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,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Eflags,bool)) => (( ! [V1b:tp__o] : ( ! [V2b0:tp__o] : ( ! [V3b1:tp__o] : ( ! [V4b2:tp__o] : ( ! [V5b3:tp__o] : ( ! [V6b4:tp__o] : p(ap(V0P,ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V1b)),inj__o(V2b0)),inj__o(V3b1)),inj__o(V4b2)),inj__o(V5b3)),inj__o(V6b4)))))))))) => ( ! [V7f:tp__ty_2Ebinary__ieee_2Eflags] : p(ap(V0P,inj__ty_2Ebinary__ieee_2Eflags(V7f))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__case__cong,lemma,(( ! [A_27a:del]: ( ! [V0f_27:$i] : (mem(V0f_27,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,A_27a))))))) => ( ! [V1M:tp__ty_2Ebinary__ieee_2Eflags] : ( ! [V2M_27:tp__ty_2Ebinary__ieee_2Eflags] : ( ! [V3f:$i] : (mem(V3f,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,A_27a))))))) => (((V1M = V2M_27) & ( ! [V4a0:tp__o] : ( ! [V5a1:tp__o] : ( ! [V6a2:tp__o] : ( ! [V7a3:tp__o] : ( ! [V8a4:tp__o] : ( ! [V9a5:tp__o] : ((V2M_27 = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V4a0)),inj__o(V5a1)),inj__o(V6a2)),inj__o(V7a3)),inj__o(V8a4)),inj__o(V9a5)))) => (ap(ap(ap(ap(ap(ap(V3f,inj__o(V4a0)),inj__o(V5a1)),inj__o(V6a2)),inj__o(V7a3)),inj__o(V8a4)),inj__o(V9a5)) = ap(ap(ap(ap(ap(ap(V0f_27,inj__o(V4a0)),inj__o(V5a1)),inj__o(V6a2)),inj__o(V7a3)),inj__o(V8a4)),inj__o(V9a5))))))))))) => (ap(ap(c_2Ebinary__ieee_2Eflags__CASE(A_27a),inj__ty_2Ebinary__ieee_2Eflags(V1M)),V3f) = ap(ap(c_2Ebinary__ieee_2Eflags__CASE(A_27a),inj__ty_2Ebinary__ieee_2Eflags(V2M_27)),V0f_27)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eflags__case__eq,lemma,(( ! [A_27a:del]: ( ! [V0x:tp__ty_2Ebinary__ieee_2Eflags] : ( ! [V1f:$i] : (mem(V1f,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,arr(bool,A_27a))))))) => ( ! [V2v:$i] : (mem(V2v,A_27a) => ((ap(ap(c_2Ebinary__ieee_2Eflags__CASE(A_27a),inj__ty_2Ebinary__ieee_2Eflags(V0x)),V1f) = V2v) <=> (? [V3b:tp__o] : (? [V4b0:tp__o] : (? [V5b1:tp__o] : (? [V6b2:tp__o] : (? [V7b3:tp__o] : (? [V8b4:tp__o] : ((V0x = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erecordtype_2Eflags,inj__o(V3b)),inj__o(V4b0)),inj__o(V5b1)),inj__o(V6b2)),inj__o(V7b3)),inj__o(V8b4)))) & (ap(ap(ap(ap(ap(ap(V1f,inj__o(V3b)),inj__o(V4b0)),inj__o(V5b1)),inj__o(V6b2)),inj__o(V7b3)),inj__o(V8b4)) = V2v))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eclear__flags__def,axiom,(fo__c_2Ebinary__ieee_2Eclear__flags = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(fo__c_2Ebool_2EF))),ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(fo__c_2Ebool_2EF))),ap(ap(c_2Ebinary__ieee_2Eflags__Overflow__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(fo__c_2Ebool_2EF))),ap(ap(c_2Ebinary__ieee_2Eflags__Precision__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(fo__c_2Ebool_2EF))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(fo__c_2Ebool_2EF))),ap(ap(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(fo__c_2Ebool_2EF))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Eflags)))))))))).
tff(ax_thm_2Ebinary__ieee_2Einvalidop__flags__def,axiom,(fo__c_2Ebinary__ieee_2Einvalidop__flags = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(fo__c_2Ebool_2ET))),inj__ty_2Ebinary__ieee_2Eflags(fo__c_2Ebinary__ieee_2Eclear__flags))))).
tff(ax_thm_2Ebinary__ieee_2Edividezero__flags__def,axiom,(fo__c_2Ebinary__ieee_2Edividezero__flags = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,ap(c_2Ecombin_2EK(bool,bool),inj__o(fo__c_2Ebool_2ET))),inj__ty_2Ebinary__ieee_2Eflags(fo__c_2Ebinary__ieee_2Eclear__flags))))).
tff(ax_thm_2Ebinary__ieee_2Erounding__TY__DEF,axiom,(? [V0rep:$i] : (mem(V0rep,arr(ty_2Ebinary__ieee_2Erounding,ty_2Enum_2Enum)) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Enum_2Enum,ty_2Ebinary__ieee_2Erounding),f3035),V0rep))))).
tff(ax_thm_2Ebinary__ieee_2Erounding__BIJ,axiom,(( ! [V0a:tp__ty_2Ebinary__ieee_2Erounding] : (surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(V0a)))) = V0a)) & ( ! [V1r:tp__ty_2Enum_2Enum] : (p(ap(f3036,inj__ty_2Enum_2Enum(V1r))) <=> (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,ap(c_2Ebinary__ieee_2Enum2rounding,inj__ty_2Enum_2Enum(V1r)))) = V1r))))).
tff(conj_thm_2Ebinary__ieee_2Enum2rounding__rounding2num,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Erounding] : (surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(V0a)))) = V0a)))).
tff(conj_thm_2Ebinary__ieee_2Erounding2num__num2rounding,lemma,(( ! [V0r:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) <=> (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,ap(c_2Ebinary__ieee_2Enum2rounding,inj__ty_2Enum_2Enum(V0r)))) = V0r))))).
tff(conj_thm_2Ebinary__ieee_2Enum2rounding__11,lemma,(( ! [V0r:tp__ty_2Enum_2Enum] : ( ! [V1r_27:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) => (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1r_27)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) => ((surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,inj__ty_2Enum_2Enum(V0r))) = surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,inj__ty_2Enum_2Enum(V1r_27)))) <=> (V0r = V1r_27)))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding2num__11,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1a_27:tp__ty_2Ebinary__ieee_2Erounding] : ((surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(V0a))) = surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(V1a_27)))) <=> (V0a = V1a_27)))))).
tff(conj_thm_2Ebinary__ieee_2Enum2rounding__ONTO,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Erounding] : (? [V1r:tp__ty_2Enum_2Enum] : ((V0a = surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,inj__ty_2Enum_2Enum(V1r)))) & p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding2num__ONTO,lemma,(( ! [V0r:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) <=> (? [V1a:tp__ty_2Ebinary__ieee_2Erounding] : (V0r = surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(V1a))))))))).
tff(conj_thm_2Ebinary__ieee_2Enum2rounding__thm,lemma,(((surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = fo__c_2Ebinary__ieee_2EroundTiesToEven) & ((surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = fo__c_2Ebinary__ieee_2EroundTowardPositive) & ((surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = fo__c_2Ebinary__ieee_2EroundTowardNegative) & (surj__ty_2Ebinary__ieee_2Erounding(ap(c_2Ebinary__ieee_2Enum2rounding,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = fo__c_2Ebinary__ieee_2EroundTowardZero)))))).
tff(conj_thm_2Ebinary__ieee_2Erounding2num__thm,lemma,(((surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven))) = fo__c_2Enum_2E0) & ((surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive))) = 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_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) & (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding__EQ__rounding,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1a_27:tp__ty_2Ebinary__ieee_2Erounding] : ((V0a = V1a_27) <=> (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(V0a))) = surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(V1a_27))))))))).
tff(ax_thm_2Ebinary__ieee_2Erounding__size__def,axiom,( ! [V0x:tp__ty_2Ebinary__ieee_2Erounding] : (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(V0x))) = fo__c_2Enum_2E0))).
tff(ax_thm_2Ebinary__ieee_2Erounding__CASE,axiom,( ! [A_27a:del]: ( ! [V0x:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1v0:$i] : (mem(V1v0,A_27a) => ( ! [V2v1:$i] : (mem(V2v1,A_27a) => ( ! [V3v2:$i] : (mem(V3v2,A_27a) => ( ! [V4v3:$i] : (mem(V4v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(A_27a),inj__ty_2Ebinary__ieee_2Erounding(V0x)),V1v0),V2v1),V3v2),V4v3) = ap(f3037(A_27a,V2v1,V3v2,V4v3,V1v0),ap(c_2Ebinary__ieee_2Erounding2num,inj__ty_2Ebinary__ieee_2Erounding(V0x))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding__case__def,lemma,(( ! [A_27a:del]: (( ! [V0v0:$i] : (mem(V0v0,A_27a) => ( ! [V1v1:$i] : (mem(V1v1,A_27a) => ( ! [V2v2:$i] : (mem(V2v2,A_27a) => ( ! [V3v3:$i] : (mem(V3v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(A_27a),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),V0v0),V1v1),V2v2),V3v3) = V0v0))))))))) & (( ! [V4v0:$i] : (mem(V4v0,A_27a) => ( ! [V5v1:$i] : (mem(V5v1,A_27a) => ( ! [V6v2:$i] : (mem(V6v2,A_27a) => ( ! [V7v3:$i] : (mem(V7v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(A_27a),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive)),V4v0),V5v1),V6v2),V7v3) = V5v1))))))))) & (( ! [V8v0:$i] : (mem(V8v0,A_27a) => ( ! [V9v1:$i] : (mem(V9v1,A_27a) => ( ! [V10v2:$i] : (mem(V10v2,A_27a) => ( ! [V11v3:$i] : (mem(V11v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(A_27a),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)),V8v0),V9v1),V10v2),V11v3) = V10v2))))))))) & ( ! [V12v0:$i] : (mem(V12v0,A_27a) => ( ! [V13v1:$i] : (mem(V13v1,A_27a) => ( ! [V14v2:$i] : (mem(V14v2,A_27a) => ( ! [V15v3:$i] : (mem(V15v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(A_27a),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),V12v0),V13v1),V14v2),V15v3) = V15v3))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Edatatype__rounding,lemma,(( ! [V0rounding:$i] : (mem(V0rounding,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Erounding,bool))))) => p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(ap(V0rounding,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive)),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding__distinct,lemma,(((~~ (fo__c_2Ebinary__ieee_2EroundTiesToEven = fo__c_2Ebinary__ieee_2EroundTowardPositive)) & ((~~ (fo__c_2Ebinary__ieee_2EroundTiesToEven = fo__c_2Ebinary__ieee_2EroundTowardNegative)) & ((~~ (fo__c_2Ebinary__ieee_2EroundTiesToEven = fo__c_2Ebinary__ieee_2EroundTowardZero)) & ((~~ (fo__c_2Ebinary__ieee_2EroundTowardPositive = fo__c_2Ebinary__ieee_2EroundTowardNegative)) & ((~~ (fo__c_2Ebinary__ieee_2EroundTowardPositive = fo__c_2Ebinary__ieee_2EroundTowardZero)) & (~~ (fo__c_2Ebinary__ieee_2EroundTowardNegative = fo__c_2Ebinary__ieee_2EroundTowardZero))))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding__nchotomy,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Erounding] : ((V0a = fo__c_2Ebinary__ieee_2EroundTiesToEven) | ((V0a = fo__c_2Ebinary__ieee_2EroundTowardPositive) | ((V0a = fo__c_2Ebinary__ieee_2EroundTowardNegative) | (V0a = fo__c_2Ebinary__ieee_2EroundTowardZero))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding__Axiom,lemma,(( ! [A_27a:del]: ( ! [V0x0:$i] : (mem(V0x0,A_27a) => ( ! [V1x1:$i] : (mem(V1x1,A_27a) => ( ! [V2x2:$i] : (mem(V2x2,A_27a) => ( ! [V3x3:$i] : (mem(V3x3,A_27a) => (? [V4f:$i] : (mem(V4f,arr(ty_2Ebinary__ieee_2Erounding,A_27a)) & ((ap(V4f,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)) = V0x0) & ((ap(V4f,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive)) = V1x1) & ((ap(V4f,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)) = V2x2) & (ap(V4f,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)) = V3x3))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding__induction,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Erounding,bool)) => ((p(ap(V0P,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven))) & (p(ap(V0P,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative))) & (p(ap(V0P,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive))) & p(ap(V0P,inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)))))) => ( ! [V1a:tp__ty_2Ebinary__ieee_2Erounding] : p(ap(V0P,inj__ty_2Ebinary__ieee_2Erounding(V1a))))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding__case__cong,lemma,(( ! [A_27a:del]: ( ! [V0v0_27:$i] : (mem(V0v0_27,A_27a) => ( ! [V1v1_27:$i] : (mem(V1v1_27,A_27a) => ( ! [V2v2_27:$i] : (mem(V2v2_27,A_27a) => ( ! [V3v3_27:$i] : (mem(V3v3_27,A_27a) => ( ! [V4M:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V5M_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V6v0:$i] : (mem(V6v0,A_27a) => ( ! [V7v1:$i] : (mem(V7v1,A_27a) => ( ! [V8v2:$i] : (mem(V8v2,A_27a) => ( ! [V9v3:$i] : (mem(V9v3,A_27a) => (((V4M = V5M_27) & (((V5M_27 = fo__c_2Ebinary__ieee_2EroundTiesToEven) => (V6v0 = V0v0_27)) & (((V5M_27 = fo__c_2Ebinary__ieee_2EroundTowardPositive) => (V7v1 = V1v1_27)) & (((V5M_27 = fo__c_2Ebinary__ieee_2EroundTowardNegative) => (V8v2 = V2v2_27)) & ((V5M_27 = fo__c_2Ebinary__ieee_2EroundTowardZero) => (V9v3 = V3v3_27)))))) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(A_27a),inj__ty_2Ebinary__ieee_2Erounding(V4M)),V6v0),V7v1),V8v2),V9v3) = ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(A_27a),inj__ty_2Ebinary__ieee_2Erounding(V5M_27)),V0v0_27),V1v1_27),V2v2_27),V3v3_27)))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Erounding__case__eq,lemma,(( ! [A_27a:del]: ( ! [V0x:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1v0:$i] : (mem(V1v0,A_27a) => ( ! [V2v1:$i] : (mem(V2v1,A_27a) => ( ! [V3v2:$i] : (mem(V3v2,A_27a) => ( ! [V4v3:$i] : (mem(V4v3,A_27a) => ( ! [V5v:$i] : (mem(V5v,A_27a) => ((ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(A_27a),inj__ty_2Ebinary__ieee_2Erounding(V0x)),V1v0),V2v1),V3v2),V4v3) = V5v) <=> (((V0x = fo__c_2Ebinary__ieee_2EroundTiesToEven) & (V1v0 = V5v)) | (((V0x = fo__c_2Ebinary__ieee_2EroundTowardPositive) & (V2v1 = V5v)) | (((V0x = fo__c_2Ebinary__ieee_2EroundTowardNegative) & (V3v2 = V5v)) | ((V0x = fo__c_2Ebinary__ieee_2EroundTowardZero) & (V4v3 = V5v)))))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eis__closest__def,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0s:$i] : (mem(V0s,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2a:$i] : (mem(V2a,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (p(ap(ap(ap(c_2Ebinary__ieee_2Eis__closest(A_27a,A_27b),V0s),inj__ty_2Erealax_2Ereal(V1x)),V2a)) <=> (p(ap(ap(c_2Ebool_2EIN(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),V2a),V0s)) & ( ! [V3b:$i] : (mem(V3b,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (p(ap(ap(c_2Ebool_2EIN(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),V3b),V0s)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V2a)),inj__ty_2Erealax_2Ereal(V1x)))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V3b)),inj__ty_2Erealax_2Ereal(V1x)))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eclosest__such__def,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0p:$i] : (mem(V0p,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool)) => ( ! [V1s:$i] : (mem(V1s,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (ap(ap(ap(c_2Ebinary__ieee_2Eclosest__such(A_27a,A_27b),V0p),V1s),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Emin_2E_40(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),f3039(A_27a,A_27b,V0p,V1s,V2x))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eclosest__def,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: (c_2Ebinary__ieee_2Eclosest(A_27a,A_27b) = ap(c_2Ebinary__ieee_2Eclosest__such(A_27a,A_27b),ap(c_2Ecombin_2EK(bool,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),inj__o(fo__c_2Ebool_2ET))))))).
tff(ax_thm_2Ebinary__ieee_2Elargest__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,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(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2EUINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,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_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Erealax_2Einv,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_2Ethreshold__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,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(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2EUINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,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_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Erealax_2Einv,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_2Enum_2ESUC,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t)))))))))))).
tff(ax_thm_2Ebinary__ieee_2EULP__primitive__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (c_2Ebinary__ieee_2EULP(A_27t,A_27w) = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ty_2Erealax_2Ereal),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),bool))),f3040(A_27t,A_27w))),k(arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ty_2Erealax_2Ereal),f3042(A_27w,A_27t))))))).
tff(conj_thm_2Ebinary__ieee_2EULP__ind,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0P:$i] : (mem(V0P,arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),bool)) => (( ! [V1e:$i] : (mem(V1e,ty_2Efcp_2Ecart(bool,A_27w)) => p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),V1e),c_2Ebool_2Ethe__value(A_27t)))))) => ( ! [V2v:$i] : (mem(V2v,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V3v1:$i] : (mem(V3v1,ty_2Ebool_2Eitself(A_27t)) => p(ap(V0P,ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),V2v),V3v1)))))))))))))).
tff(conj_thm_2Ebinary__ieee_2EULP__def,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0e:$i] : (mem(V0e,ty_2Efcp_2Ecart(bool,A_27w)) => (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),V0e),c_2Ebool_2Ethe__value(A_27t)))) = surj__ty_2Erealax_2Ereal(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(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27w)),V0e),ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Ewords_2Ew2n(A_27w),V0e)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eulp__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),c_2Ebool_2Ethe__value(A_27t)))))))).
tff(ax_thm_2Ebinary__ieee_2Eround__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__ty_2Erealax_2Ereal(V1x)) = ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3044(A_27t,A_27w,V1x)),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))),ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3046(A_27w,A_27t,V1x)),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))),ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3048(A_27w,A_27t,V1x)),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))),ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3050(A_27t,A_27w,V1x)),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))).
tff(ax_thm_2Ebinary__ieee_2Eintegral__round__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : (ap(ap(c_2Ebinary__ieee_2Eintegral__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__ty_2Erealax_2Ereal(V1x)) = ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Erounding__CASE(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3053(A_27t,A_27w,V1x)),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))),ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3055(A_27w,A_27t,V1x)),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))),ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3057(A_27w,A_27t,V1x)),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))),ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3059(A_27t,A_27w,V1x)),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efp__op__TY__DEF,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (? [V0rep:$i] : (mem(V0rep,arr(ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w),ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Erounding,ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Erounding,ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)),f3106(A_27t,A_27w)),V0rep))))))).
tff(ax_thm_2Ebinary__ieee_2Efp__op__case__def,axiom,( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: (( ! [V0a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1a1:$i] : (mem(V1a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2f:$i] : (mem(V2f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V3f1:$i] : (mem(V3f1,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)))) => ( ! [V4f2:$i] : (mem(V4f2,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V5f3:$i] : (mem(V5f3,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)))) => ( ! [V6f4:$i] : (mem(V6f4,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V7f5:$i] : (mem(V7f5,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))))) => ( ! [V8f6:$i] : (mem(V8f6,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => (ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0a0)),V1a1)),V2f),V3f1),V4f2),V5f3),V6f4),V7f5),V8f6) = ap(ap(V2f,inj__ty_2Ebinary__ieee_2Erounding(V0a0)),V1a1))))))))))))))))))) & (( ! [V9a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V10a1:$i] : (mem(V10a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V11a2:$i] : (mem(V11a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V12f:$i] : (mem(V12f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V13f1:$i] : (mem(V13f1,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V14f2:$i] : (mem(V14f2,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)))) => ( ! [V15f3:$i] : (mem(V15f3,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V16f4:$i] : (mem(V16f4,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)))) => ( ! [V17f5:$i] : (mem(V17f5,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => ( ! [V18f6:$i] : (mem(V18f6,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))))) => (ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V9a0)),V10a1),V11a2)),V12f),V13f1),V14f2),V15f3),V16f4),V17f5),V18f6) = ap(ap(ap(V13f1,inj__ty_2Ebinary__ieee_2Erounding(V9a0)),V10a1),V11a2))))))))))))))))))))) & (( ! [V19a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V20a1:$i] : (mem(V20a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V21a2:$i] : (mem(V21a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V22f:$i] : (mem(V22f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V23f1:$i] : (mem(V23f1,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)))) => ( ! [V24f2:$i] : (mem(V24f2,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V25f3:$i] : (mem(V25f3,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)))) => ( ! [V26f4:$i] : (mem(V26f4,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V27f5:$i] : (mem(V27f5,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))))) => ( ! [V28f6:$i] : (mem(V28f6,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => (ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V19a0)),V20a1),V21a2)),V22f),V23f1),V24f2),V25f3),V26f4),V27f5),V28f6) = ap(ap(ap(V24f2,inj__ty_2Ebinary__ieee_2Erounding(V19a0)),V20a1),V21a2))))))))))))))))))))) & (( ! [V29a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V30a1:$i] : (mem(V30a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V31a2:$i] : (mem(V31a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V32f:$i] : (mem(V32f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V33f1:$i] : (mem(V33f1,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V34f2:$i] : (mem(V34f2,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)))) => ( ! [V35f3:$i] : (mem(V35f3,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V36f4:$i] : (mem(V36f4,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)))) => ( ! [V37f5:$i] : (mem(V37f5,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => ( ! [V38f6:$i] : (mem(V38f6,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))))) => (ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V29a0)),V30a1),V31a2)),V32f),V33f1),V34f2),V35f3),V36f4),V37f5),V38f6) = ap(ap(ap(V35f3,inj__ty_2Ebinary__ieee_2Erounding(V29a0)),V30a1),V31a2))))))))))))))))))))) & (( ! [V39a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V40a1:$i] : (mem(V40a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V41a2:$i] : (mem(V41a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V42f:$i] : (mem(V42f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V43f1:$i] : (mem(V43f1,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)))) => ( ! [V44f2:$i] : (mem(V44f2,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V45f3:$i] : (mem(V45f3,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)))) => ( ! [V46f4:$i] : (mem(V46f4,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V47f5:$i] : (mem(V47f5,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))))) => ( ! [V48f6:$i] : (mem(V48f6,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => (ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V39a0)),V40a1),V41a2)),V42f),V43f1),V44f2),V45f3),V46f4),V47f5),V48f6) = ap(ap(ap(V46f4,inj__ty_2Ebinary__ieee_2Erounding(V39a0)),V40a1),V41a2))))))))))))))))))))) & (( ! [V49a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V50a1:$i] : (mem(V50a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V51a2:$i] : (mem(V51a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V52a3:$i] : (mem(V52a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V53f:$i] : (mem(V53f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V54f1:$i] : (mem(V54f1,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)))) => ( ! [V55f2:$i] : (mem(V55f2,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V56f3:$i] : (mem(V56f3,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)))) => ( ! [V57f4:$i] : (mem(V57f4,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V58f5:$i] : (mem(V58f5,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))))) => ( ! [V59f6:$i] : (mem(V59f6,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => (ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V49a0)),V50a1),V51a2),V52a3)),V53f),V54f1),V55f2),V56f3),V57f4),V58f5),V59f6) = ap(ap(ap(ap(V58f5,inj__ty_2Ebinary__ieee_2Erounding(V49a0)),V50a1),V51a2),V52a3))))))))))))))))))))))) & ( ! [V60a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V61a1:$i] : (mem(V61a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V62a2:$i] : (mem(V62a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V63a3:$i] : (mem(V63a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V64f:$i] : (mem(V64f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V65f1:$i] : (mem(V65f1,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)))) => ( ! [V66f2:$i] : (mem(V66f2,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V67f3:$i] : (mem(V67f3,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)))) => ( ! [V68f4:$i] : (mem(V68f4,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V69f5:$i] : (mem(V69f5,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))))) => ( ! [V70f6:$i] : (mem(V70f6,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => (ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V60a0)),V61a1),V62a2),V63a3)),V64f),V65f1),V66f2),V67f3),V68f4),V69f5),V70f6) = ap(ap(ap(ap(V70f6,inj__ty_2Ebinary__ieee_2Erounding(V60a0)),V61a1),V62a2),V63a3))))))))))))))))))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efp__op__size__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (( ! [V0f:$i] : (mem(V0f,arr(A_27t,ty_2Enum_2Enum)) => ( ! [V1f1:$i] : (mem(V1f1,arr(A_27w,ty_2Enum_2Enum)) => ( ! [V2a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V3a1:$i] : (mem(V3a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__size(A_27t,A_27w),V0f),V1f1),ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V2a0)),V3a1))) = 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_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(V2a0))),ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V0f),V1f1),V3a1)))))))))))) & (( ! [V4f:$i] : (mem(V4f,arr(A_27t,ty_2Enum_2Enum)) => ( ! [V5f1:$i] : (mem(V5f1,arr(A_27w,ty_2Enum_2Enum)) => ( ! [V6a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V7a1:$i] : (mem(V7a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V8a2:$i] : (mem(V8a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__size(A_27t,A_27w),V4f),V5f1),ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V6a0)),V7a1),V8a2))) = 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_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(V6a0))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V4f),V5f1),V7a1)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V4f),V5f1),V8a2))))))))))))))) & (( ! [V9f:$i] : (mem(V9f,arr(A_27t,ty_2Enum_2Enum)) => ( ! [V10f1:$i] : (mem(V10f1,arr(A_27w,ty_2Enum_2Enum)) => ( ! [V11a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V12a1:$i] : (mem(V12a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V13a2:$i] : (mem(V13a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__size(A_27t,A_27w),V9f),V10f1),ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V11a0)),V12a1),V13a2))) = 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_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(V11a0))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V9f),V10f1),V12a1)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V9f),V10f1),V13a2))))))))))))))) & (( ! [V14f:$i] : (mem(V14f,arr(A_27t,ty_2Enum_2Enum)) => ( ! [V15f1:$i] : (mem(V15f1,arr(A_27w,ty_2Enum_2Enum)) => ( ! [V16a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V17a1:$i] : (mem(V17a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V18a2:$i] : (mem(V18a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__size(A_27t,A_27w),V14f),V15f1),ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V16a0)),V17a1),V18a2))) = 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_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(V16a0))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V14f),V15f1),V17a1)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V14f),V15f1),V18a2))))))))))))))) & (( ! [V19f:$i] : (mem(V19f,arr(A_27t,ty_2Enum_2Enum)) => ( ! [V20f1:$i] : (mem(V20f1,arr(A_27w,ty_2Enum_2Enum)) => ( ! [V21a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V22a1:$i] : (mem(V22a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V23a2:$i] : (mem(V23a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__size(A_27t,A_27w),V19f),V20f1),ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V21a0)),V22a1),V23a2))) = 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_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(V21a0))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V19f),V20f1),V22a1)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V19f),V20f1),V23a2))))))))))))))) & (( ! [V24f:$i] : (mem(V24f,arr(A_27t,ty_2Enum_2Enum)) => ( ! [V25f1:$i] : (mem(V25f1,arr(A_27w,ty_2Enum_2Enum)) => ( ! [V26a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V27a1:$i] : (mem(V27a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V28a2:$i] : (mem(V28a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V29a3:$i] : (mem(V29a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__size(A_27t,A_27w),V24f),V25f1),ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V26a0)),V27a1),V28a2),V29a3))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(V26a0))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V24f),V25f1),V27a1)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V24f),V25f1),V28a2)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V24f),V25f1),V29a3)))))))))))))))))) & ( ! [V30f:$i] : (mem(V30f,arr(A_27t,ty_2Enum_2Enum)) => ( ! [V31f1:$i] : (mem(V31f1,arr(A_27w,ty_2Enum_2Enum)) => ( ! [V32a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V33a1:$i] : (mem(V33a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V34a2:$i] : (mem(V34a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V35a3:$i] : (mem(V35a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Enum_2Enum(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__size(A_27t,A_27w),V30f),V31f1),ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V32a0)),V33a1),V34a2),V35a3))) = 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_2Ebinary__ieee_2Erounding__size,inj__ty_2Ebinary__ieee_2Erounding(V32a0))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V30f),V31f1),V33a1)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V30f),V31f1),V34a2)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__size(A_27t,A_27w),V30f),V31f1),V35a3))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Edatatype__fp__op,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0fp__op:$i] : (mem(V0fp__op,arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),arr(arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),bool)))))))) => p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(ap(ap(ap(ap(V0fp__op,c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w)),c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w)),c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w)),c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w)),c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w)),c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w)),c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w)))))))))).
tff(conj_thm_2Ebinary__ieee_2Efp__op__11,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: (( ! [V0a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1a1:$i] : (mem(V1a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V3a1_27:$i] : (mem(V3a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0a0)),V1a1) = ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V2a0_27)),V3a1_27)) <=> ((V0a0 = V2a0_27) & (V1a1 = V3a1_27))))))))) & (( ! [V4a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V5a1:$i] : (mem(V5a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V6a2:$i] : (mem(V6a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V7a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V8a1_27:$i] : (mem(V8a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V9a2_27:$i] : (mem(V9a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V4a0)),V5a1),V6a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V7a0_27)),V8a1_27),V9a2_27)) <=> ((V4a0 = V7a0_27) & ((V5a1 = V8a1_27) & (V6a2 = V9a2_27)))))))))))))) & (( ! [V10a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V11a1:$i] : (mem(V11a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V12a2:$i] : (mem(V12a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V13a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V14a1_27:$i] : (mem(V14a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V15a2_27:$i] : (mem(V15a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V10a0)),V11a1),V12a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V13a0_27)),V14a1_27),V15a2_27)) <=> ((V10a0 = V13a0_27) & ((V11a1 = V14a1_27) & (V12a2 = V15a2_27)))))))))))))) & (( ! [V16a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V17a1:$i] : (mem(V17a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V18a2:$i] : (mem(V18a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V19a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V20a1_27:$i] : (mem(V20a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V21a2_27:$i] : (mem(V21a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V16a0)),V17a1),V18a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V19a0_27)),V20a1_27),V21a2_27)) <=> ((V16a0 = V19a0_27) & ((V17a1 = V20a1_27) & (V18a2 = V21a2_27)))))))))))))) & (( ! [V22a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V23a1:$i] : (mem(V23a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V24a2:$i] : (mem(V24a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V25a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V26a1_27:$i] : (mem(V26a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V27a2_27:$i] : (mem(V27a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V22a0)),V23a1),V24a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V25a0_27)),V26a1_27),V27a2_27)) <=> ((V22a0 = V25a0_27) & ((V23a1 = V26a1_27) & (V24a2 = V27a2_27)))))))))))))) & (( ! [V28a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V29a1:$i] : (mem(V29a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V30a2:$i] : (mem(V30a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V31a3:$i] : (mem(V31a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V32a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V33a1_27:$i] : (mem(V33a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V34a2_27:$i] : (mem(V34a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V35a3_27:$i] : (mem(V35a3_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V28a0)),V29a1),V30a2),V31a3) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V32a0_27)),V33a1_27),V34a2_27),V35a3_27)) <=> ((V28a0 = V32a0_27) & ((V29a1 = V33a1_27) & ((V30a2 = V34a2_27) & (V31a3 = V35a3_27))))))))))))))))))) & ( ! [V36a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V37a1:$i] : (mem(V37a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V38a2:$i] : (mem(V38a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V39a3:$i] : (mem(V39a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V40a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V41a1_27:$i] : (mem(V41a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V42a2_27:$i] : (mem(V42a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V43a3_27:$i] : (mem(V43a3_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V36a0)),V37a1),V38a2),V39a3) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V40a0_27)),V41a1_27),V42a2_27),V43a3_27)) <=> ((V36a0 = V40a0_27) & ((V37a1 = V41a1_27) & ((V38a2 = V42a2_27) & (V39a3 = V43a3_27))))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efp__op__distinct,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: (( ! [V0a2:$i] : (mem(V0a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1a1_27:$i] : (mem(V1a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2a1:$i] : (mem(V2a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V3a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V4a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V4a0)),V2a1) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V3a0_27)),V1a1_27),V0a2))))))))))) & (( ! [V5a2:$i] : (mem(V5a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V6a1_27:$i] : (mem(V6a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V7a1:$i] : (mem(V7a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V8a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V9a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V9a0)),V7a1) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V8a0_27)),V6a1_27),V5a2))))))))))) & (( ! [V10a2:$i] : (mem(V10a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V11a1_27:$i] : (mem(V11a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V12a1:$i] : (mem(V12a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V13a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V14a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V14a0)),V12a1) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V13a0_27)),V11a1_27),V10a2))))))))))) & (( ! [V15a2:$i] : (mem(V15a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V16a1_27:$i] : (mem(V16a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V17a1:$i] : (mem(V17a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V18a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V19a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V19a0)),V17a1) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V18a0_27)),V16a1_27),V15a2))))))))))) & (( ! [V20a3:$i] : (mem(V20a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V21a2:$i] : (mem(V21a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V22a1_27:$i] : (mem(V22a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V23a1:$i] : (mem(V23a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V24a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V25a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V25a0)),V23a1) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V24a0_27)),V22a1_27),V21a2),V20a3))))))))))))) & (( ! [V26a3:$i] : (mem(V26a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V27a2:$i] : (mem(V27a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V28a1_27:$i] : (mem(V28a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V29a1:$i] : (mem(V29a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V30a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V31a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V31a0)),V29a1) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V30a0_27)),V28a1_27),V27a2),V26a3))))))))))))) & (( ! [V32a2_27:$i] : (mem(V32a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V33a2:$i] : (mem(V33a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V34a1_27:$i] : (mem(V34a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V35a1:$i] : (mem(V35a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V36a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V37a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V37a0)),V35a1),V33a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V36a0_27)),V34a1_27),V32a2_27))))))))))))) & (( ! [V38a2_27:$i] : (mem(V38a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V39a2:$i] : (mem(V39a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V40a1_27:$i] : (mem(V40a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V41a1:$i] : (mem(V41a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V42a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V43a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V43a0)),V41a1),V39a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V42a0_27)),V40a1_27),V38a2_27))))))))))))) & (( ! [V44a2_27:$i] : (mem(V44a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V45a2:$i] : (mem(V45a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V46a1_27:$i] : (mem(V46a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V47a1:$i] : (mem(V47a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V48a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V49a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V49a0)),V47a1),V45a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V48a0_27)),V46a1_27),V44a2_27))))))))))))) & (( ! [V50a3:$i] : (mem(V50a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V51a2_27:$i] : (mem(V51a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V52a2:$i] : (mem(V52a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V53a1_27:$i] : (mem(V53a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V54a1:$i] : (mem(V54a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V55a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V56a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V56a0)),V54a1),V52a2) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V55a0_27)),V53a1_27),V51a2_27),V50a3))))))))))))))) & (( ! [V57a3:$i] : (mem(V57a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V58a2_27:$i] : (mem(V58a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V59a2:$i] : (mem(V59a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V60a1_27:$i] : (mem(V60a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V61a1:$i] : (mem(V61a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V62a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V63a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V63a0)),V61a1),V59a2) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V62a0_27)),V60a1_27),V58a2_27),V57a3))))))))))))))) & (( ! [V64a2_27:$i] : (mem(V64a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V65a2:$i] : (mem(V65a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V66a1_27:$i] : (mem(V66a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V67a1:$i] : (mem(V67a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V68a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V69a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V69a0)),V67a1),V65a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V68a0_27)),V66a1_27),V64a2_27))))))))))))) & (( ! [V70a2_27:$i] : (mem(V70a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V71a2:$i] : (mem(V71a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V72a1_27:$i] : (mem(V72a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V73a1:$i] : (mem(V73a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V74a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V75a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V75a0)),V73a1),V71a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V74a0_27)),V72a1_27),V70a2_27))))))))))))) & (( ! [V76a3:$i] : (mem(V76a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V77a2_27:$i] : (mem(V77a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V78a2:$i] : (mem(V78a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V79a1_27:$i] : (mem(V79a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V80a1:$i] : (mem(V80a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V81a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V82a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V82a0)),V80a1),V78a2) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V81a0_27)),V79a1_27),V77a2_27),V76a3))))))))))))))) & (( ! [V83a3:$i] : (mem(V83a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V84a2_27:$i] : (mem(V84a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V85a2:$i] : (mem(V85a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V86a1_27:$i] : (mem(V86a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V87a1:$i] : (mem(V87a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V88a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V89a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V89a0)),V87a1),V85a2) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V88a0_27)),V86a1_27),V84a2_27),V83a3))))))))))))))) & (( ! [V90a2_27:$i] : (mem(V90a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V91a2:$i] : (mem(V91a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V92a1_27:$i] : (mem(V92a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V93a1:$i] : (mem(V93a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V94a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V95a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V95a0)),V93a1),V91a2) = ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V94a0_27)),V92a1_27),V90a2_27))))))))))))) & (( ! [V96a3:$i] : (mem(V96a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V97a2_27:$i] : (mem(V97a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V98a2:$i] : (mem(V98a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V99a1_27:$i] : (mem(V99a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V100a1:$i] : (mem(V100a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V101a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V102a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V102a0)),V100a1),V98a2) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V101a0_27)),V99a1_27),V97a2_27),V96a3))))))))))))))) & (( ! [V103a3:$i] : (mem(V103a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V104a2_27:$i] : (mem(V104a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V105a2:$i] : (mem(V105a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V106a1_27:$i] : (mem(V106a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V107a1:$i] : (mem(V107a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V108a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V109a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V109a0)),V107a1),V105a2) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V108a0_27)),V106a1_27),V104a2_27),V103a3))))))))))))))) & (( ! [V110a3:$i] : (mem(V110a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V111a2_27:$i] : (mem(V111a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V112a2:$i] : (mem(V112a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V113a1_27:$i] : (mem(V113a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V114a1:$i] : (mem(V114a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V115a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V116a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V116a0)),V114a1),V112a2) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V115a0_27)),V113a1_27),V111a2_27),V110a3))))))))))))))) & (( ! [V117a3:$i] : (mem(V117a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V118a2_27:$i] : (mem(V118a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V119a2:$i] : (mem(V119a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V120a1_27:$i] : (mem(V120a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V121a1:$i] : (mem(V121a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V122a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V123a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V123a0)),V121a1),V119a2) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V122a0_27)),V120a1_27),V118a2_27),V117a3))))))))))))))) & ( ! [V124a3_27:$i] : (mem(V124a3_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V125a3:$i] : (mem(V125a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V126a2_27:$i] : (mem(V126a2_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V127a2:$i] : (mem(V127a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V128a1_27:$i] : (mem(V128a1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V129a1:$i] : (mem(V129a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V130a0_27:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V131a0:tp__ty_2Ebinary__ieee_2Erounding] : (~~ (ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V131a0)),V129a1),V127a2),V125a3) = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V130a0_27)),V128a1_27),V126a2_27),V124a3_27))))))))))))))))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efp__op__nchotomy,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0ff:$i] : (mem(V0ff,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => ((? [V1r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V2f:$i] : (mem(V2f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (V0ff = ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V1r)),V2f))))) | ((? [V3r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V4f:$i] : (mem(V4f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V5f0:$i] : (mem(V5f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (V0ff = ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V3r)),V4f),V5f0))))))) | ((? [V6r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V7f:$i] : (mem(V7f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V8f0:$i] : (mem(V8f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (V0ff = ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V6r)),V7f),V8f0))))))) | ((? [V9r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V10f:$i] : (mem(V10f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V11f0:$i] : (mem(V11f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (V0ff = ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V9r)),V10f),V11f0))))))) | ((? [V12r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V13f:$i] : (mem(V13f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V14f0:$i] : (mem(V14f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (V0ff = ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V12r)),V13f),V14f0))))))) | ((? [V15r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V16f:$i] : (mem(V16f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V17f0:$i] : (mem(V17f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V18f1:$i] : (mem(V18f1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (V0ff = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V15r)),V16f),V17f0),V18f1))))))))) | (? [V19r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V20f:$i] : (mem(V20f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V21f0:$i] : (mem(V21f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V22f1:$i] : (mem(V22f1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (V0ff = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V19r)),V20f),V21f0),V22f1))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efp__op__Axiom,lemma,(( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f0:$i] : (mem(V0f0,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V1f1:$i] : (mem(V1f1,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V2f2:$i] : (mem(V2f2,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)))) => ( ! [V3f3:$i] : (mem(V3f3,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V4f4:$i] : (mem(V4f4,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)))) => ( ! [V5f5:$i] : (mem(V5f5,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => ( ! [V6f6:$i] : (mem(V6f6,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))))) => (? [V7fn:$i] : (mem(V7fn,arr(ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w),A_27a)) & (( ! [V8a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V9a1:$i] : (mem(V9a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(V7fn,ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V8a0)),V9a1)) = ap(ap(V0f0,inj__ty_2Ebinary__ieee_2Erounding(V8a0)),V9a1))))) & (( ! [V10a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V11a1:$i] : (mem(V11a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V12a2:$i] : (mem(V12a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(V7fn,ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V10a0)),V11a1),V12a2)) = ap(ap(ap(V1f1,inj__ty_2Ebinary__ieee_2Erounding(V10a0)),V11a1),V12a2))))))) & (( ! [V13a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V14a1:$i] : (mem(V14a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V15a2:$i] : (mem(V15a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(V7fn,ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V13a0)),V14a1),V15a2)) = ap(ap(ap(V2f2,inj__ty_2Ebinary__ieee_2Erounding(V13a0)),V14a1),V15a2))))))) & (( ! [V16a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V17a1:$i] : (mem(V17a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V18a2:$i] : (mem(V18a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(V7fn,ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V16a0)),V17a1),V18a2)) = ap(ap(ap(V3f3,inj__ty_2Ebinary__ieee_2Erounding(V16a0)),V17a1),V18a2))))))) & (( ! [V19a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V20a1:$i] : (mem(V20a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V21a2:$i] : (mem(V21a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(V7fn,ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V19a0)),V20a1),V21a2)) = ap(ap(ap(V4f4,inj__ty_2Ebinary__ieee_2Erounding(V19a0)),V20a1),V21a2))))))) & (( ! [V22a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V23a1:$i] : (mem(V23a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V24a2:$i] : (mem(V24a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V25a3:$i] : (mem(V25a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(V7fn,ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V22a0)),V23a1),V24a2),V25a3)) = ap(ap(ap(ap(V5f5,inj__ty_2Ebinary__ieee_2Erounding(V22a0)),V23a1),V24a2),V25a3))))))))) & ( ! [V26a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V27a1:$i] : (mem(V27a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V28a2:$i] : (mem(V28a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V29a3:$i] : (mem(V29a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(V7fn,ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V26a0)),V27a1),V28a2),V29a3)) = ap(ap(ap(ap(V6f6,inj__ty_2Ebinary__ieee_2Erounding(V26a0)),V27a1),V28a2),V29a3)))))))))))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efp__op__induction,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w),bool)) => ((( ! [V1r:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V2f:$i] : (mem(V2f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => p(ap(V0P,ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V1r)),V2f)))))) & (( ! [V3r:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V4f:$i] : (mem(V4f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V5f0:$i] : (mem(V5f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => p(ap(V0P,ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V3r)),V4f),V5f0)))))))) & (( ! [V6r:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V7f:$i] : (mem(V7f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V8f0:$i] : (mem(V8f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => p(ap(V0P,ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V6r)),V7f),V8f0)))))))) & (( ! [V9r:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V10f:$i] : (mem(V10f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V11f0:$i] : (mem(V11f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => p(ap(V0P,ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V9r)),V10f),V11f0)))))))) & (( ! [V12r:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V13f:$i] : (mem(V13f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V14f0:$i] : (mem(V14f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => p(ap(V0P,ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V12r)),V13f),V14f0)))))))) & (( ! [V15r:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V16f:$i] : (mem(V16f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V17f0:$i] : (mem(V17f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V18f1:$i] : (mem(V18f1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => p(ap(V0P,ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V15r)),V16f),V17f0),V18f1)))))))))) & ( ! [V19r:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V20f:$i] : (mem(V20f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V21f0:$i] : (mem(V21f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V22f1:$i] : (mem(V22f1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => p(ap(V0P,ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V19r)),V20f),V21f0),V22f1)))))))))))))))) => ( ! [V23f:$i] : (mem(V23f,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => p(ap(V0P,V23f))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efp__op__case__cong,lemma,(( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f_27:$i] : (mem(V0f_27,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V1f1_27:$i] : (mem(V1f1_27,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V2f2_27:$i] : (mem(V2f2_27,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)))) => ( ! [V3f3_27:$i] : (mem(V3f3_27,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V4f4_27:$i] : (mem(V4f4_27,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)))) => ( ! [V5f5_27:$i] : (mem(V5f5_27,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => ( ! [V6f6_27:$i] : (mem(V6f6_27,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))))) => ( ! [V7M:$i] : (mem(V7M,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => ( ! [V8M_27:$i] : (mem(V8M_27,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => ( ! [V9f:$i] : (mem(V9f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V10f1:$i] : (mem(V10f1,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)))) => ( ! [V11f2:$i] : (mem(V11f2,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V12f3:$i] : (mem(V12f3,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)))) => ( ! [V13f4:$i] : (mem(V13f4,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V14f5:$i] : (mem(V14f5,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))))) => ( ! [V15f6:$i] : (mem(V15f6,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => (((V7M = V8M_27) & (( ! [V16a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V17a1:$i] : (mem(V17a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((V8M_27 = ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V16a0)),V17a1)) => (ap(ap(V9f,inj__ty_2Ebinary__ieee_2Erounding(V16a0)),V17a1) = ap(ap(V0f_27,inj__ty_2Ebinary__ieee_2Erounding(V16a0)),V17a1)))))) & (( ! [V18a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V19a1:$i] : (mem(V19a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V20a2:$i] : (mem(V20a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((V8M_27 = ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V18a0)),V19a1),V20a2)) => (ap(ap(ap(V10f1,inj__ty_2Ebinary__ieee_2Erounding(V18a0)),V19a1),V20a2) = ap(ap(ap(V1f1_27,inj__ty_2Ebinary__ieee_2Erounding(V18a0)),V19a1),V20a2)))))))) & (( ! [V21a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V22a1:$i] : (mem(V22a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V23a2:$i] : (mem(V23a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((V8M_27 = ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V21a0)),V22a1),V23a2)) => (ap(ap(ap(V11f2,inj__ty_2Ebinary__ieee_2Erounding(V21a0)),V22a1),V23a2) = ap(ap(ap(V2f2_27,inj__ty_2Ebinary__ieee_2Erounding(V21a0)),V22a1),V23a2)))))))) & (( ! [V24a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V25a1:$i] : (mem(V25a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V26a2:$i] : (mem(V26a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((V8M_27 = ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V24a0)),V25a1),V26a2)) => (ap(ap(ap(V12f3,inj__ty_2Ebinary__ieee_2Erounding(V24a0)),V25a1),V26a2) = ap(ap(ap(V3f3_27,inj__ty_2Ebinary__ieee_2Erounding(V24a0)),V25a1),V26a2)))))))) & (( ! [V27a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V28a1:$i] : (mem(V28a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V29a2:$i] : (mem(V29a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((V8M_27 = ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V27a0)),V28a1),V29a2)) => (ap(ap(ap(V13f4,inj__ty_2Ebinary__ieee_2Erounding(V27a0)),V28a1),V29a2) = ap(ap(ap(V4f4_27,inj__ty_2Ebinary__ieee_2Erounding(V27a0)),V28a1),V29a2)))))))) & (( ! [V30a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V31a1:$i] : (mem(V31a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V32a2:$i] : (mem(V32a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V33a3:$i] : (mem(V33a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((V8M_27 = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V30a0)),V31a1),V32a2),V33a3)) => (ap(ap(ap(ap(V14f5,inj__ty_2Ebinary__ieee_2Erounding(V30a0)),V31a1),V32a2),V33a3) = ap(ap(ap(ap(V5f5_27,inj__ty_2Ebinary__ieee_2Erounding(V30a0)),V31a1),V32a2),V33a3)))))))))) & ( ! [V34a0:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V35a1:$i] : (mem(V35a1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V36a2:$i] : (mem(V36a2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V37a3:$i] : (mem(V37a3,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((V8M_27 = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V34a0)),V35a1),V36a2),V37a3)) => (ap(ap(ap(ap(V15f6,inj__ty_2Ebinary__ieee_2Erounding(V34a0)),V35a1),V36a2),V37a3) = ap(ap(ap(ap(V6f6_27,inj__ty_2Ebinary__ieee_2Erounding(V34a0)),V35a1),V36a2),V37a3))))))))))))))))) => (ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),V7M),V9f),V10f1),V11f2),V12f3),V13f4),V14f5),V15f6) = ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),V8M_27),V0f_27),V1f1_27),V2f2_27),V3f3_27),V4f4_27),V5f5_27),V6f6_27)))))))))))))))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efp__op__case__eq,lemma,(( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => ( ! [V1f:$i] : (mem(V1f,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))) => ( ! [V2f1:$i] : (mem(V2f1,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V3f2:$i] : (mem(V3f2,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)))) => ( ! [V4f3:$i] : (mem(V4f3,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))) => ( ! [V5f4:$i] : (mem(V5f4,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)))) => ( ! [V6f5:$i] : (mem(V6f5,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))))) => ( ! [V7f6:$i] : (mem(V7f6,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))))) => ( ! [V8v:$i] : (mem(V8v,A_27a) => ((ap(ap(ap(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efp__op__CASE(A_27a,A_27t,A_27w),V0x),V1f),V2f1),V3f2),V4f3),V5f4),V6f5),V7f6) = V8v) <=> ((? [V9r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V10f_27:$i] : (mem(V10f_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & ((V0x = ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V9r)),V10f_27)) & (ap(ap(V1f,inj__ty_2Ebinary__ieee_2Erounding(V9r)),V10f_27) = V8v))))) | ((? [V11r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V12f_27:$i] : (mem(V12f_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V13f0:$i] : (mem(V13f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & ((V0x = ap(ap(ap(c_2Ebinary__ieee_2EFP__Add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V11r)),V12f_27),V13f0)) & (ap(ap(ap(V2f1,inj__ty_2Ebinary__ieee_2Erounding(V11r)),V12f_27),V13f0) = V8v))))))) | ((? [V14r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V15f_27:$i] : (mem(V15f_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V16f0:$i] : (mem(V16f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & ((V0x = ap(ap(ap(c_2Ebinary__ieee_2EFP__Sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V14r)),V15f_27),V16f0)) & (ap(ap(ap(V3f2,inj__ty_2Ebinary__ieee_2Erounding(V14r)),V15f_27),V16f0) = V8v))))))) | ((? [V17r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V18f_27:$i] : (mem(V18f_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V19f0:$i] : (mem(V19f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & ((V0x = ap(ap(ap(c_2Ebinary__ieee_2EFP__Mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V17r)),V18f_27),V19f0)) & (ap(ap(ap(V4f3,inj__ty_2Ebinary__ieee_2Erounding(V17r)),V18f_27),V19f0) = V8v))))))) | ((? [V20r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V21f_27:$i] : (mem(V21f_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V22f0:$i] : (mem(V22f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & ((V0x = ap(ap(ap(c_2Ebinary__ieee_2EFP__Div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V20r)),V21f_27),V22f0)) & (ap(ap(ap(V5f4,inj__ty_2Ebinary__ieee_2Erounding(V20r)),V21f_27),V22f0) = V8v))))))) | ((? [V23r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V24f_27:$i] : (mem(V24f_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V25f0:$i] : (mem(V25f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V26f1_27:$i] : (mem(V26f1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & ((V0x = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulAdd(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V23r)),V24f_27),V25f0),V26f1_27)) & (ap(ap(ap(ap(V6f5,inj__ty_2Ebinary__ieee_2Erounding(V23r)),V24f_27),V25f0),V26f1_27) = V8v))))))))) | (? [V27r:tp__ty_2Ebinary__ieee_2Erounding] : (? [V28f_27:$i] : (mem(V28f_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V29f0:$i] : (mem(V29f0,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & (? [V30f1_27:$i] : (mem(V30f1_27,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) & ((V0x = ap(ap(ap(ap(c_2Ebinary__ieee_2EFP__MulSub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V27r)),V28f_27),V29f0),V30f1_27)) & (ap(ap(ap(ap(V7f6,inj__ty_2Ebinary__ieee_2Erounding(V27r)),V28f_27),V29f0),V30f1_27) = V8v))))))))))))))))))))))))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__some__qnan__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0fp__op:$i] : (mem(V0fp__op,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => (ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V0fp__op) = ap(ap(c_2Emin_2E_40(arr(ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))),f3108(A_27t,A_27w,V0fp__op)),V0fp__op))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__round__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1toneg:tp__o] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__o(V1toneg)),inj__ty_2Erealax_2Ereal(V2r)) = ap(ap(c_2Ebool_2ELET(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),f3109(A_27t,A_27w,V1toneg)),ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__ty_2Erealax_2Ereal(V2r)))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__round__with__flags__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1to__neg:tp__o] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round__with__flags(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__o(V1to__neg)),inj__ty_2Erealax_2Ereal(V2r)) = ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))),ap(ap(c_2Ebool_2ELET(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Erealax_2Ereal,ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),f3112(A_27w,A_27t,V0mode,V1to__neg,V2r)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__o(V1to__neg)),inj__ty_2Erealax_2Ereal(V2r)))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2r)))))))))).
tff(ax_thm_2Ebinary__ieee_2Echeck__for__signalling__def,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0l:$i] : (mem(V0l,ty_2Elist_2Elist(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))) => (surj__ty_2Ebinary__ieee_2Eflags(ap(c_2Ebinary__ieee_2Echeck__for__signalling(A_27a,A_27b),V0l)) = surj__ty_2Ebinary__ieee_2Eflags(ap(ap(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,ap(c_2Ecombin_2EK(bool,bool),ap(ap(c_2Elist_2EEXISTS(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__is__signalling(A_27a,A_27b)),V0l))),inj__ty_2Ebinary__ieee_2Eflags(fo__c_2Ebinary__ieee_2Eclear__flags))))))))).
tff(ax_thm_2Ebinary__ieee_2Ereal__to__float__def,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0m:tp__ty_2Ebinary__ieee_2Erounding] : (ap(c_2Ebinary__ieee_2Ereal__to__float(A_27a,A_27b),inj__ty_2Ebinary__ieee_2Erounding(V0m)) = ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27a,A_27b),inj__ty_2Ebinary__ieee_2Erounding(V0m)),ap(ap(c_2Emin_2E_3D(ty_2Ebinary__ieee_2Erounding),inj__ty_2Ebinary__ieee_2Erounding(V0m)),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)))))))).
tff(ax_thm_2Ebinary__ieee_2Ereal__to__float__with__flags__def,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0m:tp__ty_2Ebinary__ieee_2Erounding] : (ap(c_2Ebinary__ieee_2Ereal__to__float__with__flags(A_27a,A_27b),inj__ty_2Ebinary__ieee_2Erounding(V0m)) = ap(ap(c_2Ebinary__ieee_2Efloat__round__with__flags(A_27a,A_27b),inj__ty_2Ebinary__ieee_2Erounding(V0m)),ap(ap(c_2Emin_2E_3D(ty_2Ebinary__ieee_2Erounding),inj__ty_2Ebinary__ieee_2Erounding(V0m)),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__round__to__integral__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(c_2Ebinary__ieee_2Efloat__round__to__integral(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x) = ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V1x)),f3113(A_27w,A_27t,V0mode)),V1x),V1x)))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__to__int__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint(ap(ap(c_2Ebinary__ieee_2Efloat__to__int(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x)) = surj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(ty_2Eoption_2Eoption(ty_2Einteger_2Eint)),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V1x)),f3116(A_27w,A_27t,V1x,V0mode)),c_2Eoption_2ENONE(ty_2Einteger_2Eint)),c_2Eoption_2ENONE(ty_2Einteger_2Eint)))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__sqrt__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V1x)),ap(c_2Ewords_2En2w(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__value__CASE(ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V1x)),f3117(A_27t,A_27w,V0mode)),ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),inj__ty_2Ebinary__ieee_2Eflags(fo__c_2Ebinary__ieee_2Eclear__flags)),ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))),ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Echeck__for__signalling(A_27t,A_27w),ap(ap(c_2Elist_2ECONS(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V1x),c_2Elist_2ENIL(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x))))),ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),inj__ty_2Ebinary__ieee_2Eflags(fo__c_2Ebinary__ieee_2Einvalidop__flags)),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),ap(ap(c_2Ebinary__ieee_2EFP__Sqrt(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__add__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2y:$i] : (mem(V2y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x),V2y) = ap(ap(c_2Epair_2Epair__CASE(ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V1x)),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V2y))),f3121(A_27t,A_27w,V0mode,V1x,V2y))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__sub__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2y:$i] : (mem(V2y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x),V2y) = ap(ap(c_2Epair_2Epair__CASE(ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V1x)),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V2y))),f3125(A_27t,A_27w,V0mode,V1x,V2y))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__mul__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2y:$i] : (mem(V2y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x),V2y) = ap(ap(c_2Epair_2Epair__CASE(ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V1x)),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V2y))),f3130(A_27t,A_27w,V0mode,V1x,V2y))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__div__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2y:$i] : (mem(V2y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__div(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x),V2y) = ap(ap(c_2Epair_2Epair__CASE(ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V1x)),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V2y))),f3134(A_27t,A_27w,V0mode,V1x,V2y))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__mul__add__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2y:$i] : (mem(V2y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V3z:$i] : (mem(V3z,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__add(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x),V2y),V3z) = ap(ap(c_2Ebool_2ELET(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))),f3138(A_27t,A_27w,V0mode,V3z,V1x,V2y)),ap(ap(c_2Ewords_2Eword__xor(ty_2Eone_2Eone),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V1x)),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V2y)))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__mul__sub__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2y:$i] : (mem(V2y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V3z:$i] : (mem(V3z,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__sub(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),V1x),V2y),V3z) = ap(ap(c_2Ebool_2ELET(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))),f3142(A_27t,A_27w,V0mode,V3z,V1x,V2y)),ap(ap(c_2Ewords_2Eword__xor(ty_2Eone_2Eone),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V1x)),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V2y)))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__compare__TY__DEF,axiom,(? [V0rep:$i] : (mem(V0rep,arr(ty_2Ebinary__ieee_2Efloat__compare,ty_2Enum_2Enum)) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Enum_2Enum,ty_2Ebinary__ieee_2Efloat__compare),f3035),V0rep))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__compare__BIJ,axiom,(( ! [V0a:tp__ty_2Ebinary__ieee_2Efloat__compare] : (surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(V0a)))) = V0a)) & ( ! [V1r:tp__ty_2Enum_2Enum] : (p(ap(f3036,inj__ty_2Enum_2Enum(V1r))) <=> (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,ap(c_2Ebinary__ieee_2Enum2float__compare,inj__ty_2Enum_2Enum(V1r)))) = V1r))))).
tff(conj_thm_2Ebinary__ieee_2Enum2float__compare__float__compare2num,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Efloat__compare] : (surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(V0a)))) = V0a)))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare2num__num2float__compare,lemma,(( ! [V0r:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) <=> (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,ap(c_2Ebinary__ieee_2Enum2float__compare,inj__ty_2Enum_2Enum(V0r)))) = V0r))))).
tff(conj_thm_2Ebinary__ieee_2Enum2float__compare__11,lemma,(( ! [V0r:tp__ty_2Enum_2Enum] : ( ! [V1r_27:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) => (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1r_27)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) => ((surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,inj__ty_2Enum_2Enum(V0r))) = surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,inj__ty_2Enum_2Enum(V1r_27)))) <=> (V0r = V1r_27)))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare2num__11,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Efloat__compare] : ( ! [V1a_27:tp__ty_2Ebinary__ieee_2Efloat__compare] : ((surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(V0a))) = surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(V1a_27)))) <=> (V0a = V1a_27)))))).
tff(conj_thm_2Ebinary__ieee_2Enum2float__compare__ONTO,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Efloat__compare] : (? [V1r:tp__ty_2Enum_2Enum] : ((V0a = surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,inj__ty_2Enum_2Enum(V1r)))) & p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V1r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare2num__ONTO,lemma,(( ! [V0r:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V0r)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) <=> (? [V1a:tp__ty_2Ebinary__ieee_2Efloat__compare] : (V0r = surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(V1a))))))))).
tff(conj_thm_2Ebinary__ieee_2Enum2float__compare__thm,lemma,(((surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = fo__c_2Ebinary__ieee_2ELT) & ((surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = fo__c_2Ebinary__ieee_2EEQ) & ((surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) = fo__c_2Ebinary__ieee_2EGT) & (surj__ty_2Ebinary__ieee_2Efloat__compare(ap(c_2Ebinary__ieee_2Enum2float__compare,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) = fo__c_2Ebinary__ieee_2EUN)))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare2num__thm,lemma,(((surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2ELT))) = fo__c_2Enum_2E0) & ((surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EEQ))) = 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__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EGT))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) & (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EUN))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare__EQ__float__compare,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Efloat__compare] : ( ! [V1a_27:tp__ty_2Ebinary__ieee_2Efloat__compare] : ((V0a = V1a_27) <=> (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(V0a))) = surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(V1a_27))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__compare__size__def,axiom,( ! [V0x:tp__ty_2Ebinary__ieee_2Efloat__compare] : (surj__ty_2Enum_2Enum(ap(c_2Ebinary__ieee_2Efloat__compare__size,inj__ty_2Ebinary__ieee_2Efloat__compare(V0x))) = fo__c_2Enum_2E0))).
tff(ax_thm_2Ebinary__ieee_2Efloat__compare__CASE,axiom,( ! [A_27a:del]: ( ! [V0x:tp__ty_2Ebinary__ieee_2Efloat__compare] : ( ! [V1v0:$i] : (mem(V1v0,A_27a) => ( ! [V2v1:$i] : (mem(V2v1,A_27a) => ( ! [V3v2:$i] : (mem(V3v2,A_27a) => ( ! [V4v3:$i] : (mem(V4v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__compare(V0x)),V1v0),V2v1),V3v2),V4v3) = ap(f3037(A_27a,V2v1,V3v2,V4v3,V1v0),ap(c_2Ebinary__ieee_2Efloat__compare2num,inj__ty_2Ebinary__ieee_2Efloat__compare(V0x))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare__case__def,lemma,(( ! [A_27a:del]: (( ! [V0v0:$i] : (mem(V0v0,A_27a) => ( ! [V1v1:$i] : (mem(V1v1,A_27a) => ( ! [V2v2:$i] : (mem(V2v2,A_27a) => ( ! [V3v3:$i] : (mem(V3v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2ELT)),V0v0),V1v1),V2v2),V3v3) = V0v0))))))))) & (( ! [V4v0:$i] : (mem(V4v0,A_27a) => ( ! [V5v1:$i] : (mem(V5v1,A_27a) => ( ! [V6v2:$i] : (mem(V6v2,A_27a) => ( ! [V7v3:$i] : (mem(V7v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EEQ)),V4v0),V5v1),V6v2),V7v3) = V5v1))))))))) & (( ! [V8v0:$i] : (mem(V8v0,A_27a) => ( ! [V9v1:$i] : (mem(V9v1,A_27a) => ( ! [V10v2:$i] : (mem(V10v2,A_27a) => ( ! [V11v3:$i] : (mem(V11v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EGT)),V8v0),V9v1),V10v2),V11v3) = V10v2))))))))) & ( ! [V12v0:$i] : (mem(V12v0,A_27a) => ( ! [V13v1:$i] : (mem(V13v1,A_27a) => ( ! [V14v2:$i] : (mem(V14v2,A_27a) => ( ! [V15v3:$i] : (mem(V15v3,A_27a) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EUN)),V12v0),V13v1),V14v2),V15v3) = V15v3))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Edatatype__float__compare,lemma,(( ! [V0float__compare:$i] : (mem(V0float__compare,arr(ty_2Ebinary__ieee_2Efloat__compare,arr(ty_2Ebinary__ieee_2Efloat__compare,arr(ty_2Ebinary__ieee_2Efloat__compare,arr(ty_2Ebinary__ieee_2Efloat__compare,bool))))) => p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(ap(V0float__compare,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2ELT)),inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EEQ)),inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EGT)),inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EUN)))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare__distinct,lemma,(((~~ (fo__c_2Ebinary__ieee_2ELT = fo__c_2Ebinary__ieee_2EEQ)) & ((~~ (fo__c_2Ebinary__ieee_2ELT = fo__c_2Ebinary__ieee_2EGT)) & ((~~ (fo__c_2Ebinary__ieee_2ELT = fo__c_2Ebinary__ieee_2EUN)) & ((~~ (fo__c_2Ebinary__ieee_2EEQ = fo__c_2Ebinary__ieee_2EGT)) & ((~~ (fo__c_2Ebinary__ieee_2EEQ = fo__c_2Ebinary__ieee_2EUN)) & (~~ (fo__c_2Ebinary__ieee_2EGT = fo__c_2Ebinary__ieee_2EUN))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare__nchotomy,lemma,(( ! [V0a:tp__ty_2Ebinary__ieee_2Efloat__compare] : ((V0a = fo__c_2Ebinary__ieee_2ELT) | ((V0a = fo__c_2Ebinary__ieee_2EEQ) | ((V0a = fo__c_2Ebinary__ieee_2EGT) | (V0a = fo__c_2Ebinary__ieee_2EUN))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare__Axiom,lemma,(( ! [A_27a:del]: ( ! [V0x0:$i] : (mem(V0x0,A_27a) => ( ! [V1x1:$i] : (mem(V1x1,A_27a) => ( ! [V2x2:$i] : (mem(V2x2,A_27a) => ( ! [V3x3:$i] : (mem(V3x3,A_27a) => (? [V4f:$i] : (mem(V4f,arr(ty_2Ebinary__ieee_2Efloat__compare,A_27a)) & ((ap(V4f,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2ELT)) = V0x0) & ((ap(V4f,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EEQ)) = V1x1) & ((ap(V4f,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EGT)) = V2x2) & (ap(V4f,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EUN)) = V3x3))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare__induction,lemma,(( ! [V0P:$i] : (mem(V0P,arr(ty_2Ebinary__ieee_2Efloat__compare,bool)) => ((p(ap(V0P,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EEQ))) & (p(ap(V0P,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EGT))) & (p(ap(V0P,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2ELT))) & p(ap(V0P,inj__ty_2Ebinary__ieee_2Efloat__compare(fo__c_2Ebinary__ieee_2EUN)))))) => ( ! [V1a:tp__ty_2Ebinary__ieee_2Efloat__compare] : p(ap(V0P,inj__ty_2Ebinary__ieee_2Efloat__compare(V1a))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare__case__cong,lemma,(( ! [A_27a:del]: ( ! [V0v0_27:$i] : (mem(V0v0_27,A_27a) => ( ! [V1v1_27:$i] : (mem(V1v1_27,A_27a) => ( ! [V2v2_27:$i] : (mem(V2v2_27,A_27a) => ( ! [V3v3_27:$i] : (mem(V3v3_27,A_27a) => ( ! [V4M:tp__ty_2Ebinary__ieee_2Efloat__compare] : ( ! [V5M_27:tp__ty_2Ebinary__ieee_2Efloat__compare] : ( ! [V6v0:$i] : (mem(V6v0,A_27a) => ( ! [V7v1:$i] : (mem(V7v1,A_27a) => ( ! [V8v2:$i] : (mem(V8v2,A_27a) => ( ! [V9v3:$i] : (mem(V9v3,A_27a) => (((V4M = V5M_27) & (((V5M_27 = fo__c_2Ebinary__ieee_2ELT) => (V6v0 = V0v0_27)) & (((V5M_27 = fo__c_2Ebinary__ieee_2EEQ) => (V7v1 = V1v1_27)) & (((V5M_27 = fo__c_2Ebinary__ieee_2EGT) => (V8v2 = V2v2_27)) & ((V5M_27 = fo__c_2Ebinary__ieee_2EUN) => (V9v3 = V3v3_27)))))) => (ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__compare(V4M)),V6v0),V7v1),V8v2),V9v3) = ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__compare(V5M_27)),V0v0_27),V1v1_27),V2v2_27),V3v3_27)))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__compare__case__eq,lemma,(( ! [A_27a:del]: ( ! [V0x:tp__ty_2Ebinary__ieee_2Efloat__compare] : ( ! [V1v0:$i] : (mem(V1v0,A_27a) => ( ! [V2v1:$i] : (mem(V2v1,A_27a) => ( ! [V3v2:$i] : (mem(V3v2,A_27a) => ( ! [V4v3:$i] : (mem(V4v3,A_27a) => ( ! [V5v:$i] : (mem(V5v,A_27a) => ((ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(A_27a),inj__ty_2Ebinary__ieee_2Efloat__compare(V0x)),V1v0),V2v1),V3v2),V4v3) = V5v) <=> (((V0x = fo__c_2Ebinary__ieee_2ELT) & (V1v0 = V5v)) | (((V0x = fo__c_2Ebinary__ieee_2EEQ) & (V2v1 = V5v)) | (((V0x = fo__c_2Ebinary__ieee_2EGT) & (V3v2 = V5v)) | ((V0x = fo__c_2Ebinary__ieee_2EUN) & (V4v3 = V5v)))))))))))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__compare__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (surj__ty_2Ebinary__ieee_2Efloat__compare(ap(ap(c_2Ebinary__ieee_2Efloat__compare(A_27t,A_27w),V0x),V1y)) = surj__ty_2Ebinary__ieee_2Efloat__compare(ap(ap(c_2Epair_2Epair__CASE(ty_2Ebinary__ieee_2Efloat__compare,ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Efloat__value,ty_2Ebinary__ieee_2Efloat__value),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0x)),ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V1y))),f3146(A_27w,A_27t,V1y,V0x))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__less__than__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(ap(c_2Ebinary__ieee_2Efloat__less__than(A_27t,A_27w),V0x),V1y)) <=> (surj__ty_2Ebinary__ieee_2Efloat__compare(ap(ap(c_2Ebinary__ieee_2Efloat__compare(A_27t,A_27w),V0x),V1y)) = fo__c_2Ebinary__ieee_2ELT))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__less__equal__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(ap(c_2Ebinary__ieee_2Efloat__less__equal(A_27t,A_27w),V0x),V1y)) <=> p(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(bool),ap(ap(c_2Ebinary__ieee_2Efloat__compare(A_27t,A_27w),V0x),V1y)),inj__o(fo__c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2EF))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__greater__than__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(ap(c_2Ebinary__ieee_2Efloat__greater__than(A_27t,A_27w),V0x),V1y)) <=> (surj__ty_2Ebinary__ieee_2Efloat__compare(ap(ap(c_2Ebinary__ieee_2Efloat__compare(A_27t,A_27w),V0x),V1y)) = fo__c_2Ebinary__ieee_2EGT))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__greater__equal__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(ap(c_2Ebinary__ieee_2Efloat__greater__equal(A_27t,A_27w),V0x),V1y)) <=> p(ap(ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__compare__CASE(bool),ap(ap(c_2Ebinary__ieee_2Efloat__compare(A_27t,A_27w),V0x),V1y)),inj__o(fo__c_2Ebool_2EF)),inj__o(fo__c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2ET)),inj__o(fo__c_2Ebool_2EF))))))))))).
tff(ax_thm_2Ebinary__ieee_2Efloat__equal__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(ap(c_2Ebinary__ieee_2Efloat__equal(A_27t,A_27w),V0x),V1y)) <=> (surj__ty_2Ebinary__ieee_2Efloat__compare(ap(ap(c_2Ebinary__ieee_2Efloat__compare(A_27t,A_27w),V0x),V1y)) = fo__c_2Ebinary__ieee_2EEQ))))))))).
tff(ax_thm_2Ebinary__ieee_2Eexponent__boundary__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:$i] : (mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(ap(c_2Ebinary__ieee_2Eexponent__boundary(A_27t,A_27w),V0y),V1x)) <=> ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V1x)) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0y))) & ((surj__ty_2Enum_2Enum(ap(c_2Ewords_2Ew2n(A_27w),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V1x))) = surj__ty_2Enum_2Enum(ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2Ew2n(A_27w),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V1x) = ap(c_2Ewords_2En2w(A_27w),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & ((ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0y) = ap(c_2Ewords_2Eword__2comp(A_27t),ap(c_2Ewords_2En2w(A_27t),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V1x) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Ezero__lt__twopow,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),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))))),inj__ty_2Enum_2Enum(V0n))))))).
tff(conj_thm_2Ebinary__ieee_2Ezero__le__twopow,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),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))))),inj__ty_2Enum_2Enum(V0n))))))).
tff(conj_thm_2Ebinary__ieee_2Ezero__neq__twopow,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : (~~ (surj__ty_2Erealax_2Ereal(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))))),inj__ty_2Enum_2Enum(V0n))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))).
tff(conj_thm_2Ebinary__ieee_2Ezero__le__pos__div__twopow,lemma,(( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(V0m))),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))))),inj__ty_2Enum_2Enum(V1n))))))))).
tff(conj_thm_2Ebinary__ieee_2Ediv__eq0,lemma,(( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),inj__ty_2Erealax_2Ereal(V1b))) => ((surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,inj__ty_2Erealax_2Ereal(V0a)),inj__ty_2Erealax_2Ereal(V1b))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) <=> (V0a = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))))).
tff(conj_thm_2Ebinary__ieee_2Eexp__ge2,lemma,(( ! [V0b:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0b)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0b))))))).
tff(conj_thm_2Ebinary__ieee_2Eexp__gt2,lemma,(( ! [V0b:tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0b)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(V0b))))))).
tff(conj_thm_2Ebinary__ieee_2Ele2,lemma,(( ! [V0n:tp__ty_2Erealax_2Ereal] : ( ! [V1m:tp__ty_2Erealax_2Ereal] : ((p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Erealax_2Ereal(V0n))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),inj__ty_2Erealax_2Ereal(V1m)))) => p(ap(ap(c_2Ereal_2Ereal__lte,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_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V0n)),inj__ty_2Erealax_2Ereal(V1m))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__components,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [A_27d:del]: ( ! [A_27e:del]: ( ! [A_27f:del]: ( ! [A_27g:del]: ( ! [A_27h:del]: ( ! [A_27i:del]: ( ! [A_27j:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(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))))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2En2w(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(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)))) = c_2Ewords_2Eword__T(A_27w)) & ((ap(c_2Ebinary__ieee_2Efloat__Significand(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)))) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2En2w(ty_2Eone_2Eone),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = c_2Ewords_2Eword__T(A_27w)) & ((ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2En2w(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(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)))) = ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((ap(c_2Ebinary__ieee_2Efloat__Significand(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)))) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2En2w(ty_2Eone_2Eone),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2En2w(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(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)))) = ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((ap(c_2Ebinary__ieee_2Efloat__Significand(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)))) = ap(c_2Ewords_2En2w(A_27t),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2En2w(ty_2Eone_2Eone),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = ap(c_2Ewords_2En2w(A_27t),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(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))))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2En2w(ty_2Eone_2Eone),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(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)))) = 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(c_2Ebinary__ieee_2Efloat__Significand(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)))) = c_2Ewords_2Eword__T(A_27t)) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2En2w(ty_2Eone_2Eone),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & ((ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,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(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = c_2Ewords_2Eword__T(A_27t)) & (( ! [V0fp__op:$i] : (mem(V0fp__op,ty_2Ebinary__ieee_2Efp__op(A_27a,A_27b)) => (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op)) = c_2Ewords_2Eword__T(A_27b)))) & (( ! [V1fp__op:$i] : (mem(V1fp__op,ty_2Ebinary__ieee_2Efp__op(A_27c,A_27d)) => (~~ (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27c,A_27d),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27c,A_27d),V1fp__op)) = ap(c_2Ewords_2En2w(A_27c),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))) & (( ! [V2x:$i] : (mem(V2x,ty_2Ebinary__ieee_2Efloat(A_27e,A_27f)) => (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ebinary__ieee_2Efloat__Sign(A_27e,A_27f),ap(c_2Ebinary__ieee_2Efloat__negate(A_27e,A_27f),V2x))) = surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(ap(c_2Ewords_2Eword__1comp(ty_2Eone_2Eone),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27e,A_27f),V2x)))))) & (( ! [V3x:$i] : (mem(V3x,ty_2Ebinary__ieee_2Efloat(A_27g,A_27h)) => (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27g,A_27h),ap(c_2Ebinary__ieee_2Efloat__negate(A_27g,A_27h),V3x)) = ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27g,A_27h),V3x)))) & ( ! [V4x:$i] : (mem(V4x,ty_2Ebinary__ieee_2Efloat(A_27i,A_27j)) => (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27i,A_27j),ap(c_2Ebinary__ieee_2Efloat__negate(A_27i,A_27j),V4x)) = ap(c_2Ebinary__ieee_2Efloat__Significand(A_27i,A_27j),V4x)))))))))))))))))))))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__distinct,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [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(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__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(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))) = ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(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))) = 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__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(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))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (( ! [V0fp__op:$i] : (mem(V0fp__op,ty_2Ebinary__ieee_2Efp__op(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))) = ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V0fp__op))))) & ((~~ (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__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(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__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(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))))) & ((~~ (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__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (( ! [V1fp__op:$i] : (mem(V1fp__op,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => (~~ (ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V1fp__op))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (( ! [V2fp__op:$i] : (mem(V2fp__op,ty_2Ebinary__ieee_2Efp__op(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))) = ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V2fp__op))))) & ((~~ (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__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(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__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(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))))) & ((~~ (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__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (( ! [V3fp__op:$i] : (mem(V3fp__op,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => (~~ (ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V3fp__op))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (( ! [V4fp__op:$i] : (mem(V4fp__op,ty_2Ebinary__ieee_2Efp__op(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))) = ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V4fp__op))))) & ((~~ (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__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (( ! [V5fp__op:$i] : (mem(V5fp__op,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => (~~ (ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V5fp__op))))) & (( ! [V6fp__op:$i] : (mem(V6fp__op,ty_2Ebinary__ieee_2Efp__op(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))) = ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V6fp__op))))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (( ! [V7fp__op:$i] : (mem(V7fp__op,ty_2Ebinary__ieee_2Efp__op(A_27t,A_27w)) => (~~ (ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27t,A_27w),V7fp__op))))) & ( ! [V8x:$i] : (mem(V8x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (~~ (ap(c_2Ebinary__ieee_2Efloat__negate(A_27a,A_27b),V8x) = V8x)))))))))))))))))))))))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__values,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = fo__c_2Ebinary__ieee_2EInfinity) & ((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = fo__c_2Ebinary__ieee_2EInfinity) & (( ! [V0fp__op:$i] : (mem(V0fp__op,ty_2Ebinary__ieee_2Efp__op(A_27a,A_27b)) => (surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op))) = fo__c_2Ebinary__ieee_2ENaN))) & ((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & ((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) & ((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t)))))))) & (surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,ap(ap(c_2Ereal_2E_2F,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t)))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Ezero__to__real,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ((surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) & (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))).
tff(conj_thm_2Ebinary__ieee_2Esign__not__zero,lemma,(( ! [V0s:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (~~ (surj__ty_2Erealax_2Ereal(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),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0s)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__sets,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ((c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w) = ap(ap(c_2Epred__set_2EINSERT(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),ap(ap(c_2Epred__set_2EINSERT(ty_2Ebinary__ieee_2Efloat(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)))),c_2Epred__set_2EEMPTY(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))) & (c_2Ebinary__ieee_2Efloat__is__infinite(A_27t,A_27w) = ap(ap(c_2Epred__set_2EINSERT(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),ap(ap(c_2Epred__set_2EINSERT(ty_2Ebinary__ieee_2Efloat(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)))),c_2Epred__set_2EEMPTY(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))))).
tff(conj_thm_2Ebinary__ieee_2Einfinity__properties,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__finite(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__integral(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__integral(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__normal(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(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))))) & p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Ezero__properties,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: (p(ap(c_2Ebinary__ieee_2Efloat__is__zero(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))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__finite(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))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__integral(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))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__integral(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__normal(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(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)))))) & (~~ p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Esome__nan__properties,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0fp__op:$i] : (mem(V0fp__op,ty_2Ebinary__ieee_2Efp__op(A_27a,A_27b)) => ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op)))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op)))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__integral(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op)))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__signalling(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op)))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op)))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op)))) & (~~ p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__some__qnan(A_27a,A_27b),V0fp__op))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Emin__properties,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(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)))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__finite(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))))) & ((p(ap(c_2Ebinary__ieee_2Efloat__is__integral(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) <=> ((surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27w),c_2Ebool_2Ethe__value(A_27w))) = 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_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__normal(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)))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(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))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(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)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((p(ap(c_2Ebinary__ieee_2Efloat__is__integral(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) <=> ((surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27w),c_2Ebool_2Ethe__value(A_27w))) = 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_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & (~~ p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__minus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Etop__properties,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(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)))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__finite(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))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(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)))))) & ((p(ap(c_2Ebinary__ieee_2Efloat__is__normal(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))))) <=> (~~ (surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27w),c_2Ebool_2Ethe__value(A_27w))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & ((p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(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))))) <=> (surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27w),c_2Ebool_2Ethe__value(A_27w))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & (~~ p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(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(conj_thm_2Ebinary__ieee_2Ebottom__properties,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & (p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) & ((~~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) & ((p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) <=> (~~ (surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27w),c_2Ebool_2Ethe__value(A_27w))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) & ((p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) <=> (surj__ty_2Enum_2Enum(ap(c_2Efcp_2Edimindex(A_27w),c_2Ebool_2Ethe__value(A_27w))) = surj__ty_2Enum_2Enum(ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & (~~ p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__is__zero,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x)) <=> ((ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27a,A_27b),V0x) = ap(c_2Ewords_2En2w(A_27b),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27a,A_27b),V0x) = ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__is__finite,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x)) <=> (p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27a,A_27b),V0x)) | (p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27a,A_27b),V0x)) | p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__cases__finite,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) | (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),V0x)) | p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x)))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__distinct__finite,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x)))) & (~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__cases,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) | (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),V0x)) | (p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27a,A_27b),V0x)) | (p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27a,A_27b),V0x)) | p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__is__distinct,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27a,A_27b),V0x)))) & ((~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__normal(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x)))) & (~~ (p(ap(c_2Ebinary__ieee_2Efloat__is__subnormal(A_27a,A_27b),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__infinities,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__infinite(A_27t,A_27w),V0x)) <=> ((V0x = ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) | (V0x = ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__infinities__distinct,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (~~ ((V0x = ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) & (V0x = ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__to__real__negate,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__negate(A_27a,A_27b),V0x))) = surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x)))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__negate__negate,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (ap(c_2Ebinary__ieee_2Efloat__negate(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__negate(A_27a,A_27b),V0x)) = V0x))))))).
tff(conj_thm_2Ebinary__ieee_2Eulp,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(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(conj_thm_2Ebinary__ieee_2Eneg__ulp,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: (surj__ty_2Erealax_2Ereal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(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(conj_thm_2Ebinary__ieee_2EULP__le__mono,lemma,(( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [V0e1:$i] : (mem(V0e1,ty_2Efcp_2Ecart(bool,A_27a)) => ( ! [V1e2:$i] : (mem(V1e2,ty_2Efcp_2Ecart(bool,A_27a)) => ((~~ (V1e2 = ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) => (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ebinary__ieee_2EULP(A_27t,A_27a),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27a),ty_2Ebool_2Eitself(A_27t)),V0e1),c_2Ebool_2Ethe__value(A_27t)))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27a),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27a),ty_2Ebool_2Eitself(A_27t)),V1e2),c_2Ebool_2Ethe__value(A_27t))))) <=> p(ap(ap(c_2Ewords_2Eword__ls(A_27a),V0e1),V1e2)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eulp__lt__ULP,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0e:$i] : (mem(V0e,ty_2Efcp_2Ecart(bool,A_27w)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),V0e),c_2Ebool_2Ethe__value(A_27t))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eulp__lt__largest,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))).
tff(conj_thm_2Ebinary__ieee_2Eulp__lt__threshold,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))).
tff(conj_thm_2Ebinary__ieee_2Eabs__float__value,lemma,((( ! [V0b:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1c:tp__ty_2Erealax_2Ereal] : ( ! [V2d:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,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),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0b)))),inj__ty_2Erealax_2Ereal(V1c))),inj__ty_2Erealax_2Ereal(V2d)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,inj__ty_2Erealax_2Ereal(V1c)),inj__ty_2Erealax_2Ereal(V2d)))))))) & ( ! [V3b:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V4c:tp__ty_2Erealax_2Ereal] : (surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,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),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V3b)))),inj__ty_2Erealax_2Ereal(V4c)))) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V4c))))))))).
tff(conj_thm_2Ebinary__ieee_2Eless__than__ulp,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0a:$i] : (mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a))),ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) <=> ((ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0a) = ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & (ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0a) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__is__zero__to__real,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => (p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x)) <=> (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x)) = surj__ty_2Erealax_2Ereal(ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__to__real__eq,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ((surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x)) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1y))) <=> ((V0x = V1y) | (p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V1y))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Ediff__float__ULP,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : (mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => (((~~ (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x)) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1y)))) & (~~ p(ap(ap(c_2Ebinary__ieee_2Eexponent__boundary(A_27t,A_27w),V1y),V0x)))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x)),c_2Ebool_2Ethe__value(A_27t)))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1y)))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Ediff__lt__ulp__eq0,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0a:$i] : (mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1b:$i] : (mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (((~~ p(ap(ap(c_2Ebinary__ieee_2Eexponent__boundary(A_27t,A_27w),V1b),V0a))) & (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2x)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0a)),c_2Ebool_2Ethe__value(A_27t))))) & (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2x)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0a)),c_2Ebool_2Ethe__value(A_27t))))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2x)))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2x)))) & (~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V0a)))))))) => (V1b = V0a))))))))))).
tff(conj_thm_2Ebinary__ieee_2Ediff__lt__ulp__even,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0a:$i] : (mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1b:$i] : (mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (((~~ p(ap(ap(c_2Ebinary__ieee_2Eexponent__boundary(A_27t,A_27w),V1b),V0a))) & (p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),inj__ty_2Erealax_2Ereal(V2x))))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0a)),c_2Ebool_2Ethe__value(A_27t))))) & (p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)),inj__ty_2Erealax_2Ereal(V2x))))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0a)),c_2Ebool_2Ethe__value(A_27t))))) & (~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V0a)))))) => (V1b = V0a))))))))))).
tff(conj_thm_2Ebinary__ieee_2Ediff__lt__ulp__even4,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0a:$i] : (mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1b:$i] : (mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (((~~ p(ap(ap(c_2Ebinary__ieee_2Eexponent__boundary(A_27t,A_27w),V1b),V0a))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),inj__ty_2Erealax_2Ereal(V2x))))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0a)),c_2Ebool_2Ethe__value(A_27t))))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)),inj__ty_2Erealax_2Ereal(V2x))))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0a)),c_2Ebool_2Ethe__value(A_27t))))) & (~~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V0a)))))) => (V1b = V0a))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardZero,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0y)) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V2r)))) & (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2r)),inj__ty_2Erealax_2Ereal(V1x)))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0y)),c_2Ebool_2Ethe__value(A_27t))))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2r))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x)))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x)))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__ty_2Erealax_2Ereal(V1x)) = V0y)))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTiesToEven,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0y)) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V2r)))) & ((((ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0y) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & (~~ (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0y) = ap(c_2Ewords_2En2w(A_27w),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2r))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2r)),inj__ty_2Erealax_2Ereal(V1x))))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0y)),c_2Ebool_2Ethe__value(A_27t))))) & (((surj__ty_2Erealax_2Ereal(ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2r)),inj__ty_2Erealax_2Ereal(V1x))))) = surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0y)),c_2Ebool_2Ethe__value(A_27t))))) => (~~ p(ap(c_2Ewords_2Eword__lsb(A_27t),ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0y))))) & (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__ty_2Erealax_2Ereal(V1x)) = V0y)))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTiesToEven0,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2Efloat__value(A_27t,A_27w),V0y)) = surj__ty_2Ebinary__ieee_2Efloat__value(ap(c_2Ebinary__ieee_2EFloat,inj__ty_2Erealax_2Ereal(V2r)))) & (((ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0y) = ap(c_2Ewords_2En2w(A_27t),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) & ((~~ (ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0y) = ap(c_2Ewords_2En2w(A_27w),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))) & (~~ p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V2r))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))))))) & (p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,inj__ty_2Erealax_2Ereal(V2r)),inj__ty_2Erealax_2Ereal(V1x))))),ap(c_2Ebinary__ieee_2EULP(A_27t,A_27w),ap(ap(c_2Epair_2E_2C(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0y)),c_2Ebool_2Ethe__value(A_27t))))) & (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V1x))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__ty_2Erealax_2Ereal(V1x)) = V0y)))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardZero__is__zero,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) => ((ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__ty_2Erealax_2Ereal(V0x)) = 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_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__ty_2Erealax_2Ereal(V0x)) = ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTiesToEven__is__zero,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))),ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) => ((ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__ty_2Erealax_2Ereal(V0x)) = 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_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__ty_2Erealax_2Ereal(V0x)) = ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardZero__is__minus__zero,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__o(fo__c_2Ebool_2ET)),inj__ty_2Erealax_2Ereal(V0x)) = ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardZero__is__plus__zero,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x))),ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__o(fo__c_2Ebool_2EF)),inj__ty_2Erealax_2Ereal(V0x)) = ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTiesToEven__is__minus__zero,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))),ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__o(fo__c_2Ebool_2ET)),inj__ty_2Erealax_2Ereal(V0x)) = ap(c_2Ebinary__ieee_2Efloat__minus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTiesToEven__is__plus__zero,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Eabs,inj__ty_2Erealax_2Ereal(V0x)))),ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__o(fo__c_2Ebool_2EF)),inj__ty_2Erealax_2Ereal(V0x)) = ap(c_2Ebinary__ieee_2Efloat__plus__zero(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))).
tff(conj_thm_2Ebinary__ieee_2Elargest__is__positive,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))).
tff(conj_thm_2Ebinary__ieee_2Ethreshold__is__positive,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTiesToEven__plus__infinity,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),inj__ty_2Erealax_2Ereal(V1x))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTiesToEven__minus__infinity,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Ereal_2Ereal__lte,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTiesToEven)),inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardZero__top,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),inj__ty_2Erealax_2Ereal(V1x))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardZero__bottom,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardPositive__plus__infinity,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),inj__ty_2Erealax_2Ereal(V1x))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive)),inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardPositive__bottom,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive)),inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardNegative__top,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),inj__ty_2Erealax_2Ereal(V1x))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)),inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Eround__roundTowardNegative__minus__infinity,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0y:$i] : (mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V1x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V1x)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) => (ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)),inj__ty_2Erealax_2Ereal(V1x)) = ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__roundTowardZero__top,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0b:tp__o] : ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),inj__ty_2Erealax_2Ereal(V2x))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__o(V0b)),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__roundTowardZero__bottom,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0b:tp__o] : ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2x)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardZero)),inj__o(V0b)),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__roundTowardPositive__plus__infinity,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0b:tp__o] : ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),inj__ty_2Erealax_2Ereal(V2x))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive)),inj__o(V0b)),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__roundTowardPositive__bottom,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0b:tp__o] : ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2x)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardPositive)),inj__o(V0b)),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__roundTowardNegative__top,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0b:tp__o] : ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))),inj__ty_2Erealax_2Ereal(V2x))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)),inj__o(V0b)),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__roundTowardNegative__minus__infinity,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0b:tp__o] : ( ! [V1y:$i] : (mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ! [V2x:tp__ty_2Erealax_2Ereal] : (p(ap(ap(c_2Erealax_2Ereal__lt,inj__ty_2Erealax_2Ereal(V2x)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(fo__c_2Ebinary__ieee_2EroundTowardNegative)),inj__o(V0b)),inj__ty_2Erealax_2Ereal(V2x)) = ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__minus__zero,lemma,(( ! [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(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),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),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(conj_thm_2Ebinary__ieee_2Efloat__minus__infinity,lemma,(( ! [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(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),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),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(conj_thm_2Ebinary__ieee_2Efloat__round__non__zero,lemma,(( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1toneg:tp__o] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : ( ! [V3s:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V4e:$i] : (mem(V4e,ty_2Efcp_2Ecart(bool,A_27a)) => ( ! [V5f:$i] : (mem(V5f,ty_2Efcp_2Ecart(bool,A_27b)) => (((ap(ap(c_2Ebinary__ieee_2Eround(A_27b,A_27a),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__ty_2Erealax_2Ereal(V2r)) = ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27b,A_27a),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(V3s))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27b,A_27a,A_27a),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)),V4e)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27b,A_27b,A_27a),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27b),ty_2Efcp_2Ecart(bool,A_27b)),V5f)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27b,A_27a)))))) & ((~~ (V4e = ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) | (~~ (V5f = ap(c_2Ewords_2En2w(A_27b),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27b,A_27a),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__o(V1toneg)),inj__ty_2Erealax_2Ereal(V2r)) = ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27b,A_27a),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(V3s))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27b,A_27a,A_27a),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a)),V4e)),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27b,A_27b,A_27a),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,A_27b),ty_2Efcp_2Ecart(bool,A_27b)),V5f)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27b,A_27a))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__plus__infinity,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1toneg:tp__o] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : ((ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__ty_2Erealax_2Ereal(V2r)) = ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__o(V1toneg)),inj__ty_2Erealax_2Ereal(V2r)) = ap(c_2Ebinary__ieee_2Efloat__plus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__minus__infinity,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1toneg:tp__o] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : ((ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__ty_2Erealax_2Ereal(V2r)) = ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__o(V1toneg)),inj__ty_2Erealax_2Ereal(V2r)) = ap(c_2Ebinary__ieee_2Efloat__minus__infinity(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__top,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1toneg:tp__o] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : ((ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__ty_2Erealax_2Ereal(V2r)) = ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__o(V1toneg)),inj__ty_2Erealax_2Ereal(V2r)) = ap(c_2Ebinary__ieee_2Efloat__top(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__round__bottom,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1toneg:tp__o] : ( ! [V2r:tp__ty_2Erealax_2Ereal] : ((ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__ty_2Erealax_2Ereal(V2r)) = ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) => (ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),inj__ty_2Ebinary__ieee_2Erounding(V0mode)),inj__o(V1toneg)),inj__ty_2Erealax_2Ereal(V2r)) = ap(c_2Ebinary__ieee_2Efloat__bottom(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))))))))).
tff(conj_thm_2Ebinary__ieee_2Efloat__to__real,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0s:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1e:$i] : (mem(V1e,ty_2Efcp_2Ecart(bool,A_27w)) => ( ! [V2f:$i] : (mem(V2f,ty_2Efcp_2Ecart(bool,A_27t)) => (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Efloat__to__real(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)),inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone(V0s))),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)),V1e)),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)),V2f)),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),f3147(V0s)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27w)),V1e),ap(c_2Ewords_2En2w(A_27w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(c_2Erealax_2Ereal__mul,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(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,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),V2f))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Ewords_2Edimword(A_27t),c_2Ebool_2Ethe__value(A_27t)))))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Ewords_2Ew2n(A_27w),V1e)))),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,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),V2f))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Ewords_2Edimword(A_27t),c_2Ebool_2Ethe__value(A_27t))))))))))))))))))).
tff(conj_thm_2Ebinary__ieee_2Elargest,lemma,(( ! [A_27t:del]: ( ! [A_27w:del]: (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2EUINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))),ap(ap(c_2Ereal_2Ereal__sub,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_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(c_2Ewords_2Edimword(A_27t),c_2Ebool_2Ethe__value(A_27t))))))),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,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))))))))))).
tff(conj_thm_2Ebinary__ieee_2Ethreshold,conjecture,(( ! [A_27t:del]: ( ! [A_27w:del]: (surj__ty_2Erealax_2Ereal(ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = surj__ty_2Erealax_2Ereal(ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2EUINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))))),ap(ap(c_2Ereal_2Ereal__sub,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_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),ap(c_2Ewords_2Edimword(A_27t),c_2Ebool_2Ethe__value(A_27t)))))))),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,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))))))))))).
