earithmetic_2EEXP:$i)).
thf(mem_c_2Earithmetic_2EEXP,axiom,(mem@c_2Earithmetic_2EEXP@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EEXP,type,(fo__c_2Earithmetic_2EEXP:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EEXP,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EEXP @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EEXP @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2E_2A,type,(c_2Earithmetic_2E_2A:$i)).
thf(mem_c_2Earithmetic_2E_2A,axiom,(mem@c_2Earithmetic_2E_2A@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2A,type,(fo__c_2Earithmetic_2E_2A:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2A,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2A @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Enumeral_2EiiSUC,type,(c_2Enumeral_2EiiSUC:$i)).
thf(mem_c_2Enumeral_2EiiSUC,axiom,(mem@c_2Enumeral_2EiiSUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiiSUC,type,(fo__c_2Enumeral_2EiiSUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiiSUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiiSUC @ X0)) = (ap @ c_2Enumeral_2EiiSUC @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2E_2B,type,(c_2Earithmetic_2E_2B:$i)).
thf(mem_c_2Earithmetic_2E_2B,axiom,(mem@c_2Earithmetic_2E_2B@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2B,type,(fo__c_2Earithmetic_2E_2B:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2B @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Enumeral_2EiZ,type,(c_2Enumeral_2EiZ:$i)).
thf(mem_c_2Enumeral_2EiZ,axiom,(mem@c_2Enumeral_2EiZ@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiZ,type,(fo__c_2Enumeral_2EiZ:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiZ,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiZ @ X0)) = (ap @ c_2Enumeral_2EiZ @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2E_3C_3D,type,(c_2Earithmetic_2E_3C_3D:$i)).
thf(mem_c_2Earithmetic_2E_3C_3D,axiom,(mem@c_2Earithmetic_2E_3C_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Enumeral_2EiDUB,type,(c_2Enumeral_2EiDUB:$i)).
thf(mem_c_2Enumeral_2EiDUB,axiom,(mem@c_2Enumeral_2EiDUB@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiDUB,type,(fo__c_2Enumeral_2EiDUB:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiDUB,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiDUB @ X0)) = (ap @ c_2Enumeral_2EiDUB @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral_2EiSUB,type,(c_2Enumeral_2EiSUB:$i)).
thf(mem_c_2Enumeral_2EiSUB,axiom,(mem@c_2Enumeral_2EiSUB@(arr@bool@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))))).
thf(tp_c_2Ebool_2ECOND,type,(c_2Ebool_2ECOND:(del>$i))).
thf(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2ECOND@A_27a)@(arr@bool@(arr@A_27a@(arr@A_27a@A_27a)))))).
thf(tp_c_2Earithmetic_2EEVEN,type,(c_2Earithmetic_2EEVEN:$i)).
thf(mem_c_2Earithmetic_2EEVEN,axiom,(mem@c_2Earithmetic_2EEVEN@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Earithmetic_2EDIV2,type,(c_2Earithmetic_2EDIV2:$i)).
thf(mem_c_2Earithmetic_2EDIV2,axiom,(mem@c_2Earithmetic_2EDIV2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EDIV2,type,(fo__c_2Earithmetic_2EDIV2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EDIV2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EDIV2 @ X0)) = (ap @ c_2Earithmetic_2EDIV2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2EODD,type,(c_2Earithmetic_2EODD:$i)).
thf(mem_c_2Earithmetic_2EODD,axiom,(mem@c_2Earithmetic_2EODD@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Enum_2ESUC,type,(c_2Enum_2ESUC:$i)).
thf(mem_c_2Enum_2ESUC,axiom,(mem@c_2Enum_2ESUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enum_2ESUC,type,(fo__c_2Enum_2ESUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enum_2ESUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X0)) = (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ebool_2ET,type,(c_2Ebool_2ET:$i)).
thf(mem_c_2Ebool_2ET,axiom,(mem@c_2Ebool_2ET@bool)).
thf(ax_true_p,axiom,(p@c_2Ebool_2ET)).
thf(tp_c_2Epair_2E_2C,type,(c_2Epair_2E_2C:(del>(del>$i)))).
thf(mem_c_2Epair_2E_2C,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epair_2E_2C@A_27a@A_27b)@(arr@A_27a@(arr@A_27b@(ty_2Epair_2Eprod@A_27a@A_27b))))))).
thf(tp_c_2Epair_2Epair__CASE,type,(c_2Epair_2Epair__CASE:(del>(del>(del>$i))))).
thf(mem_c_2Epair_2Epair__CASE,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : (mem@(c_2Epair_2Epair__CASE@A_27a@A_27b@A_27c)@(arr@(ty_2Epair_2Eprod@A_27b@A_27c)@(arr@(arr@A_27b@(arr@A_27c@A_27a))@A_27a))))))).
thf(tp_c_2Ebool_2EF,type,(c_2Ebool_2EF:$i)).
thf(mem_c_2Ebool_2EF,axiom,(mem@c_2Ebool_2EF@bool)).
thf(ax_false_p,axiom,(~ (p@c_2Ebool_2EF))).
thf(tp_c_2Ebool_2E_5C_2F,type,(c_2Ebool_2E_5C_2F:$i)).
thf(mem_c_2Ebool_2E_5C_2F,axiom,(mem@c_2Ebool_2E_5C_2F@(arr@bool@(arr@bool@bool)))).
thf(ax_or_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Ebool_2E_5C_2F@Q)@R)) <=> ((p@Q) | (p@R)))))))).
thf(tp_c_2Ebool_2E_7E,type,(c_2Ebool_2E_7E:$i)).
thf(mem_c_2Ebool_2E_7E,axiom,(mem@c_2Ebool_2E_7E@(arr@bool@bool))).
thf(ax_neg_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ((p@(ap@c_2Ebool_2E_7E@Q)) <=> (~ (p@Q)))))).
thf(tp_c_2Emin_2E_3D_3D_3E,type,(c_2Emin_2E_3D_3D_3E:$i)).
thf(mem_c_2Emin_2E_3D_3D_3E,axiom,(mem@c_2Emin_2E_3D_3D_3E@(arr@bool@(arr@bool@bool)))).
thf(ax_imp_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Emin_2E_3D_3D_3E@Q)@R)) <=> ((p@Q) => (p@R)))))))).
thf(tp_c_2Ewords_2EUINT__MAX,type,(c_2Ewords_2EUINT__MAX:(del>$i))).
thf(mem_c_2Ewords_2EUINT__MAX,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2EUINT__MAX@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Eprim__rec_2E_3C,type,(c_2Eprim__rec_2E_3C:$i)).
thf(mem_c_2Eprim__rec_2E_3C,axiom,(mem@c_2Eprim__rec_2E_3C@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Ewords_2Ew2n,type,(c_2Ewords_2Ew2n:(del>$i))).
thf(mem_c_2Ewords_2Ew2n,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Ew2n@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Earithmetic_2EMOD,type,(c_2Earithmetic_2EMOD:$i)).
thf(mem_c_2Earithmetic_2EMOD,axiom,(mem@c_2Earithmetic_2EMOD@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EMOD,type,(fo__c_2Earithmetic_2EMOD:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EMOD,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EMOD @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2E_2D,type,(c_2Earithmetic_2E_2D:$i)).
thf(mem_c_2Earithmetic_2E_2D,axiom,(mem@c_2Earithmetic_2E_2D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2D,type,(fo__c_2Earithmetic_2E_2D:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2D @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ewords_2Eword__T,type,(c_2Ewords_2Eword__T:(del>$i))).
thf(mem_c_2Ewords_2Eword__T,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__T@A_27a)@(ty_2Efcp_2Ecart@bool@A_27a)))).
thf(tp_c_2Enum_2E0,type,(c_2Enum_2E0:$i)).
thf(mem_c_2Enum_2E0,axiom,(mem@c_2Enum_2E0@ty_2Enum_2Enum)).
thf(stp_fo_c_2Enum_2E0,type,(fo__c_2Enum_2E0:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Enum_2E0,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0) = c_2Enum_2E0)).
thf(tp_c_2Ewords_2Eword__1comp,type,(c_2Ewords_2Eword__1comp:(del>$i))).
thf(mem_c_2Ewords_2Eword__1comp,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__1comp@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(ty_2Efcp_2Ecart@bool@A_27a))))).
thf(tp_c_2Ebit_2EMOD__2EXP__MAX,type,(c_2Ebit_2EMOD__2EXP__MAX:$i)).
thf(mem_c_2Ebit_2EMOD__2EXP__MAX,axiom,(mem@c_2Ebit_2EMOD__2EXP__MAX@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Ewords_2Eword__2comp,type,(c_2Ewords_2Eword__2comp:(del>$i))).
thf(mem_c_2Ewords_2Eword__2comp,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__2comp@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(ty_2Efcp_2Ecart@bool@A_27a))))).
thf(tp_c_2Ebit_2EMOD__2EXP__EQ,type,(c_2Ebit_2EMOD__2EXP__EQ:$i)).
thf(mem_c_2Ebit_2EMOD__2EXP__EQ,axiom,(mem@c_2Ebit_2EMOD__2EXP__EQ@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool))))).
thf(tp_c_2Ewords_2En2w,type,(c_2Ewords_2En2w:(del>$i))).
thf(mem_c_2Ewords_2En2w,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2En2w@A_27a)@(arr@ty_2Enum_2Enum@(ty_2Efcp_2Ecart@bool@A_27a))))).
thf(tp_c_2Ebool_2E_21,type,(c_2Ebool_2E_21:(del>$i))).
thf(mem_c_2Ebool_2E_21,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2E_21@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(ax_all_p,axiom,( ! [A:del] : ( ! [Q:$i] : ((mem@Q@(arr@A@bool)) => ((p@(ap@(c_2Ebool_2E_21@A)@Q)) <=> ( ! [X:$i] : ((mem@X@A) => (p@(ap@Q@X))))))))).
thf(tp_c_2Ebool_2E_2F_5C,type,(c_2Ebool_2E_2F_5C:$i)).
thf(mem_c_2Ebool_2E_2F_5C,axiom,(mem@c_2Ebool_2E_2F_5C@(arr@bool@(arr@bool@bool)))).
thf(ax_and_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Ebool_2E_2F_5C@Q)@R)) <=> ((p@Q) & (p@R)))))))).
thf(tp_c_2Earithmetic_2EBIT1,type,(c_2Earithmetic_2EBIT1:$i)).
thf(mem_c_2Earithmetic_2EBIT1,axiom,(mem@c_2Earithmetic_2EBIT1@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT1,type,(fo__c_2Earithmetic_2EBIT1:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT1,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ X0)) = (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Efcp_2Edimindex,type,(c_2Efcp_2Edimindex:(del>$i))).
thf(mem_c_2Efcp_2Edimindex,axiom,( ! [A_27a:del] : (mem@(c_2Efcp_2Edimindex@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Earithmetic_2EZERO,type,(c_2Earithmetic_2EZERO:$i)).
thf(mem_c_2Earithmetic_2EZERO,axiom,(mem@c_2Earithmetic_2EZERO@ty_2Enum_2Enum)).
thf(stp_fo_c_2Earithmetic_2EZERO,type,(fo__c_2Earithmetic_2EZERO:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)).
thf(tp_c_2Earithmetic_2EBIT2,type,(c_2Earithmetic_2EBIT2:$i)).
thf(mem_c_2Earithmetic_2EBIT2,axiom,(mem@c_2Earithmetic_2EBIT2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT2,type,(fo__c_2Earithmetic_2EBIT2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X0)) = (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2ENUMERAL,type,(c_2Earithmetic_2ENUMERAL:$i)).
thf(mem_c_2Earithmetic_2ENUMERAL,axiom,(mem@c_2Earithmetic_2ENUMERAL@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2ENUMERAL,type,(fo__c_2Earithmetic_2ENUMERAL:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2ENUMERAL,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ X0)) = (ap @ c_2Earithmetic_2ENUMERAL @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ebool_2Ethe__value,type,(c_2Ebool_2Ethe__value:(del>$i))).
thf(mem_c_2Ebool_2Ethe__value,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2Ethe__value@A_27a)@(ty_2Ebool_2Eitself@A_27a)))).
thf(tp_c_2Ewords_2Edimword,type,(c_2Ewords_2Edimword:(del>$i))).
thf(mem_c_2Ewords_2Edimword,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Edimword@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Emin_2E_3D,type,(c_2Emin_2E_3D:(del>$i))).
thf(mem_c_2Emin_2E_3D,axiom,( ! [A_27a:del] : (mem@(c_2Emin_2E_3D@A_27a)@(arr@A_27a@(arr@A_27a@bool))))).
thf(ax_eq_p,axiom,( ! [A:del] : ( ! [X:$i] : ((mem@X@A) => ( ! [Y:$i] : ((mem@Y@A) => ((p@(ap@(ap@(c_2Emin_2E_3D@A)@X)@Y)) <=> (X = Y)))))))).
thf(ax_thm_2Earithmetic_2ENUMERAL__DEF,axiom,( ! [V0x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V0x))) = V0x))).
thf(ax_thm_2Earithmetic_2EALT__ZERO,axiom,(fo__c_2Earithmetic_2EZERO = fo__c_2Enum_2E0)).
thf(conj_thm_2Earithmetic_2ELESS__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m)))@(inj__ty_2Enum_2Enum @ V1n))))))).
thf(conj_thm_2Earithmetic_2EZERO__LESS__EQ,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n))))).
thf(conj_thm_2Earithmetic_2ESUB__0,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0m))) = fo__c_2Enum_2E0) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V0m)))).
thf(conj_thm_2Earithmetic_2EPRE__SUB1,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(inj__ty_2Enum_2Enum @ V0m))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0m))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Earithmetic_2EMULT__CLAUSES,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0m))) = fo__c_2Enum_2E0) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0m))) = V0m) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0m) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m)))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V1n)))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))))))))))).
thf(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) & (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))) => (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V2p)))))))).
thf(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V2p)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))))))).
thf(conj_thm_2Earithmetic_2ENOT__NUM__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~ (V0m = V1n)) <=> ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m)))@(inj__ty_2Enum_2Enum @ V1n))) | (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V0m)))))))).
thf(conj_thm_2Earithmetic_2ESUC__ONE__ADD,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0n)))))).
thf(conj_thm_2Earithmetic_2EMOD__UNIQUE,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1k:tp__ty_2Enum_2Enum] : ( ! [V2r:tp__ty_2Enum_2Enum] : ((? [V3q:tp__ty_2Enum_2Enum] : ((V1k = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V3q))@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Enum_2Enum @ V2r)))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V2r))@(inj__ty_2Enum_2Enum @ V0n))))) => ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V1k))@(inj__ty_2Enum_2Enum @ V0n))) = V2r)))))).
thf(conj_thm_2Earithmetic_2EZERO__MOD,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n))) => ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n))) = fo__c_2Enum_2E0)))).
thf(conj_thm_2Earithmetic_2EDIVMOD__ID,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n))) => (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EDIV@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V0n))) = fo__c_2Enum_2E0))))).
thf(conj_thm_2Earithmetic_2ESUC__ELIM__NUMERALS,lemma,( ! [A_27a:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@A_27a))) => ( ! [V1g:$i] : ((mem@V1g@(arr@ty_2Enum_2Enum@A_27a)) => (( ! [V2n:tp__ty_2Enum_2Enum] : ((ap@V1g@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2n))) = (ap@(ap@V0f@(inj__ty_2Enum_2Enum @ V2n))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2n))))) <=> (( ! [V3n:tp__ty_2Enum_2Enum] : ((ap@V1g@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3n)))) = (ap@(ap@V0f@(ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3n))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3n)))))) & ( ! [V4n:tp__ty_2Enum_2Enum] : ((ap@V1g@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V4n)))) = (ap@(ap@V0f@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V4n))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V4n)))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__accfupds,lemma,( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: (( ! [V0f0:$i] : ((mem@V0f0@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))) => ( ! [V1f:$i] : ((mem@V1f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27x)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V0f0)@V1f))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V1f))))))) & (( ! [V2f0:$i] : ((mem@V2f0@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))) => ( ! [V3f:$i] : ((mem@V3f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27u@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V2f0)@V3f))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V3f))))))) & (( ! [V4f0:$i] : ((mem@V4f0@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V5f:$i] : ((mem@V5f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V4f0)@V5f)) = (ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V5f)))))) & (( ! [V6f0:$i] : ((mem@V6f0@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))) => ( ! [V7f:$i] : ((mem@V7f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27u@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V6f0)@V7f)) = (ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V7f)))))) & (( ! [V8f0:$i] : ((mem@V8f0@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V9f:$i] : ((mem@V9f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V8f0)@V9f)) = (ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@V9f)))))) & (( ! [V10f0:$i] : ((mem@V10f0@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))) => ( ! [V11f:$i] : ((mem@V11f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27x)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V10f0)@V11f)) = (ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@V11f)))))) & (( ! [V12f0:$i] : ((mem@V12f0@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V13f:$i] : ((mem@V13f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V12f0)@V13f))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@V12f0@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V13f)))))))) & (( ! [V14f0:$i] : ((mem@V14f0@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))) => ( ! [V15f:$i] : ((mem@V15f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27x)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V14f0)@V15f)) = (ap@V14f0@(ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V15f))))))) & ( ! [V16f0:$i] : ((mem@V16f0@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))) => ( ! [V17f:$i] : ((mem@V17f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27u@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V16f0)@V17f)) = (ap@V16f0@(ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@V17f)))))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__fupdfupds,lemma,( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27v:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [A_27y:del]: (( ! [V0g:$i] : ((mem@V0g@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V1f0:$i] : ((mem@V1f0@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V2f:$i] : ((mem@V2f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V1f0)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V0g)@V2f)) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@(ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@V1f0)@V0g))@V2f)))))))) & (( ! [V3g:$i] : ((mem@V3g@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))) => ( ! [V4f0:$i] : ((mem@V4f0@(arr@(ty_2Efcp_2Ecart@bool@A_27x)@(ty_2Efcp_2Ecart@bool@A_27y))) => ( ! [V5f:$i] : ((mem@V5f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27x@A_27y)@V4f0)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V3g)@V5f)) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27y)@(ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27y)@(ty_2Efcp_2Ecart@bool@A_27x))@V4f0)@V3g))@V5f)))))))) & ( ! [V6g:$i] : ((mem@V6g@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))) => ( ! [V7f0:$i] : ((mem@V7f0@(arr@(ty_2Efcp_2Ecart@bool@A_27u)@(ty_2Efcp_2Ecart@bool@A_27v))) => ( ! [V8f:$i] : ((mem@V8f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27u@A_27v@A_27w)@V7f0)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V6g)@V8f)) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27v@A_27w)@(ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27v)@(ty_2Efcp_2Ecart@bool@A_27u))@V7f0)@V6g))@V8f))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__value__case__def,axiom,( ! [A_27a:del]: (( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1f:$i] : ((mem@V1f@(arr@ty_2Erealax_2Ereal@A_27a)) => ( ! [V2v:$i] : ((mem@V2v@A_27a) => ( ! [V3v1:$i] : ((mem@V3v1@A_27a) => ((ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(ap@c_2Ebinary__ieee_2EFloat@(inj__ty_2Erealax_2Ereal @ V0a)))@V1f)@V2v)@V3v1) = (ap@V1f@(inj__ty_2Erealax_2Ereal @ V0a)))))))))) & (( ! [V4f:$i] : ((mem@V4f@(arr@ty_2Erealax_2Ereal@A_27a)) => ( ! [V5v:$i] : ((mem@V5v@A_27a) => ( ! [V6v1:$i] : ((mem@V6v1@A_27a) => ((ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2EInfinity))@V4f)@V5v)@V6v1) = V5v))))))) & ( ! [V7f:$i] : ((mem@V7f@(arr@ty_2Erealax_2Ereal@A_27a)) => ( ! [V8v:$i] : ((mem@V8v@A_27a) => ( ! [V9v1:$i] : ((mem@V9v1@A_27a) => ((ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2ENaN))@V7f)@V8v)@V9v1) = V9v1))))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__negate__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__negate@A_27t@A_27w)@V0x) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ewords_2Eword__1comp@ty_2Eone_2Eone)@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V0x))))@V0x))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__plus__infinity__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ((ap@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27w))@(c_2Ewords_2Eword__T@A_27w)))@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27t@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27t))@(ap@(c_2Ewords_2En2w@A_27t)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(c_2Ebool_2EARB@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__minus__infinity__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ((ap@(c_2Ebinary__ieee_2Efloat__minus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))) = (ap@(c_2Ebinary__ieee_2Efloat__negate@A_27t@A_27w)@(ap@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__div__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : ((mem@V1x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ( ! [V2y:$i] : ((mem@V2y@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__div@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@V1x)@V2y) = (ap@(ap@(c_2Epair_2Epair__CASE@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@ty_2Ebinary__ieee_2Efloat__value@ty_2Ebinary__ieee_2Efloat__value)@(ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Efloat__value@ty_2Ebinary__ieee_2Efloat__value)@(ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@V1x))@(ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@V2y)))@(lam@ty_2Ebinary__ieee_2Efloat__value@(^ [V3v:$i] : (lam@ty_2Ebinary__ieee_2Efloat__value@(^ [V4v1:$i] : (ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))@V3v)@(lam@ty_2Erealax_2Ereal@(^ [V5r1:$i] : (ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))@V4v1)@(lam@ty_2Erealax_2Ereal@(^ [V6r2:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@V6r2)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@V5r1)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Einvalidop__flags))@(ap@(c_2Ebinary__ieee_2Efloat__some__qnan@A_27t@A_27w)@(ap@(ap@(ap@(c_2Ebinary__ieee_2EFP__Div@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@V1x)@V2y))))@(ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Edividezero__flags))@(ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V1x))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V2y)))@(ap@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))@(ap@(c_2Ebinary__ieee_2Efloat__minus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))))))@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__round__with__flags@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@(ap@c_2Ebool_2E_7E@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V1x))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V2y))))@(ap@(ap@c_2Ereal_2E_2F@V5r1)@V6r2))))))@(ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Eclear__flags))@(ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V1x))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V2y)))@(ap@(c_2Ebinary__ieee_2Efloat__plus__zero@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))@(ap@(c_2Ebinary__ieee_2Efloat__minus__zero@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))))@(ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(c_2Ebinary__ieee_2Echeck__for__signalling@A_27t@A_27w)@(ap@(ap@(c_2Elist_2ECONS@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@V2y)@(c_2Elist_2ENIL@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))@(ap@(c_2Ebinary__ieee_2Efloat__some__qnan@A_27t@A_27w)@(ap@(ap@(ap@(c_2Ebinary__ieee_2EFP__Div@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@V1x)@V2y)))))))@(ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))@V4v1)@(lam@ty_2Erealax_2Ereal@(^ [V7v7:$i] : (ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Eclear__flags))@(ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V1x))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V2y)))@(ap@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))@(ap@(c_2Ebinary__ieee_2Efloat__minus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))))))@(ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Einvalidop__flags))@(ap@(c_2Ebinary__ieee_2Efloat__some__qnan@A_27t@A_27w)@(ap@(ap@(ap@(c_2Ebinary__ieee_2EFP__Div@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@V1x)@V2y))))@(ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(c_2Ebinary__ieee_2Echeck__for__signalling@A_27t@A_27w)@(ap@(ap@(c_2Elist_2ECONS@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@V2y)@(c_2Elist_2ENIL@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))@(ap@(c_2Ebinary__ieee_2Efloat__some__qnan@A_27t@A_27w)@(ap@(ap@(ap@(c_2Ebinary__ieee_2EFP__Div@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@V1x)@V2y)))))@(ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(c_2Ebinary__ieee_2Echeck__for__signalling@A_27t@A_27w)@(ap@(ap@(c_2Elist_2ECONS@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@V1x)@(ap@(ap@(c_2Elist_2ECONS@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@V2y)@(c_2Elist_2ENIL@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))@(ap@(c_2Ebinary__ieee_2Efloat__some__qnan@A_27t@A_27w)@(ap@(ap@(ap@(c_2Ebinary__ieee_2EFP__Div@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@V1x)@V2y)))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__values,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: (((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@(ap@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))) = fo__c_2Ebinary__ieee_2EInfinity) & (((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@(ap@(c_2Ebinary__ieee_2Efloat__minus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))) = fo__c_2Ebinary__ieee_2EInfinity) & (( ! [V0fp__op:$i] : ((mem@V0fp__op@(ty_2Ebinary__ieee_2Efp__op@A_27a@A_27b)) => ((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27a@A_27b)@(ap@(c_2Ebinary__ieee_2Efloat__some__qnan@A_27a@A_27b)@V0fp__op))) = fo__c_2Ebinary__ieee_2ENaN))) & (((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@(ap@(c_2Ebinary__ieee_2Efloat__plus__zero@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))) = (surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@c_2Ebinary__ieee_2EFloat@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@(ap@(c_2Ebinary__ieee_2Efloat__minus__zero@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))) = (surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@c_2Ebinary__ieee_2EFloat@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@(ap@(c_2Ebinary__ieee_2Efloat__plus__min@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))) = (surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@c_2Ebinary__ieee_2EFloat@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@(c_2Ewords_2EINT__MAX@A_27w)@(c_2Ebool_2Ethe__value@A_27w)))@(ap@(c_2Efcp_2Edimindex@A_27t)@(c_2Ebool_2Ethe__value@A_27t)))))))) & ((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@(ap@(c_2Ebinary__ieee_2Efloat__minus__min@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))) = (surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@c_2Ebinary__ieee_2EFloat@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@(c_2Ewords_2EINT__MAX@A_27w)@(c_2Ebool_2Ethe__value@A_27w)))@(ap@(c_2Efcp_2Edimindex@A_27t)@(c_2Ebool_2Ethe__value@A_27t))))))))))))))))))).
thf(ax_thm_2Ebool_2ELET__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ((c_2Ebool_2ELET@A_27a@A_27b) = (lam@(arr@A_27a@A_27b)@(^ [V0f:$i] : (lam@A_27a@(^ [V1x:$i] : (ap@V0f@V1x))))))))).
thf(ax_thm_2Ebool_2EETA__AX,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0t:$i] : ((mem@V0t@(arr@A_27a@A_27b)) => ((lam@A_27a@(^ [V1x:$i] : (ap@V0t@V1x))) = V0t)))))).
thf(conj_thm_2Ebool_2ETRUTH,lemma,$true).
thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => (((p@V0t1) => (p@V1t2)) => (((p@V1t2) => (p@V0t1)) => ((p@V0t1) <=> (p@V1t2))))))))).
thf(conj_thm_2Ebool_2EFALSITY,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ($false => (p@V0t))))).
thf(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((p@V0t) | (~ (p@V0t)))))).
thf(conj_thm_2Ebool_2ELET__THM,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ((ap@(ap@(c_2Ebool_2ELET@A_27a@A_27b)@V0f)@V1x) = (ap@V0f@V1x))))))))).
thf(conj_thm_2Ebool_2EFORALL__SIMP,lemma,( ! [A_27a:del]: ( ! [V0t:$i] : ((mem@V0t@bool) => (( ! [V1x:$i] : ((mem@V1x@A_27a) => (p@V0t))) <=> (p@V0t)))))).
thf(conj_thm_2Ebool_2ECONJ__ASSOC,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => ( ! [V2t3:$i] : ((mem@V2t3@bool) => (((p@V0t1) & ((p@V1t2) & (p@V2t3))) <=> (((p@V0t1) & (p@V1t2)) & (p@V2t3)))))))))).
thf(conj_thm_2Ebool_2EAND__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true & (p@V0t)) <=> (p@V0t)) & ((((p@V0t) & $true) <=> (p@V0t)) & ((($false & (p@V0t)) <=> $false) & ((((p@V0t) & $false) <=> $false) & (((p@V0t) & (p@V0t)) <=> (p@V0t))))))))).
thf(conj_thm_2Ebool_2EOR__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true | (p@V0t)) <=> $true) & ((((p@V0t) | $true) <=> $true) & ((($false | (p@V0t)) <=> (p@V0t)) & ((((p@V0t) | $false) <=> (p@V0t)) & (((p@V0t) | (p@V0t)) <=> (p@V0t))))))))).
thf(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true => (p@V0t)) <=> (p@V0t)) & ((((p@V0t) => $true) <=> $true) & ((($false => (p@V0t)) <=> $true) & ((((p@V0t) => (p@V0t)) <=> $true) & (((p@V0t) => $false) <=> (~ (p@V0t)))))))))).
thf(conj_thm_2Ebool_2ENOT__CLAUSES,lemma,(( ! [V0t:$i] : ((mem@V0t@bool) => ((~ (~ (p@V0t))) <=> (p@V0t)))) & (((~ ($true)) <=> $false) & ((~ ($false)) <=> $true)))).
thf(conj_thm_2Ebool_2EEQ__REFL,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => (V0x = V0x))))).
thf(conj_thm_2Ebool_2EREFL__CLAUSE,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((V0x = V0x) <=> $true))))).
thf(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((V0x = V1y) <=> (V1y = V0x)))))))).
thf(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true <=> (p@V0t)) <=> (p@V0t)) & ((((p@V0t) <=> $true) <=> (p@V0t)) & ((($false <=> (p@V0t)) <=> (~ (p@V0t))) & (((p@V0t) <=> $false) <=> (~ (p@V0t))))))))).
thf(conj_thm_2Ebool_2ECOND__CLAUSES,lemma,( ! [A_27a:del]: ( ! [V0t1:$i] : ((mem@V0t1@A_27a) => ( ! [V1t2:$i] : ((mem@V1t2@A_27a) => (((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2ET)@V0t1)@V1t2) = V0t1) & ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2EF)@V0t1)@V1t2) = V1t2)))))))).
thf(conj_thm_2Ebool_2EDISJ__ASSOC,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => ( ! [V2C:$i] : ((mem@V2C@bool) => (((p@V0A) | ((p@V1B) | (p@V2C))) <=> (((p@V0A) | (p@V1B)) | (p@V2C)))))))))).
thf(conj_thm_2Ebool_2EDE__MORGAN__THM,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((p@V0A) & (p@V1B))) <=> ((~ (p@V0A)) | (~ (p@V1B)))) & ((~ ((p@V0A) | (p@V1B))) <=> ((~ (p@V0A)) & (~ (p@V1B)))))))))).
thf(conj_thm_2Ebool_2EIMP__DISJ__THM,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((p@V0A) => (p@V1B)) <=> ((~ (p@V0A)) | (p@V1B)))))))).
thf(conj_thm_2Ebool_2EIMP__F__EQ__F,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => (((p@V0t) => $false) <=> ((p@V0t) <=> $false))))).
thf(conj_thm_2Ebool_2EAND__IMP__INTRO,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => ( ! [V2t3:$i] : ((mem@V2t3@bool) => (((p@V0t1) => ((p@V1t2) => (p@V2t3))) <=> (((p@V0t1) & (p@V1t2)) => (p@V2t3)))))))))).
thf(conj_thm_2Ebool_2EIMP__CONG,lemma,( ! [V0x:$i] : ((mem@V0x@bool) => ( ! [V1x_27:$i] : ((mem@V1x_27@bool) => ( ! [V2y:$i] : ((mem@V2y@bool) => ( ! [V3y_27:$i] : ((mem@V3y_27@bool) => ((((p@V0x) <=> (p@V1x_27)) & ((p@V1x_27) => ((p@V2y) <=> (p@V3y_27)))) => (((p@V0x) => (p@V2y)) <=> ((p@V1x_27) => (p@V3y_27))))))))))))).
thf(conj_thm_2Ecombin_2EK__THM,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27b) => ((ap@(ap@(c_2Ecombin_2EK@A_27a@A_27b)@V0x)@V1y) = V0x)))))))).
thf(conj_thm_2Ecombin_2EI__THM,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((ap@(c_2Ecombin_2EI@A_27a)@V0x) = V0x))))).
thf(conj_thm_2Ecombin_2EK__o__THM,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [A_27d:del]: ( ! [A_27e:del]: ( ! [A_27f:del]: (( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => ( ! [V1v:$i] : ((mem@V1v@A_27c) => ((ap@(ap@(c_2Ecombin_2Eo@A_27a@A_27c@A_27b)@(ap@(c_2Ecombin_2EK@A_27c@A_27b)@V1v))@V0f) = (ap@(c_2Ecombin_2EK@A_27c@A_27a)@V1v)))))) & ( ! [V2f:$i] : ((mem@V2f@(arr@A_27d@A_27e)) => ( ! [V3v:$i] : ((mem@V3v@A_27d) => ((ap@(ap@(c_2Ecombin_2Eo@A_27f@A_27e@A_27d)@V2f)@(ap@(c_2Ecombin_2EK@A_27d@A_27f)@V3v)) = (ap@(c_2Ecombin_2EK@A_27e@A_27f)@(ap@V2f@V3v))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__suc,lemma,(((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) & (( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))))) & ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n))))))))).
thf(conj_thm_2Enumeral_2Enumeral__distrib,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n))) = V0n)) & (( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V1n)) & (( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))))))) & (( ! [V4n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V4n))) = fo__c_2Enum_2E0)) & (( ! [V5n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V5n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0)) & (( ! [V6n:tp__ty_2Enum_2Enum] : ( ! [V7m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V6n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V7m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V6n))@(inj__ty_2Enum_2Enum @ V7m))))))) & (( ! [V8n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V8n))) = fo__c_2Enum_2E0)) & (( ! [V9n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V9n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V9n)) & (( ! [V10n:tp__ty_2Enum_2Enum] : ( ! [V11m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V10n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V11m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V10n))@(inj__ty_2Enum_2Enum @ V11m))))))) & (( ! [V12n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V12n))))) = fo__c_2Enum_2E0)) & (( ! [V13n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V13n))))) = fo__c_2Enum_2E0)) & (( ! [V14n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V14n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) & (( ! [V15n:tp__ty_2Enum_2Enum] : ( ! [V16m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V15n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V16m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V15n))@(inj__ty_2Enum_2Enum @ V16m))))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) & (( ! [V17n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V17n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V17n)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0) & (( ! [V18n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V18n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Eprim__rec_2EPRE@(inj__ty_2Enum_2Enum @ V18n)))))) & (( ! [V19n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V19n))) = fo__c_2Enum_2E0) <=> (V19n = fo__c_2Earithmetic_2EZERO))) & (( ! [V20n:tp__ty_2Enum_2Enum] : ((fo__c_2Enum_2E0 = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V20n)))) <=> (V20n = fo__c_2Earithmetic_2EZERO))) & (( ! [V21n:tp__ty_2Enum_2Enum] : ( ! [V22m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V21n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V22m)))) <=> (V21n = V22m)))) & (( ! [V23n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V23n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> $false)) & (( ! [V24n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V24n)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V24n))))) & (( ! [V25n:tp__ty_2Enum_2Enum] : ( ! [V26m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V25n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V26m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V25n))@(inj__ty_2Enum_2Enum @ V26m)))))) & (( ! [V27n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V27n))) <=> $false)) & (( ! [V28n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V28n)))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V28n))))) & (( ! [V29n:tp__ty_2Enum_2Enum] : ( ! [V30m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V29n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V30m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V30m))@(inj__ty_2Enum_2Enum @ V29n)))))) & (( ! [V31n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V31n))) <=> $true)) & (( ! [V32n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V32n)))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V32n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) & (( ! [V33n:tp__ty_2Enum_2Enum] : ( ! [V34m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V33n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V34m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V33n))@(inj__ty_2Enum_2Enum @ V34m)))))) & (( ! [V35n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V35n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> $true)) & (( ! [V36n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V36n))) <=> (V36n = fo__c_2Enum_2E0))) & (( ! [V37n:tp__ty_2Enum_2Enum] : ( ! [V38m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V37n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V38m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V38m))@(inj__ty_2Enum_2Enum @ V37n)))))) & (( ! [V39n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EODD@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V39n)))) <=> (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ V39n))))) & (( ! [V40n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V40n)))) <=> (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V40n))))) & ((~ (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))))))))))))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__add,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n)))) = V0n) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = V0n) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(inj__ty_2Enum_2Enum @ V0n)))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(inj__ty_2Enum_2Enum @ V0n)))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__eq,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((fo__c_2Earithmetic_2EZERO = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) <=> $false) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))) = fo__c_2Earithmetic_2EZERO) <=> $false) & (((fo__c_2Earithmetic_2EZERO = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) <=> $false) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))) = fo__c_2Earithmetic_2EZERO) <=> $false) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> $false) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> $false) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (V0n = V1m)) & (((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (V0n = V1m)))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__lt,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) <=> $true) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) <=> $true) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) <=> $false) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (~ (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))) & ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__lte,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n))) <=> $true) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) <=> $false) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) <=> $false) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (~ (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))))))))).
thf(conj_thm_2Enumeral_2EiSUB__THM,lemma,( ! [V0x:tp__ty_2Enum_2Enum] : ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@V1b)@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0x))) = fo__c_2Earithmetic_2EZERO) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = V2n) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V2n)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__sub,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Enumeral_2Enumeral__evenodd,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) & ((p@(ap@c_2Earithmetic_2EEVEN@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) & ((~ (p@(ap@c_2Earithmetic_2EEVEN@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))) & ((~ (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) & ((~ (p@(ap@c_2Earithmetic_2EODD@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))))) & (p@(ap@c_2Earithmetic_2EODD@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))))))))).
thf(conj_thm_2Enumeral__bit_2EMOD__2EXP__EQ,lemma,(( ! [V0a:tp__ty_2Enum_2Enum] : ( ! [V1b:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@(ap@c_2Ebit_2EMOD__2EXP__EQ@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0a))@(inj__ty_2Enum_2Enum @ V1b))) <=> $true))) & (( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3a:tp__ty_2Enum_2Enum] : ( ! [V4b:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@(ap@c_2Ebit_2EMOD__2EXP__EQ@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ V3a))@(inj__ty_2Enum_2Enum @ V4b))) <=> (((p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ V3a))) <=> (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ V4b)))) & (p@(ap@(ap@(ap@c_2Ebit_2EMOD__2EXP__EQ@(inj__ty_2Enum_2Enum @ V2n))@(ap@c_2Earithmetic_2EDIV2@(inj__ty_2Enum_2Enum @ V3a)))@(ap@c_2Earithmetic_2EDIV2@(inj__ty_2Enum_2Enum @ V4b))))))))) & ( ! [V5n:tp__ty_2Enum_2Enum] : ( ! [V6a:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@(ap@c_2Ebit_2EMOD__2EXP__EQ@(inj__ty_2Enum_2Enum @ V5n))@(inj__ty_2Enum_2Enum @ V6a))@(inj__ty_2Enum_2Enum @ V6a))) <=> $true)))))).
thf(conj_thm_2Epair_2ECLOSED__PAIR__EQ,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27b) => ( ! [V2a:$i] : ((mem@V2a@A_27a) => ( ! [V3b:$i] : ((mem@V3b@A_27b) => (((ap@(ap@(c_2Epair_2E_2C@A_27a@A_27b)@V0x)@V1y) = (ap@(ap@(c_2Epair_2E_2C@A_27a@A_27b)@V2a)@V3b)) <=> ((V0x = V2a) & (V1y = V3b)))))))))))))).
thf(conj_thm_2Epair_2Epair__case__thm,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0x:$i] : ((mem@V0x@A_27b) => ( ! [V1y:$i] : ((mem@V1y@A_27c) => ( ! [V2f:$i] : ((mem@V2f@(arr@A_27b@(arr@A_27c@A_27a))) => ((ap@(ap@(c_2Epair_2Epair__CASE@A_27a@A_27b@A_27c)@(ap@(ap@(c_2Epair_2E_2C@A_27b@A_27c)@V0x)@V1y))@V2f) = (ap@(ap@V2f@V0x)@V1y)))))))))))).
thf(conj_thm_2Esat_2ENOT__NOT,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((~ (~ (p@V0t))) <=> (p@V0t))))).
thf(conj_thm_2Esat_2EAND__INV__IMP,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ((p@V0A) => ((~ (p@V0A)) => $false))))).
thf(conj_thm_2Esat_2EOR__DUAL2,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((p@V0A) | (p@V1B))) => $false) <=> (((p@V0A) => $false) => ((~ (p@V1B)) => $false)))))))).
thf(conj_thm_2Esat_2EOR__DUAL3,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((~ (p@V0A)) | (p@V1B))) => $false) <=> ((p@V0A) => ((~ (p@V1B)) => $false)))))))).
thf(conj_thm_2Esat_2EAND__INV2,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => (((~ (p@V0A)) => $false) => (((p@V0A) => $false) => $false))))).
thf(conj_thm_2Esat_2Edc__eq,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) <=> (p@V2r))) <=> (((p@V0p) | ((p@V1q) | (p@V2r))) & (((p@V0p) | ((~ (p@V2r)) | (~ (p@V1q)))) & (((p@V1q) | ((~ (p@V2r)) | (~ (p@V0p)))) & ((p@V2r) | ((~ (p@V1q)) | (~ (p@V0p))))))))))))))).
thf(conj_thm_2Esat_2Edc__conj,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) & (p@V2r))) <=> (((p@V0p) | ((~ (p@V1q)) | (~ (p@V2r)))) & (((p@V1q) | (~ (p@V0p))) & ((p@V2r) | (~ (p@V0p))))))))))))).
thf(conj_thm_2Esat_2Edc__disj,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) | (p@V2r))) <=> (((p@V0p) | (~ (p@V1q))) & (((p@V0p) | (~ (p@V2r))) & ((p@V1q) | ((p@V2r) | (~ (p@V0p)))))))))))))).
thf(conj_thm_2Esat_2Edc__imp,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) => (p@V2r))) <=> (((p@V0p) | (p@V1q)) & (((p@V0p) | (~ (p@V2r))) & ((~ (p@V1q)) | ((p@V2r) | (~ (p@V0p)))))))))))))).
thf(conj_thm_2Esat_2Edc__neg,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) <=> (~ (p@V1q))) <=> (((p@V0p) | (p@V1q)) & ((~ (p@V1q)) | (~ (p@V0p)))))))))).
thf(conj_thm_2Esat_2Epth__ni1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) => (p@V1q))) => (p@V0p))))))).
thf(conj_thm_2Esat_2Epth__ni2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) => (p@V1q))) => (~ (p@V1q)))))))).
thf(conj_thm_2Esat_2Epth__no1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) | (p@V1q))) => (~ (p@V0p)))))))).
thf(conj_thm_2Esat_2Epth__no2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) | (p@V1q))) => (~ (p@V1q)))))))).
thf(conj_thm_2Esat_2Epth__nn,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ((~ (~ (p@V0p))) => (p@V0p))))).
thf(ax_thm_2Ewords_2EUINT__MAX__def,axiom,( ! [A_27a:del]: ((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2EUINT__MAX@A_27a)@(c_2Ebool_2Ethe__value@A_27a))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(ax_thm_2Ewords_2Eword__T__def,axiom,( ! [A_27a:del]: ((c_2Ewords_2Eword__T@A_27a) = (ap@(c_2Ewords_2En2w@A_27a)@(ap@(c_2Ewords_2EUINT__MAX@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))).
thf(conj_thm_2Ewords_2EZERO__LT__dimword,lemma,( ! [A_27a:del]: (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))).
thf(conj_thm_2Ewords_2Ew2n__n2w,lemma,( ! [A_27a:del]: ( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2Ew2n@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V0n))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))))).
thf(conj_thm_2Ewords_2En2w__11,lemma,( ! [A_27a:del]: ( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V0m)) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V1n))) <=> ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V0m))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V1n))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))))))).
thf(conj_thm_2Ewords_2Ew2n__11,lemma,( ! [A_27a:del]: ( ! [V0v:$i] : ((mem@V0v@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1w:$i] : ((mem@V1w@(ty_2Efcp_2Ecart@bool@A_27a)) => (((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2Ew2n@A_27a)@V0v)) = (surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2Ew2n@A_27a)@V1w))) <=> (V0v = V1w)))))))).
thf(conj_thm_2Ewords_2Ew2n__lt,lemma,( ! [A_27a:del]: ( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => (p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@(c_2Ewords_2Ew2n@A_27a)@V0w))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))))).
thf(conj_thm_2Ewords_2Eword__0__n2w,lemma,( ! [A_27a:del]: ((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2Ew2n@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = fo__c_2Enum_2E0))).
thf(conj_thm_2Ewords_2Eword__2comp__n2w,lemma,( ! [A_27a:del]: ( ! [V0n:tp__ty_2Enum_2Enum] : ((ap@(c_2Ewords_2Eword__2comp@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V0n))) = (ap@(c_2Ewords_2En2w@A_27a)@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V0n))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a))))))))).
thf(conj_thm_2Ewords_2EWORD__NEG__1,lemma,( ! [A_27a:del]: ((ap@(c_2Ewords_2Eword__2comp@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (c_2Ewords_2Eword__T@A_27a)))).
thf(conj_thm_2Ewords_2EWORD__NOT__0,lemma,( ! [A_27a:del]: ((ap@(c_2Ewords_2Eword__1comp@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (c_2Ewords_2Eword__T@A_27a)))).
thf(conj_thm_2Ewords_2Eword__eq__n2w,lemma,( ! [A_27a:del]: (( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V0m)) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V1n))) <=> (p@(ap@(ap@(ap@c_2Ebit_2EMOD__2EXP__EQ@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))))) & (( ! [V2n:tp__ty_2Enum_2Enum] : (((ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V2n)) = (ap@(c_2Ewords_2Eword__2comp@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (p@(ap@(ap@c_2Ebit_2EMOD__2EXP__MAX@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(inj__ty_2Enum_2Enum @ V2n))))) & ( ! [V3n:tp__ty_2Enum_2Enum] : (((ap@(c_2Ewords_2Eword__2comp@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V3n))) <=> (p@(ap@(ap@c_2Ebit_2EMOD__2EXP__MAX@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(inj__ty_2Enum_2Enum @ V3n))))))))).
thf(conj_thm_2Ewords_2Edimindex__1,lemma,((surj__ty_2Enum_2Enum @ (ap@(c_2Efcp_2Edimindex@ty_2Eone_2Eone)@(c_2Ebool_2Ethe__value@ty_2Eone_2Eone))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))).
thf(conj_thm_2Ewords_2Edimword__1,lemma,((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2Edimword@ty_2Eone_2Eone)@(c_2Ebool_2Ethe__value@ty_2Eone_2Eone))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__div__finite__minus__infinity,conjecture,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : ((mem@V1x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ( ! [V2r:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@V1x)) = (surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@c_2Ebinary__ieee_2EFloat@(inj__ty_2Erealax_2Ereal @ V2r)))) => ((ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__div@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@V1x)@(ap@(c_2Ebinary__ieee_2Efloat__minus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))) = (ap@(ap@(c_2Epair_2E_2C@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Eclear__flags))@(ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V1x))@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(c_2Ebinary__ieee_2Efloat__minus__zero@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))))@(ap@(c_2Ebinary__ieee_2Efloat__plus__zero@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))))))))))))).
