include('Axioms/transc_2.ax').
tff(tp_ty_2Ebinary__ieee_2Eflags,type,( ty_2Ebinary__ieee_2Eflags: del )).
tff(tp_ty_2Ebinary__ieee_2Efloat,type,( ty_2Ebinary__ieee_2Efloat: ( del * del ) > del )).
tff(tp_ty_2Ebinary__ieee_2Efloat__compare,type,( ty_2Ebinary__ieee_2Efloat__compare: del )).
tff(tp_ty_2Ebinary__ieee_2Efloat__value,type,( ty_2Ebinary__ieee_2Efloat__value: del )).
tff(tp_ty_2Ebinary__ieee_2Efp__op,type,( ty_2Ebinary__ieee_2Efp__op: ( del * del ) > del )).
tff(tp_ty_2Ebinary__ieee_2Erounding,type,( ty_2Ebinary__ieee_2Erounding: del )).
tff(stp_ty_2Ebinary__ieee_2Efloat__compare,type,(tp__ty_2Ebinary__ieee_2Efloat__compare : $tType)).
tff(stp_inj_ty_2Ebinary__ieee_2Efloat__compare,type,(inj__ty_2Ebinary__ieee_2Efloat__compare : tp__ty_2Ebinary__ieee_2Efloat__compare > $i)).
tff(stp_surj_ty_2Ebinary__ieee_2Efloat__compare,type,(surj__ty_2Ebinary__ieee_2Efloat__compare : $i > tp__ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_inj_surj_ty_2Ebinary__ieee_2Efloat__compare,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Efloat__compare] : (surj__ty_2Ebinary__ieee_2Efloat__compare(inj__ty_2Ebinary__ieee_2Efloat__compare(X)) = X))).
tff(stp_inj_mem_ty_2Ebinary__ieee_2Efloat__compare,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Efloat__compare] : (mem(inj__ty_2Ebinary__ieee_2Efloat__compare(X),ty_2Ebinary__ieee_2Efloat__compare)))).
tff(stp_iso_mem_ty_2Ebinary__ieee_2Efloat__compare,axiom,( ! [X:$i] : (mem(X,ty_2Ebinary__ieee_2Efloat__compare) => (X = inj__ty_2Ebinary__ieee_2Efloat__compare(surj__ty_2Ebinary__ieee_2Efloat__compare(X)))))).
tff(tp_c_2Ebinary__ieee_2EEQ,type,(c_2Ebinary__ieee_2EEQ:$i)).
tff(mem_c_2Ebinary__ieee_2EEQ,axiom,mem(c_2Ebinary__ieee_2EEQ,ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_fo_c_2Ebinary__ieee_2EEQ,type,(fo__c_2Ebinary__ieee_2EEQ:tp__ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EEQ,axiom,(inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EEQ) = c_2Ebinary__ieee_2EEQ)).
tff(stp_ty_2Ebinary__ieee_2Erounding,type,(tp__ty_2Ebinary__ieee_2Erounding : $tType)).
tff(stp_inj_ty_2Ebinary__ieee_2Erounding,type,(inj__ty_2Ebinary__ieee_2Erounding : tp__ty_2Ebinary__ieee_2Erounding > $i)).
tff(stp_surj_ty_2Ebinary__ieee_2Erounding,type,(surj__ty_2Ebinary__ieee_2Erounding : $i > tp__ty_2Ebinary__ieee_2Erounding)).
tff(stp_inj_surj_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Erounding] : (surj__ty_2Ebinary__ieee_2Erounding(inj__ty_2Ebinary__ieee_2Erounding(X)) = X))).
tff(stp_inj_mem_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Erounding] : (mem(inj__ty_2Ebinary__ieee_2Erounding(X),ty_2Ebinary__ieee_2Erounding)))).
tff(stp_iso_mem_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:$i] : (mem(X,ty_2Ebinary__ieee_2Erounding) => (X = inj__ty_2Ebinary__ieee_2Erounding(surj__ty_2Ebinary__ieee_2Erounding(X)))))).
tff(tp_c_2Ebinary__ieee_2EFP__Add,type,(c_2Ebinary__ieee_2EFP__Add:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2EFP__Add,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2EFP__Add(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)))))))).
tff(tp_c_2Ebinary__ieee_2EFP__Div,type,(c_2Ebinary__ieee_2EFP__Div:(del * del) > $i)).
tff(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)))))))).
tff(tp_c_2Ebinary__ieee_2EFP__Mul,type,(c_2Ebinary__ieee_2EFP__Mul:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2EFP__Mul,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2EFP__Mul(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)))))))).
tff(tp_c_2Ebinary__ieee_2EFP__MulAdd,type,(c_2Ebinary__ieee_2EFP__MulAdd:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2EFP__MulAdd,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2EFP__MulAdd(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),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))))))).
tff(tp_c_2Ebinary__ieee_2EFP__MulSub,type,(c_2Ebinary__ieee_2EFP__MulSub:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2EFP__MulSub,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2EFP__MulSub(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),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))))))).
tff(tp_c_2Ebinary__ieee_2EFP__Sqrt,type,(c_2Ebinary__ieee_2EFP__Sqrt:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2EFP__Sqrt,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))))).
tff(tp_c_2Ebinary__ieee_2EFP__Sub,type,(c_2Ebinary__ieee_2EFP__Sub:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2EFP__Sub,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2EFP__Sub(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)))))))).
tff(stp_ty_2Ebinary__ieee_2Efloat__value,type,(tp__ty_2Ebinary__ieee_2Efloat__value : $tType)).
tff(stp_inj_ty_2Ebinary__ieee_2Efloat__value,type,(inj__ty_2Ebinary__ieee_2Efloat__value : tp__ty_2Ebinary__ieee_2Efloat__value > $i)).
tff(stp_surj_ty_2Ebinary__ieee_2Efloat__value,type,(surj__ty_2Ebinary__ieee_2Efloat__value : $i > tp__ty_2Ebinary__ieee_2Efloat__value)).
tff(stp_inj_surj_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Efloat__value] : (surj__ty_2Ebinary__ieee_2Efloat__value(inj__ty_2Ebinary__ieee_2Efloat__value(X)) = X))).
tff(stp_inj_mem_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Efloat__value] : (mem(inj__ty_2Ebinary__ieee_2Efloat__value(X),ty_2Ebinary__ieee_2Efloat__value)))).
tff(stp_iso_mem_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:$i] : (mem(X,ty_2Ebinary__ieee_2Efloat__value) => (X = inj__ty_2Ebinary__ieee_2Efloat__value(surj__ty_2Ebinary__ieee_2Efloat__value(X)))))).
tff(tp_c_2Ebinary__ieee_2EFloat,type,(c_2Ebinary__ieee_2EFloat:$i)).
tff(mem_c_2Ebinary__ieee_2EFloat,axiom,mem(c_2Ebinary__ieee_2EFloat,arr(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat__value))).
tff(stp_fo_c_2Ebinary__ieee_2EFloat,type,(fo__c_2Ebinary__ieee_2EFloat:(tp__ty_2Erealax_2Ereal) > tp__ty_2Ebinary__ieee_2Efloat__value)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EFloat,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : (inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2EFloat(X0)) = ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ebinary__ieee_2EGT,type,(c_2Ebinary__ieee_2EGT:$i)).
tff(mem_c_2Ebinary__ieee_2EGT,axiom,mem(c_2Ebinary__ieee_2EGT,ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_fo_c_2Ebinary__ieee_2EGT,type,(fo__c_2Ebinary__ieee_2EGT:tp__ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EGT,axiom,(inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EGT) = c_2Ebinary__ieee_2EGT)).
tff(tp_c_2Ebinary__ieee_2EInfinity,type,(c_2Ebinary__ieee_2EInfinity:$i)).
tff(mem_c_2Ebinary__ieee_2EInfinity,axiom,mem(c_2Ebinary__ieee_2EInfinity,ty_2Ebinary__ieee_2Efloat__value)).
tff(stp_fo_c_2Ebinary__ieee_2EInfinity,type,(fo__c_2Ebinary__ieee_2EInfinity:tp__ty_2Ebinary__ieee_2Efloat__value)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EInfinity,axiom,(inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2EInfinity) = c_2Ebinary__ieee_2EInfinity)).
tff(tp_c_2Ebinary__ieee_2ELT,type,(c_2Ebinary__ieee_2ELT:$i)).
tff(mem_c_2Ebinary__ieee_2ELT,axiom,mem(c_2Ebinary__ieee_2ELT,ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_fo_c_2Ebinary__ieee_2ELT,type,(fo__c_2Ebinary__ieee_2ELT:tp__ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_eq_fo_c_2Ebinary__ieee_2ELT,axiom,(inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2ELT) = c_2Ebinary__ieee_2ELT)).
tff(tp_c_2Ebinary__ieee_2ENaN,type,(c_2Ebinary__ieee_2ENaN:$i)).
tff(mem_c_2Ebinary__ieee_2ENaN,axiom,mem(c_2Ebinary__ieee_2ENaN,ty_2Ebinary__ieee_2Efloat__value)).
tff(stp_fo_c_2Ebinary__ieee_2ENaN,type,(fo__c_2Ebinary__ieee_2ENaN:tp__ty_2Ebinary__ieee_2Efloat__value)).
tff(stp_eq_fo_c_2Ebinary__ieee_2ENaN,axiom,(inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2ENaN) = c_2Ebinary__ieee_2ENaN)).
tff(tp_c_2Ebinary__ieee_2EULP,type,(c_2Ebinary__ieee_2EULP:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2EULP,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2EULP(A_27t,A_27w),arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ty_2Erealax_2Ereal))))).
tff(tp_c_2Ebinary__ieee_2EUN,type,(c_2Ebinary__ieee_2EUN:$i)).
tff(mem_c_2Ebinary__ieee_2EUN,axiom,mem(c_2Ebinary__ieee_2EUN,ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_fo_c_2Ebinary__ieee_2EUN,type,(fo__c_2Ebinary__ieee_2EUN:tp__ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EUN,axiom,(inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EUN) = c_2Ebinary__ieee_2EUN)).
tff(stp_ty_2Ebinary__ieee_2Eflags,type,(tp__ty_2Ebinary__ieee_2Eflags : $tType)).
tff(stp_inj_ty_2Ebinary__ieee_2Eflags,type,(inj__ty_2Ebinary__ieee_2Eflags : tp__ty_2Ebinary__ieee_2Eflags > $i)).
tff(stp_surj_ty_2Ebinary__ieee_2Eflags,type,(surj__ty_2Ebinary__ieee_2Eflags : $i > tp__ty_2Ebinary__ieee_2Eflags)).
tff(stp_inj_surj_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(inj__ty_2Ebinary__ieee_2Eflags(X)) = X))).
tff(stp_inj_mem_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Eflags] : (mem(inj__ty_2Ebinary__ieee_2Eflags(X),ty_2Ebinary__ieee_2Eflags)))).
tff(stp_iso_mem_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:$i] : (mem(X,ty_2Ebinary__ieee_2Eflags) => (X = inj__ty_2Ebinary__ieee_2Eflags(surj__ty_2Ebinary__ieee_2Eflags(X)))))).
tff(tp_c_2Ebinary__ieee_2Echeck__for__signalling,type,(c_2Ebinary__ieee_2Echeck__for__signalling:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Echeck__for__signalling,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ebinary__ieee_2Echeck__for__signalling(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),ty_2Ebinary__ieee_2Eflags))))).
tff(tp_c_2Ebinary__ieee_2Eclear__flags,type,(c_2Ebinary__ieee_2Eclear__flags:$i)).
tff(mem_c_2Ebinary__ieee_2Eclear__flags,axiom,mem(c_2Ebinary__ieee_2Eclear__flags,ty_2Ebinary__ieee_2Eflags)).
tff(stp_fo_c_2Ebinary__ieee_2Eclear__flags,type,(fo__c_2Ebinary__ieee_2Eclear__flags:tp__ty_2Ebinary__ieee_2Eflags)).
tff(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)).
tff(tp_c_2Ebinary__ieee_2Eclosest,type,(c_2Ebinary__ieee_2Eclosest:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Eclosest,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ebinary__ieee_2Eclosest(A_27a,A_27b),arr(arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool),arr(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))))))).
tff(tp_c_2Ebinary__ieee_2Eclosest__such,type,(c_2Ebinary__ieee_2Eclosest__such:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Eclosest__such,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ebinary__ieee_2Eclosest__such(A_27a,A_27b),arr(arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool),arr(arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool),arr(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)))))))).
tff(tp_c_2Ebinary__ieee_2Edividezero__flags,type,(c_2Ebinary__ieee_2Edividezero__flags:$i)).
tff(mem_c_2Ebinary__ieee_2Edividezero__flags,axiom,mem(c_2Ebinary__ieee_2Edividezero__flags,ty_2Ebinary__ieee_2Eflags)).
tff(stp_fo_c_2Ebinary__ieee_2Edividezero__flags,type,(fo__c_2Ebinary__ieee_2Edividezero__flags:tp__ty_2Ebinary__ieee_2Eflags)).
tff(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)).
tff(tp_c_2Ebinary__ieee_2Eexponent__boundary,type,(c_2Ebinary__ieee_2Eexponent__boundary:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Eexponent__boundary,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Eexponent__boundary(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)))))).
tff(tp_c_2Ebinary__ieee_2Eflags__CASE,type,(c_2Ebinary__ieee_2Eflags__CASE:del > $i)).
tff(mem_c_2Ebinary__ieee_2Eflags__CASE,axiom,( ! [A_27a:del] : mem(c_2Ebinary__ieee_2Eflags__CASE(A_27a),arr(ty_2Ebinary__ieee_2Eflags,arr(arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,A_27a)))))),A_27a))))).
tff(tp_c_2Ebinary__ieee_2Eflags__DivideByZero,type,(c_2Ebinary__ieee_2Eflags__DivideByZero:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__DivideByZero,axiom,mem(c_2Ebinary__ieee_2Eflags__DivideByZero,arr(ty_2Ebinary__ieee_2Eflags,bool))).
tff(stp_fo_c_2Ebinary__ieee_2Eflags__DivideByZero,type,(fo__c_2Ebinary__ieee_2Eflags__DivideByZero:(tp__ty_2Ebinary__ieee_2Eflags) > tp__o)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Eflags__DivideByZero,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Eflags] : (inj__o(fo__c_2Ebinary__ieee_2Eflags__DivideByZero(X0)) = ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(X0))))).
tff(tp_c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,type,(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,axiom,mem(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,arr(arr(bool,bool),arr(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags)))).
tff(tp_c_2Ebinary__ieee_2Eflags__InvalidOp,type,(c_2Ebinary__ieee_2Eflags__InvalidOp:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__InvalidOp,axiom,mem(c_2Ebinary__ieee_2Eflags__InvalidOp,arr(ty_2Ebinary__ieee_2Eflags,bool))).
tff(stp_fo_c_2Ebinary__ieee_2Eflags__InvalidOp,type,(fo__c_2Ebinary__ieee_2Eflags__InvalidOp:(tp__ty_2Ebinary__ieee_2Eflags) > tp__o)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Eflags__InvalidOp,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Eflags] : (inj__o(fo__c_2Ebinary__ieee_2Eflags__InvalidOp(X0)) = ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(X0))))).
tff(tp_c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,type,(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,axiom,mem(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,arr(arr(bool,bool),arr(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags)))).
tff(tp_c_2Ebinary__ieee_2Eflags__Overflow,type,(c_2Ebinary__ieee_2Eflags__Overflow:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__Overflow,axiom,mem(c_2Ebinary__ieee_2Eflags__Overflow,arr(ty_2Ebinary__ieee_2Eflags,bool))).
tff(stp_fo_c_2Ebinary__ieee_2Eflags__Overflow,type,(fo__c_2Ebinary__ieee_2Eflags__Overflow:(tp__ty_2Ebinary__ieee_2Eflags) > tp__o)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Eflags__Overflow,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Eflags] : (inj__o(fo__c_2Ebinary__ieee_2Eflags__Overflow(X0)) = ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(X0))))).
tff(tp_c_2Ebinary__ieee_2Eflags__Overflow__fupd,type,(c_2Ebinary__ieee_2Eflags__Overflow__fupd:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__Overflow__fupd,axiom,mem(c_2Ebinary__ieee_2Eflags__Overflow__fupd,arr(arr(bool,bool),arr(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags)))).
tff(tp_c_2Ebinary__ieee_2Eflags__Precision,type,(c_2Ebinary__ieee_2Eflags__Precision:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__Precision,axiom,mem(c_2Ebinary__ieee_2Eflags__Precision,arr(ty_2Ebinary__ieee_2Eflags,bool))).
tff(stp_fo_c_2Ebinary__ieee_2Eflags__Precision,type,(fo__c_2Ebinary__ieee_2Eflags__Precision:(tp__ty_2Ebinary__ieee_2Eflags) > tp__o)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Eflags__Precision,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Eflags] : (inj__o(fo__c_2Ebinary__ieee_2Eflags__Precision(X0)) = ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(X0))))).
tff(tp_c_2Ebinary__ieee_2Eflags__Precision__fupd,type,(c_2Ebinary__ieee_2Eflags__Precision__fupd:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__Precision__fupd,axiom,mem(c_2Ebinary__ieee_2Eflags__Precision__fupd,arr(arr(bool,bool),arr(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags)))).
tff(tp_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,type,(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,axiom,mem(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,arr(ty_2Ebinary__ieee_2Eflags,bool))).
tff(stp_fo_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,type,(fo__c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding:(tp__ty_2Ebinary__ieee_2Eflags) > tp__o)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Eflags] : (inj__o(fo__c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding(X0)) = ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(X0))))).
tff(tp_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,type,(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,axiom,mem(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,arr(arr(bool,bool),arr(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags)))).
tff(tp_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,type,(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,axiom,mem(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,arr(ty_2Ebinary__ieee_2Eflags,bool))).
tff(stp_fo_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,type,(fo__c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding:(tp__ty_2Ebinary__ieee_2Eflags) > tp__o)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Eflags] : (inj__o(fo__c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding(X0)) = ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(X0))))).
tff(tp_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,type,(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,axiom,mem(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,arr(arr(bool,bool),arr(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags)))).
tff(tp_c_2Ebinary__ieee_2Eflags__size,type,(c_2Ebinary__ieee_2Eflags__size:$i)).
tff(mem_c_2Ebinary__ieee_2Eflags__size,axiom,mem(c_2Ebinary__ieee_2Eflags__size,arr(ty_2Ebinary__ieee_2Eflags,ty_2Enum_2Enum))).
tff(stp_fo_c_2Ebinary__ieee_2Eflags__size,type,(fo__c_2Ebinary__ieee_2Eflags__size:(tp__ty_2Ebinary__ieee_2Eflags) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Eflags__size,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Eflags] : (inj__ty_2Enum_2Enum(fo__c_2Ebinary__ieee_2Eflags__size(X0)) = ap(c_2Ebinary__ieee_2Eflags__size,inj__ty_2Ebinary__ieee_2Eflags(X0))))).
tff(tp_c_2Ebinary__ieee_2Efloat__CASE,type,(c_2Ebinary__ieee_2Efloat__CASE:(del * del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__CASE,axiom,( ! [A_27a:del] : ( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__CASE(A_27a,A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27w),arr(ty_2Efcp_2Ecart(bool,A_27t),A_27a))),A_27a))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__Exponent,type,(c_2Ebinary__ieee_2Efloat__Exponent:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__Exponent__fupd,type,(c_2Ebinary__ieee_2Efloat__Exponent__fupd:(del * del * del) > $i)).
tff(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)))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__Sign,type,(c_2Ebinary__ieee_2Efloat__Sign:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__Sign__fupd,type,(c_2Ebinary__ieee_2Efloat__Sign__fupd:(del * del) > $i)).
tff(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))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__Significand,type,(c_2Ebinary__ieee_2Efloat__Significand:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__Significand__fupd,type,(c_2Ebinary__ieee_2Efloat__Significand__fupd:(del * del * del) > $i)).
tff(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)))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__abs,type,(c_2Ebinary__ieee_2Efloat__abs:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__abs,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__abs(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__add,type,(c_2Ebinary__ieee_2Efloat__add:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__add,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__add(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))))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__bottom,type,(c_2Ebinary__ieee_2Efloat__bottom:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__bottom,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__compare,type,(c_2Ebinary__ieee_2Efloat__compare:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__compare,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__compare(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat__compare)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__compare2num,type,(c_2Ebinary__ieee_2Efloat__compare2num:$i)).
tff(mem_c_2Ebinary__ieee_2Efloat__compare2num,axiom,mem(c_2Ebinary__ieee_2Efloat__compare2num,arr(ty_2Ebinary__ieee_2Efloat__compare,ty_2Enum_2Enum))).
tff(stp_fo_c_2Ebinary__ieee_2Efloat__compare2num,type,(fo__c_2Ebinary__ieee_2Efloat__compare2num:(tp__ty_2Ebinary__ieee_2Efloat__compare) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Efloat__compare2num,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Efloat__compare] : (inj__ty_2Enum_2Enum(fo__c_2Ebinary__ieee_2Efloat__compare2num(X0)) = ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(X0))))).
tff(tp_c_2Ebinary__ieee_2Efloat__compare__CASE,type,(c_2Ebinary__ieee_2Efloat__compare__CASE:del > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__compare__CASE,axiom,( ! [A_27a:del] : mem(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),arr(ty_2Ebinary__ieee_2Efloat__compare,arr(A_27a,arr(A_27a,arr(A_27a,arr(A_27a,A_27a)))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__compare__size,type,(c_2Ebinary__ieee_2Efloat__compare__size:$i)).
tff(mem_c_2Ebinary__ieee_2Efloat__compare__size,axiom,mem(c_2Ebinary__ieee_2Efloat__compare__size,arr(ty_2Ebinary__ieee_2Efloat__compare,ty_2Enum_2Enum))).
tff(stp_fo_c_2Ebinary__ieee_2Efloat__compare__size,type,(fo__c_2Ebinary__ieee_2Efloat__compare__size:(tp__ty_2Ebinary__ieee_2Efloat__compare) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Efloat__compare__size,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Efloat__compare] : (inj__ty_2Enum_2Enum(fo__c_2Ebinary__ieee_2Efloat__compare__size(X0)) = ap(c_2Ebinary__ieee_2Efloat__compare__size,inj__ty_2Ebinary__ieee_2Efloat__compare(X0))))).
tff(tp_c_2Ebinary__ieee_2Efloat__div,type,(c_2Ebinary__ieee_2Efloat__div:(del * del) > $i)).
tff(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))))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__equal,type,(c_2Ebinary__ieee_2Efloat__equal:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__equal,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__equal(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__greater__equal,type,(c_2Ebinary__ieee_2Efloat__greater__equal:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__greater__equal,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__greater__equal(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__greater__than,type,(c_2Ebinary__ieee_2Efloat__greater__than:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__greater__than,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__greater__than(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__is__finite,type,(c_2Ebinary__ieee_2Efloat__is__finite:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__is__finite,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))))).
tff(tp_c_2Ebinary__ieee_2Efloat__is__infinite,type,(c_2Ebinary__ieee_2Efloat__is__infinite:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__is__infinite,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__is__infinite(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))))).
tff(tp_c_2Ebinary__ieee_2Efloat__is__integral,type,(c_2Ebinary__ieee_2Efloat__is__integral:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__is__integral,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__is__integral(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))))).
tff(tp_c_2Ebinary__ieee_2Efloat__is__nan,type,(c_2Ebinary__ieee_2Efloat__is__nan:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__is__nan,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__is__nan(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))))).
tff(tp_c_2Ebinary__ieee_2Efloat__is__normal,type,(c_2Ebinary__ieee_2Efloat__is__normal:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__is__normal,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__is__normal(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))))).
tff(tp_c_2Ebinary__ieee_2Efloat__is__signalling,type,(c_2Ebinary__ieee_2Efloat__is__signalling:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__is__signalling,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__is__signalling(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))))).
tff(tp_c_2Ebinary__ieee_2Efloat__is__subnormal,type,(c_2Ebinary__ieee_2Efloat__is__subnormal:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__is__subnormal,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))))).
tff(tp_c_2Ebinary__ieee_2Efloat__is__zero,type,(c_2Ebinary__ieee_2Efloat__is__zero:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__is__zero,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))))).
tff(tp_c_2Ebinary__ieee_2Efloat__less__equal,type,(c_2Ebinary__ieee_2Efloat__less__equal:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__less__equal,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__less__equal(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__less__than,type,(c_2Ebinary__ieee_2Efloat__less__than:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__less__than,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__less__than(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__minus__infinity,type,(c_2Ebinary__ieee_2Efloat__minus__infinity:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__minus__min,type,(c_2Ebinary__ieee_2Efloat__minus__min:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__minus__zero,type,(c_2Ebinary__ieee_2Efloat__minus__zero:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__mul,type,(c_2Ebinary__ieee_2Efloat__mul:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__mul,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__mul(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))))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__mul__add,type,(c_2Ebinary__ieee_2Efloat__mul__add:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__mul__add,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__mul__add(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),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__mul__sub,type,(c_2Ebinary__ieee_2Efloat__mul__sub:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__mul__sub,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__mul__sub(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),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__negate,type,(c_2Ebinary__ieee_2Efloat__negate:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__plus__infinity,type,(c_2Ebinary__ieee_2Efloat__plus__infinity:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__plus__min,type,(c_2Ebinary__ieee_2Efloat__plus__min:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__plus__zero,type,(c_2Ebinary__ieee_2Efloat__plus__zero:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__round,type,(c_2Ebinary__ieee_2Efloat__round:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__round,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Erounding,arr(bool,arr(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__round__to__integral,type,(c_2Ebinary__ieee_2Efloat__round__to__integral:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__round__to__integral,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__round__to__integral(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__round__with__flags,type,(c_2Ebinary__ieee_2Efloat__round__with__flags:(del * del) > $i)).
tff(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))))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__size,type,(c_2Ebinary__ieee_2Efloat__size:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__size,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),arr(arr(A_27t,ty_2Enum_2Enum),arr(arr(A_27w,ty_2Enum_2Enum),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Enum_2Enum))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__some__qnan,type,(c_2Ebinary__ieee_2Efloat__some__qnan:(del * del) > $i)).
tff(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)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__sqrt,type,(c_2Ebinary__ieee_2Efloat__sqrt:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__sqrt,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__sub,type,(c_2Ebinary__ieee_2Efloat__sub:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__sub,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__sub(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))))))))).
tff(stp_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,type,(tp__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint : $tType)).
tff(stp_inj_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,type,(inj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint : tp__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint > $i)).
tff(stp_surj_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,type,(surj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint : $i > tp__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint)).
tff(stp_inj_surj_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,axiom,( ! [X:tp__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint] : (surj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint(inj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint(X)) = X))).
tff(stp_inj_mem_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,axiom,( ! [X:tp__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint] : (mem(inj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint(X),ty_2Eoption_2Eoption(ty_2Einteger_2Eint))))).
tff(stp_iso_mem_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,axiom,( ! [X:$i] : (mem(X,ty_2Eoption_2Eoption(ty_2Einteger_2Eint)) => (X = inj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint(surj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint(X)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__to__int,type,(c_2Ebinary__ieee_2Efloat__to__int:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__to__int,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__to__int(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Eoption_2Eoption(ty_2Einteger_2Eint))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__to__real,type,(c_2Ebinary__ieee_2Efloat__to__real:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__to__real,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Erealax_2Ereal))))).
tff(tp_c_2Ebinary__ieee_2Efloat__top,type,(c_2Ebinary__ieee_2Efloat__top:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__top,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))).
tff(tp_c_2Ebinary__ieee_2Efloat__value,type,(c_2Ebinary__ieee_2Efloat__value:(del * del) > $i)).
tff(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))))).
tff(tp_c_2Ebinary__ieee_2Efloat__value__CASE,type,(c_2Ebinary__ieee_2Efloat__value__CASE:del > $i)).
tff(mem_c_2Ebinary__ieee_2Efloat__value__CASE,axiom,( ! [A_27a:del] : mem(c_2Ebinary__ieee_2Efloat__value__CASE(A_27a),arr(ty_2Ebinary__ieee_2Efloat__value,arr(arr(ty_2Erealax_2Ereal,A_27a),arr(A_27a,arr(A_27a,A_27a))))))).
tff(tp_c_2Ebinary__ieee_2Efloat__value__size,type,(c_2Ebinary__ieee_2Efloat__value__size:$i)).
tff(mem_c_2Ebinary__ieee_2Efloat__value__size,axiom,mem(c_2Ebinary__ieee_2Efloat__value__size,arr(ty_2Ebinary__ieee_2Efloat__value,ty_2Enum_2Enum))).
tff(stp_fo_c_2Ebinary__ieee_2Efloat__value__size,type,(fo__c_2Ebinary__ieee_2Efloat__value__size:(tp__ty_2Ebinary__ieee_2Efloat__value) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Efloat__value__size,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Efloat__value] : (inj__ty_2Enum_2Enum(fo__c_2Ebinary__ieee_2Efloat__value__size(X0)) = ap(c_2Ebinary__ieee_2Efloat__value__size,inj__ty_2Ebinary__ieee_2Efloat__value(X0))))).
tff(tp_c_2Ebinary__ieee_2Efp__op__CASE,type,(c_2Ebinary__ieee_2Efp__op__CASE:(del * del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efp__op__CASE,axiom,( ! [A_27a:del] : ( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a))))))))))))).
tff(tp_c_2Ebinary__ieee_2Efp__op__size,type,(c_2Ebinary__ieee_2Efp__op__size:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Efp__op__size,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Efp__op__size(A_27t,A_27w),arr(arr(A_27t,ty_2Enum_2Enum),arr(arr(A_27w,ty_2Enum_2Enum),arr(ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w),ty_2Enum_2Enum))))))).
tff(tp_c_2Ebinary__ieee_2Eintegral__round,type,(c_2Ebinary__ieee_2Eintegral__round:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Eintegral__round,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Eintegral__round(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))).
tff(tp_c_2Ebinary__ieee_2Einvalidop__flags,type,(c_2Ebinary__ieee_2Einvalidop__flags:$i)).
tff(mem_c_2Ebinary__ieee_2Einvalidop__flags,axiom,mem(c_2Ebinary__ieee_2Einvalidop__flags,ty_2Ebinary__ieee_2Eflags)).
tff(stp_fo_c_2Ebinary__ieee_2Einvalidop__flags,type,(fo__c_2Ebinary__ieee_2Einvalidop__flags:tp__ty_2Ebinary__ieee_2Eflags)).
tff(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)).
tff(tp_c_2Ebinary__ieee_2Eis__closest,type,(c_2Ebinary__ieee_2Eis__closest:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Eis__closest,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ebinary__ieee_2Eis__closest(A_27a,A_27b),arr(arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool),arr(ty_2Erealax_2Ereal,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))))))).
tff(tp_c_2Ebinary__ieee_2Eis__integral,type,(c_2Ebinary__ieee_2Eis__integral:$i)).
tff(mem_c_2Ebinary__ieee_2Eis__integral,axiom,mem(c_2Ebinary__ieee_2Eis__integral,arr(ty_2Erealax_2Ereal,bool))).
tff(stp_fo_c_2Ebinary__ieee_2Eis__integral,type,(fo__c_2Ebinary__ieee_2Eis__integral:(tp__ty_2Erealax_2Ereal) > tp__o)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Eis__integral,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : (inj__o(fo__c_2Ebinary__ieee_2Eis__integral(X0)) = ap(c_2Ebinary__ieee_2Eis__integral,inj__ty_2Erealax_2Ereal(X0))))).
tff(tp_c_2Ebinary__ieee_2Elargest,type,(c_2Ebinary__ieee_2Elargest:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Elargest,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Erealax_2Ereal))))).
tff(tp_c_2Ebinary__ieee_2Enum2float__compare,type,(c_2Ebinary__ieee_2Enum2float__compare:$i)).
tff(mem_c_2Ebinary__ieee_2Enum2float__compare,axiom,mem(c_2Ebinary__ieee_2Enum2float__compare,arr(ty_2Enum_2Enum,ty_2Ebinary__ieee_2Efloat__compare))).
tff(stp_fo_c_2Ebinary__ieee_2Enum2float__compare,type,(fo__c_2Ebinary__ieee_2Enum2float__compare:(tp__ty_2Enum_2Enum) > tp__ty_2Ebinary__ieee_2Efloat__compare)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Enum2float__compare,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2Enum2float__compare(X0)) = ap(c_2Ebinary__ieee_2Enum2float__compare,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Ebinary__ieee_2Enum2rounding,type,(c_2Ebinary__ieee_2Enum2rounding:$i)).
tff(mem_c_2Ebinary__ieee_2Enum2rounding,axiom,mem(c_2Ebinary__ieee_2Enum2rounding,arr(ty_2Enum_2Enum,ty_2Ebinary__ieee_2Erounding))).
tff(stp_fo_c_2Ebinary__ieee_2Enum2rounding,type,(fo__c_2Ebinary__ieee_2Enum2rounding:(tp__ty_2Enum_2Enum) > tp__ty_2Ebinary__ieee_2Erounding)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Enum2rounding,axiom,( ! [X0:tp__ty_2Enum_2Enum] : (inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2Enum2rounding(X0)) = ap(c_2Ebinary__ieee_2Enum2rounding,inj__ty_2Enum_2Enum(X0))))).
tff(tp_c_2Ebinary__ieee_2Ereal__to__float,type,(c_2Ebinary__ieee_2Ereal__to__float:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Ereal__to__float,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ebinary__ieee_2Ereal__to__float(A_27a,A_27b),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))))))).
tff(tp_c_2Ebinary__ieee_2Ereal__to__float__with__flags,type,(c_2Ebinary__ieee_2Ereal__to__float__with__flags:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Ereal__to__float__with__flags,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : mem(c_2Ebinary__ieee_2Ereal__to__float__with__flags(A_27a,A_27b),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Erealax_2Ereal,ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)))))))).
tff(tp_c_2Ebinary__ieee_2Erecordtype_2Eflags,type,(c_2Ebinary__ieee_2Erecordtype_2Eflags:$i)).
tff(mem_c_2Ebinary__ieee_2Erecordtype_2Eflags,axiom,mem(c_2Ebinary__ieee_2Erecordtype_2Eflags,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,ty_2Ebinary__ieee_2Eflags)))))))).
tff(stp_fo_c_2Ebinary__ieee_2Erecordtype_2Eflags,type,(fo__c_2Ebinary__ieee_2Erecordtype_2Eflags:(tp__o * tp__o * tp__o * tp__o * tp__o * tp__o) > tp__ty_2Ebinary__ieee_2Eflags)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Erecordtype_2Eflags,axiom,( ! [X0:tp__o] : ( ! [X1:tp__o] : ( ! [X2:tp__o] : ( ! [X3:tp__o] : ( ! [X4:tp__o] : ( ! [X5:tp__o] : (inj__ty_2Ebinary__ieee_2Eflags(fo__c_2Ebinary__ieee_2Erecordtype_2Eflags(X0,X1,X2,X3,X4,X5)) = ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(X0)),inj__o(X1)),inj__o(X2)),inj__o(X3)),inj__o(X4)),inj__o(X5)))))))))).
tff(tp_c_2Ebinary__ieee_2Erecordtype_2Efloat,type,(c_2Ebinary__ieee_2Erecordtype_2Efloat:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Erecordtype_2Efloat,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27w),arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))).
tff(tp_c_2Ebinary__ieee_2Eround,type,(c_2Ebinary__ieee_2Eround:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Eround,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Eround(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))).
tff(tp_c_2Ebinary__ieee_2EroundTiesToEven,type,(c_2Ebinary__ieee_2EroundTiesToEven:$i)).
tff(mem_c_2Ebinary__ieee_2EroundTiesToEven,axiom,mem(c_2Ebinary__ieee_2EroundTiesToEven,ty_2Ebinary__ieee_2Erounding)).
tff(stp_fo_c_2Ebinary__ieee_2EroundTiesToEven,type,(fo__c_2Ebinary__ieee_2EroundTiesToEven:tp__ty_2Ebinary__ieee_2Erounding)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EroundTiesToEven,axiom,(inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven) = c_2Ebinary__ieee_2EroundTiesToEven)).
tff(tp_c_2Ebinary__ieee_2EroundTowardNegative,type,(c_2Ebinary__ieee_2EroundTowardNegative:$i)).
tff(mem_c_2Ebinary__ieee_2EroundTowardNegative,axiom,mem(c_2Ebinary__ieee_2EroundTowardNegative,ty_2Ebinary__ieee_2Erounding)).
tff(stp_fo_c_2Ebinary__ieee_2EroundTowardNegative,type,(fo__c_2Ebinary__ieee_2EroundTowardNegative:tp__ty_2Ebinary__ieee_2Erounding)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EroundTowardNegative,axiom,(inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative) = c_2Ebinary__ieee_2EroundTowardNegative)).
tff(tp_c_2Ebinary__ieee_2EroundTowardPositive,type,(c_2Ebinary__ieee_2EroundTowardPositive:$i)).
tff(mem_c_2Ebinary__ieee_2EroundTowardPositive,axiom,mem(c_2Ebinary__ieee_2EroundTowardPositive,ty_2Ebinary__ieee_2Erounding)).
tff(stp_fo_c_2Ebinary__ieee_2EroundTowardPositive,type,(fo__c_2Ebinary__ieee_2EroundTowardPositive:tp__ty_2Ebinary__ieee_2Erounding)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EroundTowardPositive,axiom,(inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive) = c_2Ebinary__ieee_2EroundTowardPositive)).
tff(tp_c_2Ebinary__ieee_2EroundTowardZero,type,(c_2Ebinary__ieee_2EroundTowardZero:$i)).
tff(mem_c_2Ebinary__ieee_2EroundTowardZero,axiom,mem(c_2Ebinary__ieee_2EroundTowardZero,ty_2Ebinary__ieee_2Erounding)).
tff(stp_fo_c_2Ebinary__ieee_2EroundTowardZero,type,(fo__c_2Ebinary__ieee_2EroundTowardZero:tp__ty_2Ebinary__ieee_2Erounding)).
tff(stp_eq_fo_c_2Ebinary__ieee_2EroundTowardZero,axiom,(inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero) = c_2Ebinary__ieee_2EroundTowardZero)).
tff(tp_c_2Ebinary__ieee_2Erounding2num,type,(c_2Ebinary__ieee_2Erounding2num:$i)).
tff(mem_c_2Ebinary__ieee_2Erounding2num,axiom,mem(c_2Ebinary__ieee_2Erounding2num,arr(ty_2Ebinary__ieee_2Erounding,ty_2Enum_2Enum))).
tff(stp_fo_c_2Ebinary__ieee_2Erounding2num,type,(fo__c_2Ebinary__ieee_2Erounding2num:(tp__ty_2Ebinary__ieee_2Erounding) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Erounding2num,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Erounding] : (inj__ty_2Enum_2Enum(fo__c_2Ebinary__ieee_2Erounding2num(X0)) = ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(X0))))).
tff(tp_c_2Ebinary__ieee_2Erounding__CASE,type,(c_2Ebinary__ieee_2Erounding__CASE:del > $i)).
tff(mem_c_2Ebinary__ieee_2Erounding__CASE,axiom,( ! [A_27a:del] : mem(c_2Ebinary__ieee_2Erounding__CASE(A_27a),arr(ty_2Ebinary__ieee_2Erounding,arr(A_27a,arr(A_27a,arr(A_27a,arr(A_27a,A_27a)))))))).
tff(tp_c_2Ebinary__ieee_2Erounding__size,type,(c_2Ebinary__ieee_2Erounding__size:$i)).
tff(mem_c_2Ebinary__ieee_2Erounding__size,axiom,mem(c_2Ebinary__ieee_2Erounding__size,arr(ty_2Ebinary__ieee_2Erounding,ty_2Enum_2Enum))).
tff(stp_fo_c_2Ebinary__ieee_2Erounding__size,type,(fo__c_2Ebinary__ieee_2Erounding__size:(tp__ty_2Ebinary__ieee_2Erounding) > tp__ty_2Enum_2Enum)).
tff(stp_eq_fo_c_2Ebinary__ieee_2Erounding__size,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Erounding] : (inj__ty_2Enum_2Enum(fo__c_2Ebinary__ieee_2Erounding__size(X0)) = ap(c_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(X0))))).
tff(tp_c_2Ebinary__ieee_2Ethreshold,type,(c_2Ebinary__ieee_2Ethreshold:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Ethreshold,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Erealax_2Ereal))))).
tff(tp_c_2Ebinary__ieee_2Eulp,type,(c_2Ebinary__ieee_2Eulp:(del * del) > $i)).
tff(mem_c_2Ebinary__ieee_2Eulp,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : mem(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Erealax_2Ereal))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__TY__DEF,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (? [V0rep:$i] : (mem(V0rep,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27t)))))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27t)))),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3012(A_27w,A_27t)),V0rep))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__case__def,axiom,( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0a0:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1a1:$i] : (mem(V1a1,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V2a2:$i] : (mem(V2a2,ty_2Efcp_2Ecart(bool,A_27t)) => ( ! [V3f:$i] : (mem(V3f,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27w),arr(ty_2Efcp_2Ecart(bool,A_27t),A_27a)))) => (ap(ap(c_2Ebinary__ieee_2Efloat__CASE(A_27a,A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0a0)),V1a1),V2a2)),V3f) = ap(ap(ap(V3f,inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0a0)),V1a1),V2a2))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__size__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f:$i] : (mem(V0f,arr(A_27t,ty_2Enum_2Enum)) => ( ! [V1f1:$i] : (mem(V1f1,arr(A_27w,ty_2Enum_2Enum)) => ( ! [V2a0:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V3a1:$i] : (mem(V3a1,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V4a2:$i] : (mem(V4a2,ty_2Efcp_2Ecart(bool,A_27t)) => (surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V0f),V1f1),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V2a0)),V3a1),V4a2))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__Sign,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1c0:$i] : (mem(V1c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V2c1:$i] : (mem(V2c1,ty_2Efcp_2Ecart(bool,A_27t)) => (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0c)),V1c0),V2c1))) = V0c))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__Exponent,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1c0:$i] : (mem(V1c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V2c1:$i] : (mem(V2c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0c)),V1c0),V2c1)) = V1c0))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__Significand,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1c0:$i] : (mem(V1c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V2c1:$i] : (mem(V2c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0c)),V1c0),V2c1)) = V2c1))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__accessors,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: (( ! [V0c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1c0:$i] : (mem(V1c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V2c1:$i] : (mem(V2c1,ty_2Efcp_2Ecart(bool,A_27t)) => (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0c)),V1c0),V2c1))) = V0c)))))) & (( ! [V3c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V4c0:$i] : (mem(V4c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V5c1:$i] : (mem(V5c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V3c)),V4c0),V5c1)) = V4c0)))))) & ( ! [V6c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V7c0:$i] : (mem(V7c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V8c1:$i] : (mem(V8c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V6c)),V7c0),V8c1)) = V8c1)))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__Sign__fupd,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f:$i] : (mem(V0f,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ( ! [V1c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V2c0:$i] : (mem(V2c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V3c1:$i] : (mem(V3c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V0f),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c)),V2c0),V3c1)) = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),ap(V0f,inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c))),V2c0),V3c1)))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__Exponent__fupd,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [V0f:$i] : (mem(V0f,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ( ! [V1c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V2c0:$i] : (mem(V2c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V3c1:$i] : (mem(V3c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V0f),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c)),V2c0),V3c1)) = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27x),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c)),ap(V0f,V2c0)),V3c1))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__Significand__fupd,axiom,( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [V0f:$i] : (mem(V0f,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ( ! [V1c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V2c0:$i] : (mem(V2c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V3c1:$i] : (mem(V3c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V0f),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c)),V2c0),V3c1)) = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27u,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c)),V2c0),ap(V0f,V3c1)))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__fn__updates,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: (( ! [V0f:$i] : (mem(V0f,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ( ! [V1c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V2c0:$i] : (mem(V2c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V3c1:$i] : (mem(V3c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V0f),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c)),V2c0),V3c1)) = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),ap(V0f,inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c))),V2c0),V3c1))))))))) & (( ! [V4f:$i] : (mem(V4f,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ( ! [V5c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V6c0:$i] : (mem(V6c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V7c1:$i] : (mem(V7c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V4f),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V5c)),V6c0),V7c1)) = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27x),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V5c)),ap(V4f,V6c0)),V7c1))))))))) & ( ! [V8f:$i] : (mem(V8f,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ( ! [V9c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V10c0:$i] : (mem(V10c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V11c1:$i] : (mem(V11c1,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V8f),ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V9c)),V10c0),V11c1)) = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27u,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V9c)),V10c0),ap(V8f,V11c1)))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__accfupds,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: (( ! [V0f0:$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:$i] : (mem(V17f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27u,A_27w),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V16f0),V17f)) = ap(V16f0,ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V17f))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__fupdfupds,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27v:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [A_27y:del]: (( ! [V0g:$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)))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__fupdfupds__comp,lemma,(( ! [A_27a:del]: ( ! [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))) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V1f0)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V0g)) = 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))))))) & ( ! [V2h:$i] : (mem(V2h,arr(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))) => ( ! [V3g:$i] : (mem(V3g,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ( ! [V4f0:$i] : (mem(V4f0,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V4f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V3g)),V2h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),V4f0),V3g))),V2h))))))))) & ((( ! [V5g:$i] : (mem(V5g,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ( ! [V6f0:$i] : (mem(V6f0,arr(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27y))) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27y),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27x,A_27y),V6f0)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V5g)) = ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27y),ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27y),ty_2Efcp_2Ecart(bool,A_27x)),V6f0),V5g))))))) & ( ! [V7h:$i] : (mem(V7h,arr(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))) => ( ! [V8g:$i] : (mem(V8g,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ( ! [V9f0:$i] : (mem(V9f0,arr(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27y))) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27y),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27x,A_27y),V9f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V8g)),V7h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27y),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),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)),V9f0),V8g))),V7h))))))))) & (( ! [V10g:$i] : (mem(V10g,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ( ! [V11f0:$i] : (mem(V11f0,arr(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27v))) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27v,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27u,A_27v,A_27w),V11f0)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V10g)) = 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)),V11f0),V10g))))))) & ( ! [V12h:$i] : (mem(V12h,arr(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))) => ( ! [V13g:$i] : (mem(V13g,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ( ! [V14f0:$i] : (mem(V14f0,arr(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27v))) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27v,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27u,A_27v,A_27w),V14f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27u,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V13g)),V12h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27v,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27v,A_27w),ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27v),ty_2Efcp_2Ecart(bool,A_27u)),V14f0),V13g))),V12h)))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__fupdcanon,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: (( ! [V0g:$i] : (mem(V0g,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ( ! [V1f0:$i] : (mem(V1f0,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ( ! [V2f:$i] : (mem(V2f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),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_27x),V0g),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V1f0),V2f))))))))) & (( ! [V3g:$i] : (mem(V3g,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ( ! [V4f0:$i] : (mem(V4f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ( ! [V5f:$i] : (mem(V5f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V4f0),ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V3g),V5f)) = ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27w),V3g),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V4f0),V5f))))))))) & ( ! [V6g:$i] : (mem(V6g,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ( ! [V7f0:$i] : (mem(V7f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ( ! [V8f:$i] : (mem(V8f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27x),V7f0),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V6g),V8f)) = ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),V6g),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V7f0),V8f))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__fupdcanon__comp,lemma,(( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x: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,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V1f0)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V0g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27x),V0g)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V1f0))))))) & ( ! [V2h:$i] : (mem(V2h,arr(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))) => ( ! [V3g:$i] : (mem(V3g,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ( ! [V4f0:$i] : (mem(V4f0,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V4f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V3g)),V2h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27x),V3g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V4f0)),V2h)))))))))) & ((( ! [V5g:$i] : (mem(V5g,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ( ! [V6f0:$i] : (mem(V6f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V6f0)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V5g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27w),V5g)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V6f0))))))) & ( ! [V7h:$i] : (mem(V7h,arr(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))) => ( ! [V8g:$i] : (mem(V8g,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ( ! [V9f0:$i] : (mem(V9f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27u,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V9f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V8g)),V7h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27u,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27w),V8g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27u,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V9f0)),V7h)))))))))) & (( ! [V10g:$i] : (mem(V10g,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ( ! [V11f0:$i] : (mem(V11f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27x),V11f0)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V10g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27x),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),V10g)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V11f0))))))) & ( ! [V12h:$i] : (mem(V12h,arr(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))) => ( ! [V13g:$i] : (mem(V13g,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ( ! [V14f0:$i] : (mem(V14f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27u,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27x),V14f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27x),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V13g)),V12h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27u,A_27x),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),V13g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Efloat(A_27u,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V14f0)),V12h))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__component__equality,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f1:$i] : (mem(V0f1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1f2:$i] : (mem(V1f2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((V0f1 = V1f2) <=> ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0f1)) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V1f2))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0f1) = ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V1f2)) & (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0f1) = ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V1f2))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__updates__eq__literal,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [V0f:$i] : (mem(V0f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1c1:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V2c0:$i] : (mem(V2c0,ty_2Efcp_2Ecart(bool,A_27x)) => ( ! [V3c:$i] : (mem(V3c,ty_2Efcp_2Ecart(bool,A_27u)) => (ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c1))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27w)),V2c0)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27t)),V3c)),V0f))) = ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c1))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27w)),V2c0)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27t)),V3c)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__literal__nchotomy,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [V0f:$i] : (mem(V0f,ty_2Ebinary__ieee_2Efloat(A_27u,A_27x)) => (? [V1c1:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (? [V2c0:$i] : (mem(V2c0,ty_2Efcp_2Ecart(bool,A_27x)) & (? [V3c:$i] : (mem(V3c,ty_2Efcp_2Ecart(bool,A_27u)) & (V0f = ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c1))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27w)),V2c0)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27t)),V3c)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2EFORALL__float,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Efloat(A_27u,A_27x),bool)) => (( ! [V1f:$i] : (mem(V1f,ty_2Ebinary__ieee_2Efloat(A_27u,A_27x)) => p(ap(V0P,V1f)))) <=> ( ! [V2c1:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V3c0:$i] : (mem(V3c0,ty_2Efcp_2Ecart(bool,A_27x)) => ( ! [V4c:$i] : (mem(V4c,ty_2Efcp_2Ecart(bool,A_27u)) => p(ap(V0P,ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V2c1))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27w)),V3c0)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27t)),V4c)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2EEXISTS__float,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Efloat(A_27u,A_27x),bool)) => ((? [V1f:$i] : (mem(V1f,ty_2Ebinary__ieee_2Efloat(A_27u,A_27x)) & p(ap(V0P,V1f)))) <=> (? [V2c1:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (? [V3c0:$i] : (mem(V3c0,ty_2Efcp_2Ecart(bool,A_27x)) & (? [V4c:$i] : (mem(V4c,ty_2Efcp_2Ecart(bool,A_27u)) & p(ap(V0P,ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V2c1))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27w)),V3c0)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27t)),V4c)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__literal__11,lemma,(( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [V0c11:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1c01:$i] : (mem(V1c01,ty_2Efcp_2Ecart(bool,A_27x)) => ( ! [V2c1:$i] : (mem(V2c1,ty_2Efcp_2Ecart(bool,A_27u)) => ( ! [V3c12:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V4c02:$i] : (mem(V4c02,ty_2Efcp_2Ecart(bool,A_27x)) => ( ! [V5c2:$i] : (mem(V5c2,ty_2Efcp_2Ecart(bool,A_27u)) => ((ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0c11))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27w)),V1c01)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27t)),V2c1)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))) = ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27u,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V3c12))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27u,A_27w,A_27x),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27x),ty_2Efcp_2Ecart(bool,A_27w)),V4c02)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27u),ty_2Efcp_2Ecart(bool,A_27t)),V5c2)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))) <=> ((V0c11 = V3c12) & ((V1c01 = V4c02) & (V2c1 = V5c2)))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Edatatype__float,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0record:$i] : (mem(V0record,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27w),arr(ty_2Efcp_2Ecart(bool,A_27t),bool))))) => ( ! [V1float:$i] : (mem(V1float,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2Sign:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V3Exponent:$i] : (mem(V3Exponent,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V4Significand:$i] : (mem(V4Significand,ty_2Efcp_2Ecart(bool,A_27t)) => p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(ap(V0record,V1float),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V2Sign)),V3Exponent),V4Significand)))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__11,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0a0:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1a1:$i] : (mem(V1a1,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V2a2:$i] : (mem(V2a2,ty_2Efcp_2Ecart(bool,A_27t)) => ( ! [V3a0_27:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V4a1_27:$i] : (mem(V4a1_27,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V5a2_27:$i] : (mem(V5a2_27,ty_2Efcp_2Ecart(bool,A_27t)) => ((ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0a0)),V1a1),V2a2) = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V3a0_27)),V4a1_27),V5a2_27)) <=> ((V0a0 = V3a0_27) & ((V1a1 = V4a1_27) & (V2a2 = V5a2_27)))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__nchotomy,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0ff:$i] : (mem(V0ff,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (? [V1c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (? [V2c0:$i] : (mem(V2c0,ty_2Efcp_2Ecart(bool,A_27w)) & (? [V3c1:$i] : (mem(V3c1,ty_2Efcp_2Ecart(bool,A_27t)) & (V0ff = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c)),V2c0),V3c1))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__Axiom,lemma,(( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f:$i] : (mem(V0f,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27w),arr(ty_2Efcp_2Ecart(bool,A_27t),A_27a)))) => (? [V1fn:$i] : (mem(V1fn,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)) & ( ! [V2a0:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V3a1:$i] : (mem(V3a1,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V4a2:$i] : (mem(V4a2,ty_2Efcp_2Ecart(bool,A_27t)) => (ap(V1fn,ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V2a0)),V3a1),V4a2)) = ap(ap(ap(V0f,inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V2a0)),V3a1),V4a2)))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__induction,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)) => (( ! [V1c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V2c0:$i] : (mem(V2c0,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V3c1:$i] : (mem(V3c1,ty_2Efcp_2Ecart(bool,A_27t)) => p(ap(V0P,ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V1c)),V2c0),V3c1)))))))) => ( ! [V4f:$i] : (mem(V4f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => p(ap(V0P,V4f))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__case__cong,lemma,(( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f_27:$i] : (mem(V0f_27,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27w),arr(ty_2Efcp_2Ecart(bool,A_27t),A_27a)))) => ( ! [V1M:$i] : (mem(V1M,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2M_27:$i] : (mem(V2M_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V3f:$i] : (mem(V3f,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27w),arr(ty_2Efcp_2Ecart(bool,A_27t),A_27a)))) => (((V1M = V2M_27) & ( ! [V4a0:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V5a1:$i] : (mem(V5a1,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V6a2:$i] : (mem(V6a2,ty_2Efcp_2Ecart(bool,A_27t)) => ((V2M_27 = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V4a0)),V5a1),V6a2)) => (ap(ap(ap(V3f,inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V4a0)),V5a1),V6a2) = ap(ap(ap(V0f_27,inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V4a0)),V5a1),V6a2))))))))) => (ap(ap(c_2Ebinary__ieee_2Efloat__CASE(A_27a,A_27t,A_27w),V1M),V3f) = ap(ap(c_2Ebinary__ieee_2Efloat__CASE(A_27a,A_27t,A_27w),V2M_27),V0f_27)))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__case__eq,lemma,(( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1f:$i] : (mem(V1f,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),arr(ty_2Efcp_2Ecart(bool,A_27w),arr(ty_2Efcp_2Ecart(bool,A_27t),A_27a)))) => ( ! [V2v:$i] : (mem(V2v,A_27a) => ((ap(ap(c_2Ebinary__ieee_2Efloat__CASE(A_27a,A_27t,A_27w),V0x),V1f) = V2v) <=> (? [V3c:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (? [V4c0:$i] : (mem(V4c0,ty_2Efcp_2Ecart(bool,A_27w)) & (? [V5c1:$i] : (mem(V5c1,ty_2Efcp_2Ecart(bool,A_27t)) & ((V0x = ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Efloat(A_27t,A_27w),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V3c)),V4c0),V5c1)) & (ap(ap(ap(V1f,inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V3c)),V4c0),V5c1) = V2v))))))))))))))))))).
tff(stp_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,type,(tp__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal : $tType)).
tff(stp_inj_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,type,(inj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal : tp__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal > $i)).
tff(stp_surj_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,type,(surj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal : $i > tp__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal)).
tff(stp_inj_surj_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,axiom,( ! [X:tp__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal] : (surj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal(inj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal(X)) = X))).
tff(stp_inj_mem_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,axiom,( ! [X:tp__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal] : (mem(inj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal(X),ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal))))).
tff(stp_iso_mem_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,axiom,( ! [X:$i] : (mem(X,ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal)) => (X = inj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal(surj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal(X)))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__value__TY__DEF,axiom,(? [V0rep:$i] : (mem(V0rep,arr(ty_2Ebinary__ieee_2Efloat__value,ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(ty_2Erealax_2Ereal),ty_2Ebinary__ieee_2Efloat__value),f3017),V0rep))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__value__case__def,axiom,( ! [A_27a:del]: (( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1f:$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))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__value__size__def,axiom,(( ! [V0a:tp__ty_2Erealax_2Ereal] : (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__value__size,ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V0a)))) = 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(c_2Ebinary__ieee_2Efloat__value__size,inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2EInfinity))) = fo__c_2Enum_2E0) & (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__value__size,inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2ENaN))) = fo__c_2Enum_2E0)))).
tff(conj_thm_2Ebinary__ieee_2Edatatype__float__value,lemma,(( ! [V0float__value:$i] : (mem(V0float__value,arr(arr(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat__value),arr(ty_2Ebinary__ieee_2Efloat__value,arr(ty_2Ebinary__ieee_2Efloat__value,bool)))) => p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(V0float__value,c_2Ebinary__ieee_2EFloat),inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2EInfinity)),inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2ENaN)))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__value__11,lemma,(( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1a_27:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V0a))) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V1a_27)))) <=> (V0a = V1a_27)))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__value__distinct,lemma,((( ! [V0a:tp__ty_2Erealax_2Ereal] : (~~ (surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V0a))) = fo__c_2Ebinary__ieee_2EInfinity))) & (( ! [V1a:tp__ty_2Erealax_2Ereal] : (~~ (surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V1a))) = fo__c_2Ebinary__ieee_2ENaN))) & (~~ (fo__c_2Ebinary__ieee_2EInfinity = fo__c_2Ebinary__ieee_2ENaN)))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__value__nchotomy,lemma,(( ! [V0ff:tp__ty_2Ebinary__ieee_2Efloat__value] : ((? [V1r:tp__ty_2Erealax_2Ereal] : (V0ff = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V1r))))) | ((V0ff = fo__c_2Ebinary__ieee_2EInfinity) | (V0ff = fo__c_2Ebinary__ieee_2ENaN)))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__value__Axiom,lemma,(( ! [A_27a:del]: ( ! [V0f0:$i] : (mem(V0f0,arr(ty_2Erealax_2Ereal,A_27a)) => ( ! [V1f1:$i] : (mem(V1f1,A_27a) => ( ! [V2f2:$i] : (mem(V2f2,A_27a) => (? [V3fn:$i] : (mem(V3fn,arr(ty_2Ebinary__ieee_2Efloat__value,A_27a)) & (( ! [V4a:tp__ty_2Erealax_2Ereal] : (ap(V3fn,ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V4a))) = ap(V0f0,inj__ty_2Erealax_2Ereal(V4a)))) & ((ap(V3fn,inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2EInfinity)) = V1f1) & (ap(V3fn,inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2ENaN)) = V2f2)))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__value__induction,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Efloat__value,bool)) => ((( ! [V1r:tp__ty_2Erealax_2Ereal] : p(ap(V0P,ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V1r))))) & (p(ap(V0P,inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2EInfinity))) & p(ap(V0P,inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2ENaN))))) => ( ! [V2f:tp__ty_2Ebinary__ieee_2Efloat__value] : p(ap(V0P,inj__ty_2Ebinary__ieee_2Efloat__value(V2f))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__value__case__cong,lemma,(( ! [A_27a:del]: ( ! [V0f_27:$i] : (mem(V0f_27,arr(ty_2Erealax_2Ereal,A_27a)) => ( ! [V1v_27:$i] : (mem(V1v_27,A_27a) => ( ! [V2v1_27:$i] : (mem(V2v1_27,A_27a) => ( ! [V3M:tp__ty_2Ebinary__ieee_2Efloat__value] : ( ! [V4M_27:tp__ty_2Ebinary__ieee_2Efloat__value] : ( ! [V5f:$i] : (mem(V5f,arr(ty_2Erealax_2Ereal,A_27a)) => ( ! [V6v:$i] : (mem(V6v,A_27a) => ( ! [V7v1:$i] : (mem(V7v1,A_27a) => (((V3M = V4M_27) & (( ! [V8a:tp__ty_2Erealax_2Ereal] : ((V4M_27 = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V8a)))) => (ap(V5f,inj__ty_2Erealax_2Ereal(V8a)) = ap(V0f_27,inj__ty_2Erealax_2Ereal(V8a))))) & (((V4M_27 = fo__c_2Ebinary__ieee_2EInfinity) => (V6v = V1v_27)) & ((V4M_27 = fo__c_2Ebinary__ieee_2ENaN) => (V7v1 = V2v1_27))))) => (ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__value(V3M)),V5f),V6v),V7v1) = ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__value(V4M_27)),V0f_27),V1v_27),V2v1_27)))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__value__case__eq,lemma,(( ! [A_27a:del]: ( ! [V0x:tp__ty_2Ebinary__ieee_2Efloat__value] : ( ! [V1f:$i] : (mem(V1f,arr(ty_2Erealax_2Ereal,A_27a)) => ( ! [V2v:$i] : (mem(V2v,A_27a) => ( ! [V3v1:$i] : (mem(V3v1,A_27a) => ( ! [V4v_27:$i] : (mem(V4v_27,A_27a) => ((ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__value(V0x)),V1f),V2v),V3v1) = V4v_27) <=> ((? [V5r:tp__ty_2Erealax_2Ereal] : ((V0x = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V5r)))) & (ap(V1f,inj__ty_2Erealax_2Ereal(V5r)) = V4v_27))) | (((V0x = fo__c_2Ebinary__ieee_2EInfinity) & (V2v = V4v_27)) | ((V0x = fo__c_2Ebinary__ieee_2ENaN) & (V3v1 = V4v_27))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__to__real__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x)) = surj__ty_2Erealax_2Ereal(ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x)),ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(c_2Ewords_2Ew2n(ty_2Eone_2Eone),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0x)))),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(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w)))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Ewords_2Ew2n(A_27t),ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0x)))),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(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t)))))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(c_2Ewords_2Ew2n(ty_2Eone_2Eone),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0x)))),ap(ap(c_2Ereal_2E_2F,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(c_2Ewords_2Ew2n(A_27w),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x)))),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(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w)))))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Ewords_2Ew2n(A_27t),ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0x)))),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(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t)))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__value__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0x)) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(ap(ap(c_2Ebool_2ECOND(ty_2Ebinary__ieee_2Efloat__value),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x)),c_2Ewords_2Eword__T(A_27w))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Ebinary__ieee_2Efloat__value),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27t)),ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0x)),ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2EInfinity)),inj__ty_2Ebinary__ieee_2Efloat__value(fo__c_2Ebinary__ieee_2ENaN))),ap(c_2Ebinary__ieee_2EFloat,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x)))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__is__nan__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27t,A_27w),V0x)) <=> p(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(bool),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0x)),k(ty_2Erealax_2Ereal,c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2ET))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__is__signalling__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__signalling(A_27t,A_27w),V0x)) <=> (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27t,A_27w),V0x)) & (~~ p(ap(c_2Ewords_2Eword__msb(A_27t),ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0x))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__is__infinite__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27t,A_27w),V0x)) <=> p(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(bool),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0x)),k(ty_2Erealax_2Ereal,c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2EF))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__is__normal__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27t,A_27w),V0x)) <=> ((~~ (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x) = ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & (~~ (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x) = c_2Ewords_2Eword__T(A_27w)))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__is__subnormal__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27t,A_27w),V0x)) <=> ((ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x) = ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & (~~ (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0x) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__is__zero__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V0x)) <=> p(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(bool),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0x)),f3018),inj__o(fo__c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2EF))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__is__finite__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0x)) <=> p(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(bool),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0x)),k(ty_2Erealax_2Ereal,c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2EF))))))))).
tff(ax_thm_2Ebinary__ieee_2Eis__integral__def,axiom,( ! [V0r:tp__ty_2Erealax_2Ereal] : (p(ap(c_2Ebinary__ieee_2Eis__integral,inj__ty_2Erealax_2Ereal(V0r))) <=> (? [V1n:tp__ty_2Enum_2Enum] : (surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0r))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V1n)))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__is__integral__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__integral(A_27t,A_27w),V0x)) <=> p(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(bool),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0x)),f3019),inj__o(fo__c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2EF))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__negate__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(c_2Ebinary__ieee_2Efloat__negate(A_27t,A_27w),V0x) = ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ap(c_2Ewords_2Eword__1comp(ty_2Eone_2Eone),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0x)))),V0x))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__abs__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(c_2Ebinary__ieee_2Efloat__abs(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_2En2w(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),V0x))))))).
tff(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))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__plus__zero__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (ap(c_2Ebinary__ieee_2Efloat__plus__zero(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)),ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),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))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__top__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (ap(c_2Ebinary__ieee_2Efloat__top(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)),ap(ap(c_2Ewords_2Eword__sub(A_27w),c_2Ewords_2Eword__T(A_27w)),ap(c_2Ewords_2En2w(A_27w),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))),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)),c_2Ewords_2Eword__T(A_27t))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__plus__min__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (ap(c_2Ebinary__ieee_2Efloat__plus__min(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)),ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),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),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))))).
tff(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)))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__minus__zero__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (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__negate(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)))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__bottom__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (ap(c_2Ebinary__ieee_2Efloat__bottom(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__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__minus__min__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (ap(c_2Ebinary__ieee_2Efloat__minus__min(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__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))).
tff(stp_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : $tType)).
tff(stp_inj_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(inj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o > $i)).
tff(stp_surj_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(surj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : $i > tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o)).
tff(stp_inj_surj_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] : (surj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(inj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X)) = X))).
tff(stp_inj_mem_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:tp__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] : (mem(inj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X),ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)))))))))).
tff(stp_iso_mem_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:$i] : (mem(X,ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))))))) => (X = inj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(surj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X)))))).
tff(stp_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : $tType)).
tff(stp_inj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o > $i)).
tff(stp_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : $i > tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o)).
tff(stp_inj_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] : (surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X)) = X))).
tff(stp_inj_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] : (mem(inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X),ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))))))))).
tff(stp_iso_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:$i] : (mem(X,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)))))) => (X = inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X)))))).
tff(stp_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : $tType)).
tff(stp_inj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o > $i)).
tff(stp_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : $i > tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o)).
tff(stp_inj_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] : (surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X)) = X))).
tff(stp_inj_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] : (mem(inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X),ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)))))))).
tff(stp_iso_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,( ! [X:$i] : (mem(X,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool))))) => (X = inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o(X)))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__TY__DEF,axiom,(? [V0rep:$i] : (mem(V0rep,arr(ty_2Ebinary__ieee_2Eflags,ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)))))))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,ty_2Epair_2Eprod(bool,bool)))))),ty_2Ebinary__ieee_2Eflags),f3034),V0rep))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__case__def,axiom,( ! [A_27a:del]: ( ! [V0a0:tp__o] : ( ! [V1a1:tp__o] : ( ! [V2a2:tp__o] : ( ! [V3a3:tp__o] : ( ! [V4a4:tp__o] : ( ! [V5a5:tp__o] : ( ! [V6f:$i] : (mem(V6f,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,A_27a))))))) => (ap(ap(c_2Ebinary__ieee_2Eflags__CASE(A_27a),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0a0)),inj__o(V1a1)),inj__o(V2a2)),inj__o(V3a3)),inj__o(V4a4)),inj__o(V5a5))),V6f) = ap(ap(ap(ap(ap(ap(V6f,inj__o(V0a0)),inj__o(V1a1)),inj__o(V2a2)),inj__o(V3a3)),inj__o(V4a4)),inj__o(V5a5))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__size__def,axiom,( ! [V0a0:tp__o] : ( ! [V1a1:tp__o] : ( ! [V2a2:tp__o] : ( ! [V3a3:tp__o] : ( ! [V4a4:tp__o] : ( ! [V5a5:tp__o] : (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Eflags__size,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0a0)),inj__o(V1a1)),inj__o(V2a2)),inj__o(V3a3)),inj__o(V4a4)),inj__o(V5a5)))) = 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)))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2EbasicSize_2Ebool__size,inj__o(V0a0))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2EbasicSize_2Ebool__size,inj__o(V1a1))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2EbasicSize_2Ebool__size,inj__o(V2a2))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2EbasicSize_2Ebool__size,inj__o(V3a3))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2EbasicSize_2Ebool__size,inj__o(V4a4))),ap(c_2EbasicSize_2Ebool__size,inj__o(V5a5))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__DivideByZero,axiom,( ! [V0b:tp__o] : ( ! [V1b0:tp__o] : ( ! [V2b1:tp__o] : ( ! [V3b2:tp__o] : ( ! [V4b3:tp__o] : ( ! [V5b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0b)),inj__o(V1b0)),inj__o(V2b1)),inj__o(V3b2)),inj__o(V4b3)),inj__o(V5b4)))) <=> p(inj__o(V0b)))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__InvalidOp,axiom,( ! [V0b:tp__o] : ( ! [V1b0:tp__o] : ( ! [V2b1:tp__o] : ( ! [V3b2:tp__o] : ( ! [V4b3:tp__o] : ( ! [V5b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0b)),inj__o(V1b0)),inj__o(V2b1)),inj__o(V3b2)),inj__o(V4b3)),inj__o(V5b4)))) <=> p(inj__o(V1b0)))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__Overflow,axiom,( ! [V0b:tp__o] : ( ! [V1b0:tp__o] : ( ! [V2b1:tp__o] : ( ! [V3b2:tp__o] : ( ! [V4b3:tp__o] : ( ! [V5b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__Overflow,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0b)),inj__o(V1b0)),inj__o(V2b1)),inj__o(V3b2)),inj__o(V4b3)),inj__o(V5b4)))) <=> p(inj__o(V2b1)))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__Precision,axiom,( ! [V0b:tp__o] : ( ! [V1b0:tp__o] : ( ! [V2b1:tp__o] : ( ! [V3b2:tp__o] : ( ! [V4b3:tp__o] : ( ! [V5b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__Precision,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0b)),inj__o(V1b0)),inj__o(V2b1)),inj__o(V3b2)),inj__o(V4b3)),inj__o(V5b4)))) <=> p(inj__o(V3b2)))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,axiom,( ! [V0b:tp__o] : ( ! [V1b0:tp__o] : ( ! [V2b1:tp__o] : ( ! [V3b2:tp__o] : ( ! [V4b3:tp__o] : ( ! [V5b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0b)),inj__o(V1b0)),inj__o(V2b1)),inj__o(V3b2)),inj__o(V4b3)),inj__o(V5b4)))) <=> p(inj__o(V4b3)))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,axiom,( ! [V0b:tp__o] : ( ! [V1b0:tp__o] : ( ! [V2b1:tp__o] : ( ! [V3b2:tp__o] : ( ! [V4b3:tp__o] : ( ! [V5b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0b)),inj__o(V1b0)),inj__o(V2b1)),inj__o(V3b2)),inj__o(V4b3)),inj__o(V5b4)))) <=> p(inj__o(V5b4)))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__accessors,lemma,((( ! [V0b:tp__o] : ( ! [V1b0:tp__o] : ( ! [V2b1:tp__o] : ( ! [V3b2:tp__o] : ( ! [V4b3:tp__o] : ( ! [V5b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0b)),inj__o(V1b0)),inj__o(V2b1)),inj__o(V3b2)),inj__o(V4b3)),inj__o(V5b4)))) <=> p(inj__o(V0b))))))))) & (( ! [V6b:tp__o] : ( ! [V7b0:tp__o] : ( ! [V8b1:tp__o] : ( ! [V9b2:tp__o] : ( ! [V10b3:tp__o] : ( ! [V11b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V6b)),inj__o(V7b0)),inj__o(V8b1)),inj__o(V9b2)),inj__o(V10b3)),inj__o(V11b4)))) <=> p(inj__o(V7b0))))))))) & (( ! [V12b:tp__o] : ( ! [V13b0:tp__o] : ( ! [V14b1:tp__o] : ( ! [V15b2:tp__o] : ( ! [V16b3:tp__o] : ( ! [V17b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__Overflow,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V12b)),inj__o(V13b0)),inj__o(V14b1)),inj__o(V15b2)),inj__o(V16b3)),inj__o(V17b4)))) <=> p(inj__o(V14b1))))))))) & (( ! [V18b:tp__o] : ( ! [V19b0:tp__o] : ( ! [V20b1:tp__o] : ( ! [V21b2:tp__o] : ( ! [V22b3:tp__o] : ( ! [V23b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__Precision,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V18b)),inj__o(V19b0)),inj__o(V20b1)),inj__o(V21b2)),inj__o(V22b3)),inj__o(V23b4)))) <=> p(inj__o(V21b2))))))))) & (( ! [V24b:tp__o] : ( ! [V25b0:tp__o] : ( ! [V26b1:tp__o] : ( ! [V27b2:tp__o] : ( ! [V28b3:tp__o] : ( ! [V29b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V24b)),inj__o(V25b0)),inj__o(V26b1)),inj__o(V27b2)),inj__o(V28b3)),inj__o(V29b4)))) <=> p(inj__o(V28b3))))))))) & ( ! [V30b:tp__o] : ( ! [V31b0:tp__o] : ( ! [V32b1:tp__o] : ( ! [V33b2:tp__o] : ( ! [V34b3:tp__o] : ( ! [V35b4:tp__o] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V30b)),inj__o(V31b0)),inj__o(V32b1)),inj__o(V33b2)),inj__o(V34b3)),inj__o(V35b4)))) <=> p(inj__o(V35b4)))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__DivideByZero__fupd,axiom,( ! [V0f:$i] : (mem(V0f,arr(bool,bool)) => ( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V0f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,ap(V0f,inj__o(V1b))),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__InvalidOp__fupd,axiom,( ! [V0f:$i] : (mem(V0f,arr(bool,bool)) => ( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V0f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),ap(V0f,inj__o(V2b0))),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__Overflow__fupd,axiom,( ! [V0f:$i] : (mem(V0f,arr(bool,bool)) => ( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V0f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),ap(V0f,inj__o(V3b1))),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__Precision__fupd,axiom,( ! [V0f:$i] : (mem(V0f,arr(bool,bool)) => ( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V0f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),ap(V0f,inj__o(V4b2))),inj__o(V5b3)),inj__o(V6b4))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,axiom,( ! [V0f:$i] : (mem(V0f,arr(bool,bool)) => ( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V0f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),ap(V0f,inj__o(V5b3))),inj__o(V6b4))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,axiom,( ! [V0f:$i] : (mem(V0f,arr(bool,bool)) => ( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V0f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),ap(V0f,inj__o(V6b4)))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__fn__updates,lemma,((( ! [V0f:$i] : (mem(V0f,arr(bool,bool)) => ( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V0f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,ap(V0f,inj__o(V1b))),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))))))))))) & (( ! [V7f:$i] : (mem(V7f,arr(bool,bool)) => ( ! [V8b:tp__o] : ( ! [V9b0:tp__o] : ( ! [V10b1:tp__o] : ( ! [V11b2:tp__o] : ( ! [V12b3:tp__o] : ( ! [V13b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V7f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V8b)),inj__o(V9b0)),inj__o(V10b1)),inj__o(V11b2)),inj__o(V12b3)),inj__o(V13b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V8b)),ap(V7f,inj__o(V9b0))),inj__o(V10b1)),inj__o(V11b2)),inj__o(V12b3)),inj__o(V13b4)))))))))))) & (( ! [V14f:$i] : (mem(V14f,arr(bool,bool)) => ( ! [V15b:tp__o] : ( ! [V16b0:tp__o] : ( ! [V17b1:tp__o] : ( ! [V18b2:tp__o] : ( ! [V19b3:tp__o] : ( ! [V20b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V14f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V15b)),inj__o(V16b0)),inj__o(V17b1)),inj__o(V18b2)),inj__o(V19b3)),inj__o(V20b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V15b)),inj__o(V16b0)),ap(V14f,inj__o(V17b1))),inj__o(V18b2)),inj__o(V19b3)),inj__o(V20b4)))))))))))) & (( ! [V21f:$i] : (mem(V21f,arr(bool,bool)) => ( ! [V22b:tp__o] : ( ! [V23b0:tp__o] : ( ! [V24b1:tp__o] : ( ! [V25b2:tp__o] : ( ! [V26b3:tp__o] : ( ! [V27b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V21f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V22b)),inj__o(V23b0)),inj__o(V24b1)),inj__o(V25b2)),inj__o(V26b3)),inj__o(V27b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V22b)),inj__o(V23b0)),inj__o(V24b1)),ap(V21f,inj__o(V25b2))),inj__o(V26b3)),inj__o(V27b4)))))))))))) & (( ! [V28f:$i] : (mem(V28f,arr(bool,bool)) => ( ! [V29b:tp__o] : ( ! [V30b0:tp__o] : ( ! [V31b1:tp__o] : ( ! [V32b2:tp__o] : ( ! [V33b3:tp__o] : ( ! [V34b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V28f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V29b)),inj__o(V30b0)),inj__o(V31b1)),inj__o(V32b2)),inj__o(V33b3)),inj__o(V34b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V29b)),inj__o(V30b0)),inj__o(V31b1)),inj__o(V32b2)),ap(V28f,inj__o(V33b3))),inj__o(V34b4)))))))))))) & ( ! [V35f:$i] : (mem(V35f,arr(bool,bool)) => ( ! [V36b:tp__o] : ( ! [V37b0:tp__o] : ( ! [V38b1:tp__o] : ( ! [V39b2:tp__o] : ( ! [V40b3:tp__o] : ( ! [V41b4:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V35f),ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V36b)),inj__o(V37b0)),inj__o(V38b1)),inj__o(V39b2)),inj__o(V40b3)),inj__o(V41b4)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V36b)),inj__o(V37b0)),inj__o(V38b1)),inj__o(V39b2)),inj__o(V40b3)),ap(V35f,inj__o(V41b4)))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__accfupds,lemma,((( ! [V0f0:$i] : (mem(V0f0,arr(bool,bool)) => ( ! [V1f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V0f0),inj__ty_2Ebinary__ieee_2Eflags(V1f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(V1f))))))) & (( ! [V2f0:$i] : (mem(V2f0,arr(bool,bool)) => ( ! [V3f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V2f0),inj__ty_2Ebinary__ieee_2Eflags(V3f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(V3f))))))) & (( ! [V4f0:$i] : (mem(V4f0,arr(bool,bool)) => ( ! [V5f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V4f0),inj__ty_2Ebinary__ieee_2Eflags(V5f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(V5f))))))) & (( ! [V6f0:$i] : (mem(V6f0,arr(bool,bool)) => ( ! [V7f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V6f0),inj__ty_2Ebinary__ieee_2Eflags(V7f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(V7f))))))) & (( ! [V8f0:$i] : (mem(V8f0,arr(bool,bool)) => ( ! [V9f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V8f0),inj__ty_2Ebinary__ieee_2Eflags(V9f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(V9f))))))) & (( ! [V10f0:$i] : (mem(V10f0,arr(bool,bool)) => ( ! [V11f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V10f0),inj__ty_2Ebinary__ieee_2Eflags(V11f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(V11f))))))) & (( ! [V12f0:$i] : (mem(V12f0,arr(bool,bool)) => ( ! [V13f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V12f0),inj__ty_2Ebinary__ieee_2Eflags(V13f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(V13f))))))) & (( ! [V14f0:$i] : (mem(V14f0,arr(bool,bool)) => ( ! [V15f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V14f0),inj__ty_2Ebinary__ieee_2Eflags(V15f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(V15f))))))) & (( ! [V16f0:$i] : (mem(V16f0,arr(bool,bool)) => ( ! [V17f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V16f0),inj__ty_2Ebinary__ieee_2Eflags(V17f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(V17f))))))) & (( ! [V18f0:$i] : (mem(V18f0,arr(bool,bool)) => ( ! [V19f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V18f0),inj__ty_2Ebinary__ieee_2Eflags(V19f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(V19f))))))) & (( ! [V20f0:$i] : (mem(V20f0,arr(bool,bool)) => ( ! [V21f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Overflow,ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V20f0),inj__ty_2Ebinary__ieee_2Eflags(V21f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(V21f))))))) & (( ! [V22f0:$i] : (mem(V22f0,arr(bool,bool)) => ( ! [V23f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Overflow,ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V22f0),inj__ty_2Ebinary__ieee_2Eflags(V23f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(V23f))))))) & (( ! [V24f0:$i] : (mem(V24f0,arr(bool,bool)) => ( ! [V25f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Overflow,ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V24f0),inj__ty_2Ebinary__ieee_2Eflags(V25f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(V25f))))))) & (( ! [V26f0:$i] : (mem(V26f0,arr(bool,bool)) => ( ! [V27f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Overflow,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V26f0),inj__ty_2Ebinary__ieee_2Eflags(V27f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(V27f))))))) & (( ! [V28f0:$i] : (mem(V28f0,arr(bool,bool)) => ( ! [V29f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Overflow,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V28f0),inj__ty_2Ebinary__ieee_2Eflags(V29f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(V29f))))))) & (( ! [V30f0:$i] : (mem(V30f0,arr(bool,bool)) => ( ! [V31f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Precision,ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V30f0),inj__ty_2Ebinary__ieee_2Eflags(V31f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(V31f))))))) & (( ! [V32f0:$i] : (mem(V32f0,arr(bool,bool)) => ( ! [V33f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Precision,ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V32f0),inj__ty_2Ebinary__ieee_2Eflags(V33f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(V33f))))))) & (( ! [V34f0:$i] : (mem(V34f0,arr(bool,bool)) => ( ! [V35f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Precision,ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V34f0),inj__ty_2Ebinary__ieee_2Eflags(V35f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(V35f))))))) & (( ! [V36f0:$i] : (mem(V36f0,arr(bool,bool)) => ( ! [V37f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Precision,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V36f0),inj__ty_2Ebinary__ieee_2Eflags(V37f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(V37f))))))) & (( ! [V38f0:$i] : (mem(V38f0,arr(bool,bool)) => ( ! [V39f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Precision,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V38f0),inj__ty_2Ebinary__ieee_2Eflags(V39f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(V39f))))))) & (( ! [V40f0:$i] : (mem(V40f0,arr(bool,bool)) => ( ! [V41f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V40f0),inj__ty_2Ebinary__ieee_2Eflags(V41f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(V41f))))))) & (( ! [V42f0:$i] : (mem(V42f0,arr(bool,bool)) => ( ! [V43f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V42f0),inj__ty_2Ebinary__ieee_2Eflags(V43f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(V43f))))))) & (( ! [V44f0:$i] : (mem(V44f0,arr(bool,bool)) => ( ! [V45f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V44f0),inj__ty_2Ebinary__ieee_2Eflags(V45f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(V45f))))))) & (( ! [V46f0:$i] : (mem(V46f0,arr(bool,bool)) => ( ! [V47f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V46f0),inj__ty_2Ebinary__ieee_2Eflags(V47f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(V47f))))))) & (( ! [V48f0:$i] : (mem(V48f0,arr(bool,bool)) => ( ! [V49f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V48f0),inj__ty_2Ebinary__ieee_2Eflags(V49f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(V49f))))))) & (( ! [V50f0:$i] : (mem(V50f0,arr(bool,bool)) => ( ! [V51f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V50f0),inj__ty_2Ebinary__ieee_2Eflags(V51f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(V51f))))))) & (( ! [V52f0:$i] : (mem(V52f0,arr(bool,bool)) => ( ! [V53f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V52f0),inj__ty_2Ebinary__ieee_2Eflags(V53f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(V53f))))))) & (( ! [V54f0:$i] : (mem(V54f0,arr(bool,bool)) => ( ! [V55f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V54f0),inj__ty_2Ebinary__ieee_2Eflags(V55f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(V55f))))))) & (( ! [V56f0:$i] : (mem(V56f0,arr(bool,bool)) => ( ! [V57f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V56f0),inj__ty_2Ebinary__ieee_2Eflags(V57f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(V57f))))))) & (( ! [V58f0:$i] : (mem(V58f0,arr(bool,bool)) => ( ! [V59f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V58f0),inj__ty_2Ebinary__ieee_2Eflags(V59f)))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(V59f))))))) & (( ! [V60f0:$i] : (mem(V60f0,arr(bool,bool)) => ( ! [V61f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V60f0),inj__ty_2Ebinary__ieee_2Eflags(V61f)))) <=> p(ap(V60f0,ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(V61f)))))))) & (( ! [V62f0:$i] : (mem(V62f0,arr(bool,bool)) => ( ! [V63f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V62f0),inj__ty_2Ebinary__ieee_2Eflags(V63f)))) <=> p(ap(V62f0,ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(V63f)))))))) & (( ! [V64f0:$i] : (mem(V64f0,arr(bool,bool)) => ( ! [V65f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Overflow,ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V64f0),inj__ty_2Ebinary__ieee_2Eflags(V65f)))) <=> p(ap(V64f0,ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(V65f)))))))) & (( ! [V66f0:$i] : (mem(V66f0,arr(bool,bool)) => ( ! [V67f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Precision,ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V66f0),inj__ty_2Ebinary__ieee_2Eflags(V67f)))) <=> p(ap(V66f0,ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(V67f)))))))) & (( ! [V68f0:$i] : (mem(V68f0,arr(bool,bool)) => ( ! [V69f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V68f0),inj__ty_2Ebinary__ieee_2Eflags(V69f)))) <=> p(ap(V68f0,ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(V69f)))))))) & ( ! [V70f0:$i] : (mem(V70f0,arr(bool,bool)) => ( ! [V71f:tp__ty_2Ebinary__ieee_2Eflags] : (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V70f0),inj__ty_2Ebinary__ieee_2Eflags(V71f)))) <=> p(ap(V70f0,ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(V71f))))))))))))))))))))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__fupdfupds,lemma,((( ! [V0g:$i] : (mem(V0g,arr(bool,bool)) => ( ! [V1f0:$i] : (mem(V1f0,arr(bool,bool)) => ( ! [V2f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V1f0),ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V0g),inj__ty_2Ebinary__ieee_2Eflags(V2f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V1f0),V0g)),inj__ty_2Ebinary__ieee_2Eflags(V2f))))))))) & (( ! [V3g:$i] : (mem(V3g,arr(bool,bool)) => ( ! [V4f0:$i] : (mem(V4f0,arr(bool,bool)) => ( ! [V5f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V4f0),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V3g),inj__ty_2Ebinary__ieee_2Eflags(V5f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V4f0),V3g)),inj__ty_2Ebinary__ieee_2Eflags(V5f))))))))) & (( ! [V6g:$i] : (mem(V6g,arr(bool,bool)) => ( ! [V7f0:$i] : (mem(V7f0,arr(bool,bool)) => ( ! [V8f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V7f0),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V6g),inj__ty_2Ebinary__ieee_2Eflags(V8f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V7f0),V6g)),inj__ty_2Ebinary__ieee_2Eflags(V8f))))))))) & (( ! [V9g:$i] : (mem(V9g,arr(bool,bool)) => ( ! [V10f0:$i] : (mem(V10f0,arr(bool,bool)) => ( ! [V11f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V10f0),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V9g),inj__ty_2Ebinary__ieee_2Eflags(V11f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V10f0),V9g)),inj__ty_2Ebinary__ieee_2Eflags(V11f))))))))) & (( ! [V12g:$i] : (mem(V12g,arr(bool,bool)) => ( ! [V13f0:$i] : (mem(V13f0,arr(bool,bool)) => ( ! [V14f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V13f0),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V12g),inj__ty_2Ebinary__ieee_2Eflags(V14f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V13f0),V12g)),inj__ty_2Ebinary__ieee_2Eflags(V14f))))))))) & ( ! [V15g:$i] : (mem(V15g,arr(bool,bool)) => ( ! [V16f0:$i] : (mem(V16f0,arr(bool,bool)) => ( ! [V17f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V16f0),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V15g),inj__ty_2Ebinary__ieee_2Eflags(V17f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V16f0),V15g)),inj__ty_2Ebinary__ieee_2Eflags(V17f)))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__fupdfupds__comp,lemma,(( ! [A_27a:del]: ((( ! [V0g:$i] : (mem(V0g,arr(bool,bool)) => ( ! [V1f0:$i] : (mem(V1f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V1f0)),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V0g)) = ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V1f0),V0g))))))) & ( ! [V2h:$i] : (mem(V2h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V3g:$i] : (mem(V3g,arr(bool,bool)) => ( ! [V4f0:$i] : (mem(V4f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V4f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V3g)),V2h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V4f0),V3g))),V2h))))))))) & ((( ! [V5g:$i] : (mem(V5g,arr(bool,bool)) => ( ! [V6f0:$i] : (mem(V6f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V6f0)),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V5g)) = ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V6f0),V5g))))))) & ( ! [V7h:$i] : (mem(V7h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V8g:$i] : (mem(V8g,arr(bool,bool)) => ( ! [V9f0:$i] : (mem(V9f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V9f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V8g)),V7h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V9f0),V8g))),V7h))))))))) & ((( ! [V10g:$i] : (mem(V10g,arr(bool,bool)) => ( ! [V11f0:$i] : (mem(V11f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V11f0)),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V10g)) = ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V11f0),V10g))))))) & ( ! [V12h:$i] : (mem(V12h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V13g:$i] : (mem(V13g,arr(bool,bool)) => ( ! [V14f0:$i] : (mem(V14f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V14f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V13g)),V12h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V14f0),V13g))),V12h))))))))) & ((( ! [V15g:$i] : (mem(V15g,arr(bool,bool)) => ( ! [V16f0:$i] : (mem(V16f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V16f0)),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V15g)) = ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V16f0),V15g))))))) & ( ! [V17h:$i] : (mem(V17h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V18g:$i] : (mem(V18g,arr(bool,bool)) => ( ! [V19f0:$i] : (mem(V19f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V19f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V18g)),V17h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V19f0),V18g))),V17h))))))))) & ((( ! [V20g:$i] : (mem(V20g,arr(bool,bool)) => ( ! [V21f0:$i] : (mem(V21f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V21f0)),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V20g)) = ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V21f0),V20g))))))) & ( ! [V22h:$i] : (mem(V22h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V23g:$i] : (mem(V23g,arr(bool,bool)) => ( ! [V24f0:$i] : (mem(V24f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V24f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V23g)),V22h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V24f0),V23g))),V22h))))))))) & (( ! [V25g:$i] : (mem(V25g,arr(bool,bool)) => ( ! [V26f0:$i] : (mem(V26f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V26f0)),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V25g)) = ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V26f0),V25g))))))) & ( ! [V27h:$i] : (mem(V27h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V28g:$i] : (mem(V28g,arr(bool,bool)) => ( ! [V29f0:$i] : (mem(V29f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V29f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V28g)),V27h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(ap(c_2Ecombin_2Eo(bool,bool,bool),V29f0),V28g))),V27h))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__fupdcanon,lemma,((( ! [V0g:$i] : (mem(V0g,arr(bool,bool)) => ( ! [V1f0:$i] : (mem(V1f0,arr(bool,bool)) => ( ! [V2f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V1f0),ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V0g),inj__ty_2Ebinary__ieee_2Eflags(V2f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V0g),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V1f0),inj__ty_2Ebinary__ieee_2Eflags(V2f)))))))))) & (( ! [V3g:$i] : (mem(V3g,arr(bool,bool)) => ( ! [V4f0:$i] : (mem(V4f0,arr(bool,bool)) => ( ! [V5f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V4f0),ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V3g),inj__ty_2Ebinary__ieee_2Eflags(V5f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V3g),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V4f0),inj__ty_2Ebinary__ieee_2Eflags(V5f)))))))))) & (( ! [V6g:$i] : (mem(V6g,arr(bool,bool)) => ( ! [V7f0:$i] : (mem(V7f0,arr(bool,bool)) => ( ! [V8f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V7f0),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V6g),inj__ty_2Ebinary__ieee_2Eflags(V8f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V6g),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V7f0),inj__ty_2Ebinary__ieee_2Eflags(V8f)))))))))) & (( ! [V9g:$i] : (mem(V9g,arr(bool,bool)) => ( ! [V10f0:$i] : (mem(V10f0,arr(bool,bool)) => ( ! [V11f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V10f0),ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V9g),inj__ty_2Ebinary__ieee_2Eflags(V11f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V9g),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V10f0),inj__ty_2Ebinary__ieee_2Eflags(V11f)))))))))) & (( ! [V12g:$i] : (mem(V12g,arr(bool,bool)) => ( ! [V13f0:$i] : (mem(V13f0,arr(bool,bool)) => ( ! [V14f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V13f0),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V12g),inj__ty_2Ebinary__ieee_2Eflags(V14f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V12g),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V13f0),inj__ty_2Ebinary__ieee_2Eflags(V14f)))))))))) & (( ! [V15g:$i] : (mem(V15g,arr(bool,bool)) => ( ! [V16f0:$i] : (mem(V16f0,arr(bool,bool)) => ( ! [V17f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V16f0),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V15g),inj__ty_2Ebinary__ieee_2Eflags(V17f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V15g),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V16f0),inj__ty_2Ebinary__ieee_2Eflags(V17f)))))))))) & (( ! [V18g:$i] : (mem(V18g,arr(bool,bool)) => ( ! [V19f0:$i] : (mem(V19f0,arr(bool,bool)) => ( ! [V20f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V19f0),ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V18g),inj__ty_2Ebinary__ieee_2Eflags(V20f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V18g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V19f0),inj__ty_2Ebinary__ieee_2Eflags(V20f)))))))))) & (( ! [V21g:$i] : (mem(V21g,arr(bool,bool)) => ( ! [V22f0:$i] : (mem(V22f0,arr(bool,bool)) => ( ! [V23f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V22f0),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V21g),inj__ty_2Ebinary__ieee_2Eflags(V23f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V21g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V22f0),inj__ty_2Ebinary__ieee_2Eflags(V23f)))))))))) & (( ! [V24g:$i] : (mem(V24g,arr(bool,bool)) => ( ! [V25f0:$i] : (mem(V25f0,arr(bool,bool)) => ( ! [V26f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V25f0),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V24g),inj__ty_2Ebinary__ieee_2Eflags(V26f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V24g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V25f0),inj__ty_2Ebinary__ieee_2Eflags(V26f)))))))))) & (( ! [V27g:$i] : (mem(V27g,arr(bool,bool)) => ( ! [V28f0:$i] : (mem(V28f0,arr(bool,bool)) => ( ! [V29f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V28f0),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V27g),inj__ty_2Ebinary__ieee_2Eflags(V29f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V27g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V28f0),inj__ty_2Ebinary__ieee_2Eflags(V29f)))))))))) & (( ! [V30g:$i] : (mem(V30g,arr(bool,bool)) => ( ! [V31f0:$i] : (mem(V31f0,arr(bool,bool)) => ( ! [V32f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V31f0),ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V30g),inj__ty_2Ebinary__ieee_2Eflags(V32f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V30g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V31f0),inj__ty_2Ebinary__ieee_2Eflags(V32f)))))))))) & (( ! [V33g:$i] : (mem(V33g,arr(bool,bool)) => ( ! [V34f0:$i] : (mem(V34f0,arr(bool,bool)) => ( ! [V35f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V34f0),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V33g),inj__ty_2Ebinary__ieee_2Eflags(V35f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V33g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V34f0),inj__ty_2Ebinary__ieee_2Eflags(V35f)))))))))) & (( ! [V36g:$i] : (mem(V36g,arr(bool,bool)) => ( ! [V37f0:$i] : (mem(V37f0,arr(bool,bool)) => ( ! [V38f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V37f0),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V36g),inj__ty_2Ebinary__ieee_2Eflags(V38f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V36g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V37f0),inj__ty_2Ebinary__ieee_2Eflags(V38f)))))))))) & (( ! [V39g:$i] : (mem(V39g,arr(bool,bool)) => ( ! [V40f0:$i] : (mem(V40f0,arr(bool,bool)) => ( ! [V41f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V40f0),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V39g),inj__ty_2Ebinary__ieee_2Eflags(V41f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V39g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V40f0),inj__ty_2Ebinary__ieee_2Eflags(V41f)))))))))) & ( ! [V42g:$i] : (mem(V42g,arr(bool,bool)) => ( ! [V43f0:$i] : (mem(V43f0,arr(bool,bool)) => ( ! [V44f:tp__ty_2Ebinary__ieee_2Eflags] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V43f0),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V42g),inj__ty_2Ebinary__ieee_2Eflags(V44f)))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V42g),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V43f0),inj__ty_2Ebinary__ieee_2Eflags(V44f)))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__fupdcanon__comp,lemma,(( ! [A_27a:del]: ((( ! [V0g:$i] : (mem(V0g,arr(bool,bool)) => ( ! [V1f0:$i] : (mem(V1f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V1f0)),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V0g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V0g)),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V1f0))))))) & ( ! [V2h:$i] : (mem(V2h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V3g:$i] : (mem(V3g,arr(bool,bool)) => ( ! [V4f0:$i] : (mem(V4f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V4f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V3g)),V2h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V3g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V4f0)),V2h)))))))))) & ((( ! [V5g:$i] : (mem(V5g,arr(bool,bool)) => ( ! [V6f0:$i] : (mem(V6f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V6f0)),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V5g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V5g)),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V6f0))))))) & ( ! [V7h:$i] : (mem(V7h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V8g:$i] : (mem(V8g,arr(bool,bool)) => ( ! [V9f0:$i] : (mem(V9f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V9f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V8g)),V7h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V8g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V9f0)),V7h)))))))))) & ((( ! [V10g:$i] : (mem(V10g,arr(bool,bool)) => ( ! [V11f0:$i] : (mem(V11f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V11f0)),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V10g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V10g)),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V11f0))))))) & ( ! [V12h:$i] : (mem(V12h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V13g:$i] : (mem(V13g,arr(bool,bool)) => ( ! [V14f0:$i] : (mem(V14f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V14f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V13g)),V12h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V13g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V14f0)),V12h)))))))))) & ((( ! [V15g:$i] : (mem(V15g,arr(bool,bool)) => ( ! [V16f0:$i] : (mem(V16f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V16f0)),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V15g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V15g)),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V16f0))))))) & ( ! [V17h:$i] : (mem(V17h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V18g:$i] : (mem(V18g,arr(bool,bool)) => ( ! [V19f0:$i] : (mem(V19f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V19f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V18g)),V17h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V18g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V19f0)),V17h)))))))))) & ((( ! [V20g:$i] : (mem(V20g,arr(bool,bool)) => ( ! [V21f0:$i] : (mem(V21f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V21f0)),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V20g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V20g)),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V21f0))))))) & ( ! [V22h:$i] : (mem(V22h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V23g:$i] : (mem(V23g,arr(bool,bool)) => ( ! [V24f0:$i] : (mem(V24f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V24f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V23g)),V22h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V23g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V24f0)),V22h)))))))))) & ((( ! [V25g:$i] : (mem(V25g,arr(bool,bool)) => ( ! [V26f0:$i] : (mem(V26f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V26f0)),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V25g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V25g)),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V26f0))))))) & ( ! [V27h:$i] : (mem(V27h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V28g:$i] : (mem(V28g,arr(bool,bool)) => ( ! [V29f0:$i] : (mem(V29f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V29f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V28g)),V27h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V28g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V29f0)),V27h)))))))))) & ((( ! [V30g:$i] : (mem(V30g,arr(bool,bool)) => ( ! [V31f0:$i] : (mem(V31f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V31f0)),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V30g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V30g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V31f0))))))) & ( ! [V32h:$i] : (mem(V32h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V33g:$i] : (mem(V33g,arr(bool,bool)) => ( ! [V34f0:$i] : (mem(V34f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V34f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V33g)),V32h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V33g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V34f0)),V32h)))))))))) & ((( ! [V35g:$i] : (mem(V35g,arr(bool,bool)) => ( ! [V36f0:$i] : (mem(V36f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V36f0)),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V35g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V35g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V36f0))))))) & ( ! [V37h:$i] : (mem(V37h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V38g:$i] : (mem(V38g,arr(bool,bool)) => ( ! [V39f0:$i] : (mem(V39f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V39f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V38g)),V37h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V38g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V39f0)),V37h)))))))))) & ((( ! [V40g:$i] : (mem(V40g,arr(bool,bool)) => ( ! [V41f0:$i] : (mem(V41f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V41f0)),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V40g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V40g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V41f0))))))) & ( ! [V42h:$i] : (mem(V42h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V43g:$i] : (mem(V43g,arr(bool,bool)) => ( ! [V44f0:$i] : (mem(V44f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V44f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V43g)),V42h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V43g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V44f0)),V42h)))))))))) & ((( ! [V45g:$i] : (mem(V45g,arr(bool,bool)) => ( ! [V46f0:$i] : (mem(V46f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V46f0)),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V45g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V45g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V46f0))))))) & ( ! [V47h:$i] : (mem(V47h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V48g:$i] : (mem(V48g,arr(bool,bool)) => ( ! [V49f0:$i] : (mem(V49f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V49f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V48g)),V47h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V48g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V49f0)),V47h)))))))))) & ((( ! [V50g:$i] : (mem(V50g,arr(bool,bool)) => ( ! [V51f0:$i] : (mem(V51f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V51f0)),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V50g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V50g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V51f0))))))) & ( ! [V52h:$i] : (mem(V52h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V53g:$i] : (mem(V53g,arr(bool,bool)) => ( ! [V54f0:$i] : (mem(V54f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V54f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V53g)),V52h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,V53g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V54f0)),V52h)))))))))) & ((( ! [V55g:$i] : (mem(V55g,arr(bool,bool)) => ( ! [V56f0:$i] : (mem(V56f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V56f0)),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V55g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V55g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V56f0))))))) & ( ! [V57h:$i] : (mem(V57h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V58g:$i] : (mem(V58g,arr(bool,bool)) => ( ! [V59f0:$i] : (mem(V59f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V59f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V58g)),V57h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,V58g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V59f0)),V57h)))))))))) & ((( ! [V60g:$i] : (mem(V60g,arr(bool,bool)) => ( ! [V61f0:$i] : (mem(V61f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V61f0)),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V60g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V60g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V61f0))))))) & ( ! [V62h:$i] : (mem(V62h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V63g:$i] : (mem(V63g,arr(bool,bool)) => ( ! [V64f0:$i] : (mem(V64f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V64f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V63g)),V62h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,V63g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V64f0)),V62h)))))))))) & ((( ! [V65g:$i] : (mem(V65g,arr(bool,bool)) => ( ! [V66f0:$i] : (mem(V66f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V66f0)),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V65g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V65g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V66f0))))))) & ( ! [V67h:$i] : (mem(V67h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V68g:$i] : (mem(V68g,arr(bool,bool)) => ( ! [V69f0:$i] : (mem(V69f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V69f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V68g)),V67h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,V68g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V69f0)),V67h)))))))))) & (( ! [V70g:$i] : (mem(V70g,arr(bool,bool)) => ( ! [V71f0:$i] : (mem(V71f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V71f0)),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V70g)) = ap(ap(c_2Ecombin_2Eo(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V70g)),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V71f0))))))) & ( ! [V72h:$i] : (mem(V72h,arr(A_27a,ty_2Ebinary__ieee_2Eflags)) => ( ! [V73g:$i] : (mem(V73g,arr(bool,bool)) => ( ! [V74f0:$i] : (mem(V74f0,arr(bool,bool)) => (ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V74f0)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V73g)),V72h)) = ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,V73g)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Eflags),ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,V74f0)),V72h))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__component__equality,lemma,(( ! [V0f1:tp__ty_2Ebinary__ieee_2Eflags] : ( ! [V1f2:tp__ty_2Ebinary__ieee_2Eflags] : ((V0f1 = V1f2) <=> ((p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(V0f1))) <=> p(ap(c_2Ebinary__ieee_2Eflags__DivideByZero,inj__ty_2Ebinary__ieee_2Eflags(V1f2)))) & ((p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(V0f1))) <=> p(ap(c_2Ebinary__ieee_2Eflags__InvalidOp,inj__ty_2Ebinary__ieee_2Eflags(V1f2)))) & ((p(ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(V0f1))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Overflow,inj__ty_2Ebinary__ieee_2Eflags(V1f2)))) & ((p(ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(V0f1))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Precision,inj__ty_2Ebinary__ieee_2Eflags(V1f2)))) & ((p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(V0f1))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,inj__ty_2Ebinary__ieee_2Eflags(V1f2)))) & (p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(V0f1))) <=> p(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,inj__ty_2Ebinary__ieee_2Eflags(V1f2)))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__updates__eq__literal,lemma,(( ! [V0f:tp__ty_2Ebinary__ieee_2Eflags] : ( ! [V1b4:tp__o] : ( ! [V2b3:tp__o] : ( ! [V3b2:tp__o] : ( ! [V4b1:tp__o] : ( ! [V5b0:tp__o] : ( ! [V6b:tp__o] : (surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V1b4))),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V2b3))),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V3b2))),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V4b1))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V5b0))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V6b))),inj__ty_2Ebinary__ieee_2Eflags(V0f)))))))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V1b4))),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V2b3))),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V3b2))),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V4b1))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V5b0))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V6b))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Eflags)))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__literal__nchotomy,lemma,(( ! [V0f:tp__ty_2Ebinary__ieee_2Eflags] : (? [V1b4:tp__o] : (? [V2b3:tp__o] : (? [V3b2:tp__o] : (? [V4b1:tp__o] : (? [V5b0:tp__o] : (? [V6b:tp__o] : (V0f = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V1b4))),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V2b3))),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V3b2))),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V4b1))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V5b0))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V6b))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Eflags)))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2EFORALL__flags,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Eflags,bool)) => (( ! [V1f:tp__ty_2Ebinary__ieee_2Eflags] : p(ap(V0P,inj__ty_2Ebinary__ieee_2Eflags(V1f)))) <=> ( ! [V2b4:tp__o] : ( ! [V3b3:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b1:tp__o] : ( ! [V6b0:tp__o] : ( ! [V7b:tp__o] : p(ap(V0P,ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V2b4))),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V3b3))),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V4b2))),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V5b1))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V6b0))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V7b))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Eflags)))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2EEXISTS__flags,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Eflags,bool)) => ((? [V1f:tp__ty_2Ebinary__ieee_2Eflags] : p(ap(V0P,inj__ty_2Ebinary__ieee_2Eflags(V1f)))) <=> (? [V2b4:tp__o] : (? [V3b3:tp__o] : (? [V4b2:tp__o] : (? [V5b1:tp__o] : (? [V6b0:tp__o] : (? [V7b:tp__o] : p(ap(V0P,ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V2b4))),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V3b3))),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V4b2))),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V5b1))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V6b0))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V7b))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Eflags)))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__literal__11,lemma,(( ! [V0b41:tp__o] : ( ! [V1b31:tp__o] : ( ! [V2b21:tp__o] : ( ! [V3b11:tp__o] : ( ! [V4b01:tp__o] : ( ! [V5b1:tp__o] : ( ! [V6b42:tp__o] : ( ! [V7b32:tp__o] : ( ! [V8b22:tp__o] : ( ! [V9b12:tp__o] : ( ! [V10b02:tp__o] : ( ! [V11b2:tp__o] : ((surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V0b41))),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V1b31))),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V2b21))),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V3b11))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V4b01))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V5b1))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Eflags)))))))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V6b42))),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V7b32))),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V8b22))),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V9b12))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V10b02))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(V11b2))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Eflags))))))))) <=> ((p(inj__o(V0b41)) <=> p(inj__o(V6b42))) & ((p(inj__o(V1b31)) <=> p(inj__o(V7b32))) & ((p(inj__o(V2b21)) <=> p(inj__o(V8b22))) & ((p(inj__o(V3b11)) <=> p(inj__o(V9b12))) & ((p(inj__o(V4b01)) <=> p(inj__o(V10b02))) & (p(inj__o(V5b1)) <=> p(inj__o(V11b2))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Edatatype__flags,lemma,(( ! [V0record:$i] : (mem(V0record,arr(ty_2Ebinary__ieee_2Eflags,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,bool)))))))) => ( ! [V1flags:tp__ty_2Ebinary__ieee_2Eflags] : ( ! [V2DivideByZero:tp__o] : ( ! [V3InvalidOp:tp__o] : ( ! [V4Overflow:tp__o] : ( ! [V5Precision:tp__o] : ( ! [V6Underflow__BeforeRounding:tp__o] : ( ! [V7Underflow__AfterRounding:tp__o] : p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(ap(ap(ap(ap(V0record,inj__ty_2Ebinary__ieee_2Eflags(V1flags)),inj__o(V2DivideByZero)),inj__o(V3InvalidOp)),inj__o(V4Overflow)),inj__o(V5Precision)),inj__o(V6Underflow__BeforeRounding)),inj__o(V7Underflow__AfterRounding))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__11,lemma,(( ! [V0a0:tp__o] : ( ! [V1a1:tp__o] : ( ! [V2a2:tp__o] : ( ! [V3a3:tp__o] : ( ! [V4a4:tp__o] : ( ! [V5a5:tp__o] : ( ! [V6a0_27:tp__o] : ( ! [V7a1_27:tp__o] : ( ! [V8a2_27:tp__o] : ( ! [V9a3_27:tp__o] : ( ! [V10a4_27:tp__o] : ( ! [V11a5_27:tp__o] : ((surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V0a0)),inj__o(V1a1)),inj__o(V2a2)),inj__o(V3a3)),inj__o(V4a4)),inj__o(V5a5))) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V6a0_27)),inj__o(V7a1_27)),inj__o(V8a2_27)),inj__o(V9a3_27)),inj__o(V10a4_27)),inj__o(V11a5_27)))) <=> ((p(inj__o(V0a0)) <=> p(inj__o(V6a0_27))) & ((p(inj__o(V1a1)) <=> p(inj__o(V7a1_27))) & ((p(inj__o(V2a2)) <=> p(inj__o(V8a2_27))) & ((p(inj__o(V3a3)) <=> p(inj__o(V9a3_27))) & ((p(inj__o(V4a4)) <=> p(inj__o(V10a4_27))) & (p(inj__o(V5a5)) <=> p(inj__o(V11a5_27))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__nchotomy,lemma,(( ! [V0ff:tp__ty_2Ebinary__ieee_2Eflags] : (? [V1b:tp__o] : (? [V2b0:tp__o] : (? [V3b1:tp__o] : (? [V4b2:tp__o] : (? [V5b3:tp__o] : (? [V6b4:tp__o] : (V0ff = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__Axiom,lemma,(( ! [A_27a:del]: ( ! [V0f:$i] : (mem(V0f,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,A_27a))))))) => (? [V1fn:$i] : (mem(V1fn,arr(ty_2Ebinary__ieee_2Eflags,A_27a)) & ( ! [V2a0:tp__o] : ( ! [V3a1:tp__o] : ( ! [V4a2:tp__o] : ( ! [V5a3:tp__o] : ( ! [V6a4:tp__o] : ( ! [V7a5:tp__o] : (ap(V1fn,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V2a0)),inj__o(V3a1)),inj__o(V4a2)),inj__o(V5a3)),inj__o(V6a4)),inj__o(V7a5))) = ap(ap(ap(ap(ap(ap(V0f,inj__o(V2a0)),inj__o(V3a1)),inj__o(V4a2)),inj__o(V5a3)),inj__o(V6a4)),inj__o(V7a5)))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__induction,conjecture,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Eflags,bool)) => (( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : p(ap(V0P,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))))))))) => ( ! [V7f:tp__ty_2Ebinary__ieee_2Eflags] : p(ap(V0P,inj__ty_2Ebinary__ieee_2Eflags(V7f))))))))).
