include('Axioms/transc^2.ax').
thf(tp_ty_2Ebinary__ieee_2Eflags,type,( ty_2Ebinary__ieee_2Eflags:del )).
thf(tp_ty_2Ebinary__ieee_2Efloat,type,( ty_2Ebinary__ieee_2Efloat: del > del >del )).
thf(tp_ty_2Ebinary__ieee_2Efloat__compare,type,( ty_2Ebinary__ieee_2Efloat__compare:del )).
thf(tp_ty_2Ebinary__ieee_2Efloat__value,type,( ty_2Ebinary__ieee_2Efloat__value:del )).
thf(tp_ty_2Ebinary__ieee_2Efp__op,type,( ty_2Ebinary__ieee_2Efp__op: del > del >del )).
thf(tp_ty_2Ebinary__ieee_2Erounding,type,( ty_2Ebinary__ieee_2Erounding:del )).
thf(stp_ty_2Ebinary__ieee_2Efloat__compare,type,(tp__ty_2Ebinary__ieee_2Efloat__compare : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Efloat__compare,type,(inj__ty_2Ebinary__ieee_2Efloat__compare : (tp__ty_2Ebinary__ieee_2Efloat__compare > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Efloat__compare,type,(surj__ty_2Ebinary__ieee_2Efloat__compare : ($i > tp__ty_2Ebinary__ieee_2Efloat__compare))).
thf(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))).
thf(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))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Efloat__compare,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Efloat__compare) => (X = (inj__ty_2Ebinary__ieee_2Efloat__compare @ (surj__ty_2Ebinary__ieee_2Efloat__compare @ X)))))).
thf(tp_c_2Ebinary__ieee_2EEQ,type,(c_2Ebinary__ieee_2EEQ:$i)).
thf(mem_c_2Ebinary__ieee_2EEQ,axiom,(mem@c_2Ebinary__ieee_2EEQ@ty_2Ebinary__ieee_2Efloat__compare)).
thf(stp_fo_c_2Ebinary__ieee_2EEQ,type,(fo__c_2Ebinary__ieee_2EEQ:tp__ty_2Ebinary__ieee_2Efloat__compare)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EEQ,axiom,((inj__ty_2Ebinary__ieee_2Efloat__compare @ fo__c_2Ebinary__ieee_2EEQ) = c_2Ebinary__ieee_2EEQ)).
thf(stp_ty_2Ebinary__ieee_2Erounding,type,(tp__ty_2Ebinary__ieee_2Erounding : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Erounding,type,(inj__ty_2Ebinary__ieee_2Erounding : (tp__ty_2Ebinary__ieee_2Erounding > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Erounding,type,(surj__ty_2Ebinary__ieee_2Erounding : ($i > tp__ty_2Ebinary__ieee_2Erounding))).
thf(stp_inj_surj_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Erounding] : ((surj__ty_2Ebinary__ieee_2Erounding @ (inj__ty_2Ebinary__ieee_2Erounding @ X)) = X))).
thf(stp_inj_mem_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Erounding] : (mem @ (inj__ty_2Ebinary__ieee_2Erounding @ X) @ ty_2Ebinary__ieee_2Erounding))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Erounding) => (X = (inj__ty_2Ebinary__ieee_2Erounding @ (surj__ty_2Ebinary__ieee_2Erounding @ X)))))).
thf(tp_c_2Ebinary__ieee_2EFP__Add,type,(c_2Ebinary__ieee_2EFP__Add:(del>(del>$i)))).
thf(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)))))))).
thf(tp_c_2Ebinary__ieee_2EFP__Div,type,(c_2Ebinary__ieee_2EFP__Div:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2EFP__Div,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2EFP__Div@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efp__op@A_27t@A_27w)))))))).
thf(tp_c_2Ebinary__ieee_2EFP__Mul,type,(c_2Ebinary__ieee_2EFP__Mul:(del>(del>$i)))).
thf(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)))))))).
thf(tp_c_2Ebinary__ieee_2EFP__MulAdd,type,(c_2Ebinary__ieee_2EFP__MulAdd:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2EFP__MulAdd,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2EFP__MulAdd@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efp__op@A_27t@A_27w))))))))).
thf(tp_c_2Ebinary__ieee_2EFP__MulSub,type,(c_2Ebinary__ieee_2EFP__MulSub:(del>(del>$i)))).
thf(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))))))))).
thf(tp_c_2Ebinary__ieee_2EFP__Sqrt,type,(c_2Ebinary__ieee_2EFP__Sqrt:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2EFP__Sqrt,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2EFP__Sqrt@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efp__op@A_27t@A_27w))))))).
thf(tp_c_2Ebinary__ieee_2EFP__Sub,type,(c_2Ebinary__ieee_2EFP__Sub:(del>(del>$i)))).
thf(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)))))))).
thf(stp_ty_2Ebinary__ieee_2Efloat__value,type,(tp__ty_2Ebinary__ieee_2Efloat__value : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Efloat__value,type,(inj__ty_2Ebinary__ieee_2Efloat__value : (tp__ty_2Ebinary__ieee_2Efloat__value > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Efloat__value,type,(surj__ty_2Ebinary__ieee_2Efloat__value : ($i > tp__ty_2Ebinary__ieee_2Efloat__value))).
thf(stp_inj_surj_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Efloat__value] : ((surj__ty_2Ebinary__ieee_2Efloat__value @ (inj__ty_2Ebinary__ieee_2Efloat__value @ X)) = X))).
thf(stp_inj_mem_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Efloat__value] : (mem @ (inj__ty_2Ebinary__ieee_2Efloat__value @ X) @ ty_2Ebinary__ieee_2Efloat__value))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Efloat__value,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Efloat__value) => (X = (inj__ty_2Ebinary__ieee_2Efloat__value @ (surj__ty_2Ebinary__ieee_2Efloat__value @ X)))))).
thf(tp_c_2Ebinary__ieee_2EFloat,type,(c_2Ebinary__ieee_2EFloat:$i)).
thf(mem_c_2Ebinary__ieee_2EFloat,axiom,(mem@c_2Ebinary__ieee_2EFloat@(arr@ty_2Erealax_2Ereal@ty_2Ebinary__ieee_2Efloat__value))).
thf(stp_fo_c_2Ebinary__ieee_2EFloat,type,(fo__c_2Ebinary__ieee_2EFloat:(tp__ty_2Erealax_2Ereal > tp__ty_2Ebinary__ieee_2Efloat__value))).
thf(stp_eq_fo_c_2Ebinary__ieee_2EFloat,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Ebinary__ieee_2Efloat__value @ (fo__c_2Ebinary__ieee_2EFloat @ X0)) = (ap @ c_2Ebinary__ieee_2EFloat @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Ebinary__ieee_2EGT,type,(c_2Ebinary__ieee_2EGT:$i)).
thf(mem_c_2Ebinary__ieee_2EGT,axiom,(mem@c_2Ebinary__ieee_2EGT@ty_2Ebinary__ieee_2Efloat__compare)).
thf(stp_fo_c_2Ebinary__ieee_2EGT,type,(fo__c_2Ebinary__ieee_2EGT:tp__ty_2Ebinary__ieee_2Efloat__compare)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EGT,axiom,((inj__ty_2Ebinary__ieee_2Efloat__compare @ fo__c_2Ebinary__ieee_2EGT) = c_2Ebinary__ieee_2EGT)).
thf(tp_c_2Ebinary__ieee_2EInfinity,type,(c_2Ebinary__ieee_2EInfinity:$i)).
thf(mem_c_2Ebinary__ieee_2EInfinity,axiom,(mem@c_2Ebinary__ieee_2EInfinity@ty_2Ebinary__ieee_2Efloat__value)).
thf(stp_fo_c_2Ebinary__ieee_2EInfinity,type,(fo__c_2Ebinary__ieee_2EInfinity:tp__ty_2Ebinary__ieee_2Efloat__value)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EInfinity,axiom,((inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2EInfinity) = c_2Ebinary__ieee_2EInfinity)).
thf(tp_c_2Ebinary__ieee_2ELT,type,(c_2Ebinary__ieee_2ELT:$i)).
thf(mem_c_2Ebinary__ieee_2ELT,axiom,(mem@c_2Ebinary__ieee_2ELT@ty_2Ebinary__ieee_2Efloat__compare)).
thf(stp_fo_c_2Ebinary__ieee_2ELT,type,(fo__c_2Ebinary__ieee_2ELT:tp__ty_2Ebinary__ieee_2Efloat__compare)).
thf(stp_eq_fo_c_2Ebinary__ieee_2ELT,axiom,((inj__ty_2Ebinary__ieee_2Efloat__compare @ fo__c_2Ebinary__ieee_2ELT) = c_2Ebinary__ieee_2ELT)).
thf(tp_c_2Ebinary__ieee_2ENaN,type,(c_2Ebinary__ieee_2ENaN:$i)).
thf(mem_c_2Ebinary__ieee_2ENaN,axiom,(mem@c_2Ebinary__ieee_2ENaN@ty_2Ebinary__ieee_2Efloat__value)).
thf(stp_fo_c_2Ebinary__ieee_2ENaN,type,(fo__c_2Ebinary__ieee_2ENaN:tp__ty_2Ebinary__ieee_2Efloat__value)).
thf(stp_eq_fo_c_2Ebinary__ieee_2ENaN,axiom,((inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2ENaN) = c_2Ebinary__ieee_2ENaN)).
thf(tp_c_2Ebinary__ieee_2EULP,type,(c_2Ebinary__ieee_2EULP:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2EULP,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2EULP@A_27t@A_27w)@(arr@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Ebool_2Eitself@A_27t))@ty_2Erealax_2Ereal))))).
thf(tp_c_2Ebinary__ieee_2EUN,type,(c_2Ebinary__ieee_2EUN:$i)).
thf(mem_c_2Ebinary__ieee_2EUN,axiom,(mem@c_2Ebinary__ieee_2EUN@ty_2Ebinary__ieee_2Efloat__compare)).
thf(stp_fo_c_2Ebinary__ieee_2EUN,type,(fo__c_2Ebinary__ieee_2EUN:tp__ty_2Ebinary__ieee_2Efloat__compare)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EUN,axiom,((inj__ty_2Ebinary__ieee_2Efloat__compare @ fo__c_2Ebinary__ieee_2EUN) = c_2Ebinary__ieee_2EUN)).
thf(stp_ty_2Ebinary__ieee_2Eflags,type,(tp__ty_2Ebinary__ieee_2Eflags : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Eflags,type,(inj__ty_2Ebinary__ieee_2Eflags : (tp__ty_2Ebinary__ieee_2Eflags > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Eflags,type,(surj__ty_2Ebinary__ieee_2Eflags : ($i > tp__ty_2Ebinary__ieee_2Eflags))).
thf(stp_inj_surj_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Eflags] : ((surj__ty_2Ebinary__ieee_2Eflags @ (inj__ty_2Ebinary__ieee_2Eflags @ X)) = X))).
thf(stp_inj_mem_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Eflags] : (mem @ (inj__ty_2Ebinary__ieee_2Eflags @ X) @ ty_2Ebinary__ieee_2Eflags))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Eflags) => (X = (inj__ty_2Ebinary__ieee_2Eflags @ (surj__ty_2Ebinary__ieee_2Eflags @ X)))))).
thf(tp_c_2Ebinary__ieee_2Echeck__for__signalling,type,(c_2Ebinary__ieee_2Echeck__for__signalling:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Echeck__for__signalling,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ebinary__ieee_2Echeck__for__signalling@A_27a@A_27b)@(arr@(ty_2Elist_2Elist@(ty_2Ebinary__ieee_2Efloat@A_27a@A_27b))@ty_2Ebinary__ieee_2Eflags))))).
thf(tp_c_2Ebinary__ieee_2Eclear__flags,type,(c_2Ebinary__ieee_2Eclear__flags:$i)).
thf(mem_c_2Ebinary__ieee_2Eclear__flags,axiom,(mem@c_2Ebinary__ieee_2Eclear__flags@ty_2Ebinary__ieee_2Eflags)).
thf(stp_fo_c_2Ebinary__ieee_2Eclear__flags,type,(fo__c_2Ebinary__ieee_2Eclear__flags:tp__ty_2Ebinary__ieee_2Eflags)).
thf(stp_eq_fo_c_2Ebinary__ieee_2Eclear__flags,axiom,((inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Eclear__flags) = c_2Ebinary__ieee_2Eclear__flags)).
thf(tp_c_2Ebinary__ieee_2Eclosest,type,(c_2Ebinary__ieee_2Eclosest:(del>(del>$i)))).
thf(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))))))).
thf(tp_c_2Ebinary__ieee_2Eclosest__such,type,(c_2Ebinary__ieee_2Eclosest__such:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Eclosest__such,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ebinary__ieee_2Eclosest__such@A_27a@A_27b)@(arr@(arr@(ty_2Ebinary__ieee_2Efloat@A_27a@A_27b)@bool)@(arr@(arr@(ty_2Ebinary__ieee_2Efloat@A_27a@A_27b)@bool)@(arr@ty_2Erealax_2Ereal@(ty_2Ebinary__ieee_2Efloat@A_27a@A_27b)))))))).
thf(tp_c_2Ebinary__ieee_2Edividezero__flags,type,(c_2Ebinary__ieee_2Edividezero__flags:$i)).
thf(mem_c_2Ebinary__ieee_2Edividezero__flags,axiom,(mem@c_2Ebinary__ieee_2Edividezero__flags@ty_2Ebinary__ieee_2Eflags)).
thf(stp_fo_c_2Ebinary__ieee_2Edividezero__flags,type,(fo__c_2Ebinary__ieee_2Edividezero__flags:tp__ty_2Ebinary__ieee_2Eflags)).
thf(stp_eq_fo_c_2Ebinary__ieee_2Edividezero__flags,axiom,((inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Edividezero__flags) = c_2Ebinary__ieee_2Edividezero__flags)).
thf(tp_c_2Ebinary__ieee_2Eexponent__boundary,type,(c_2Ebinary__ieee_2Eexponent__boundary:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Eexponent__boundary,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Eexponent__boundary@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool)))))).
thf(tp_c_2Ebinary__ieee_2Eflags__CASE,type,(c_2Ebinary__ieee_2Eflags__CASE:(del>$i))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Eflags__DivideByZero,type,(c_2Ebinary__ieee_2Eflags__DivideByZero:$i)).
thf(mem_c_2Ebinary__ieee_2Eflags__DivideByZero,axiom,(mem@c_2Ebinary__ieee_2Eflags__DivideByZero@(arr@ty_2Ebinary__ieee_2Eflags@bool))).
thf(tp_c_2Ebinary__ieee_2Eflags__DivideByZero__fupd,type,(c_2Ebinary__ieee_2Eflags__DivideByZero__fupd:$i)).
thf(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)))).
thf(tp_c_2Ebinary__ieee_2Eflags__InvalidOp,type,(c_2Ebinary__ieee_2Eflags__InvalidOp:$i)).
thf(mem_c_2Ebinary__ieee_2Eflags__InvalidOp,axiom,(mem@c_2Ebinary__ieee_2Eflags__InvalidOp@(arr@ty_2Ebinary__ieee_2Eflags@bool))).
thf(tp_c_2Ebinary__ieee_2Eflags__InvalidOp__fupd,type,(c_2Ebinary__ieee_2Eflags__InvalidOp__fupd:$i)).
thf(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)))).
thf(tp_c_2Ebinary__ieee_2Eflags__Overflow,type,(c_2Ebinary__ieee_2Eflags__Overflow:$i)).
thf(mem_c_2Ebinary__ieee_2Eflags__Overflow,axiom,(mem@c_2Ebinary__ieee_2Eflags__Overflow@(arr@ty_2Ebinary__ieee_2Eflags@bool))).
thf(tp_c_2Ebinary__ieee_2Eflags__Overflow__fupd,type,(c_2Ebinary__ieee_2Eflags__Overflow__fupd:$i)).
thf(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)))).
thf(tp_c_2Ebinary__ieee_2Eflags__Precision,type,(c_2Ebinary__ieee_2Eflags__Precision:$i)).
thf(mem_c_2Ebinary__ieee_2Eflags__Precision,axiom,(mem@c_2Ebinary__ieee_2Eflags__Precision@(arr@ty_2Ebinary__ieee_2Eflags@bool))).
thf(tp_c_2Ebinary__ieee_2Eflags__Precision__fupd,type,(c_2Ebinary__ieee_2Eflags__Precision__fupd:$i)).
thf(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)))).
thf(tp_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,type,(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding:$i)).
thf(mem_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,axiom,(mem@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding@(arr@ty_2Ebinary__ieee_2Eflags@bool))).
thf(tp_c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,type,(c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd:$i)).
thf(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)))).
thf(tp_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,type,(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding:$i)).
thf(mem_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,axiom,(mem@c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding@(arr@ty_2Ebinary__ieee_2Eflags@bool))).
thf(tp_c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,type,(c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd:$i)).
thf(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)))).
thf(tp_c_2Ebinary__ieee_2Eflags__size,type,(c_2Ebinary__ieee_2Eflags__size:$i)).
thf(mem_c_2Ebinary__ieee_2Eflags__size,axiom,(mem@c_2Ebinary__ieee_2Eflags__size@(arr@ty_2Ebinary__ieee_2Eflags@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ebinary__ieee_2Eflags__size,type,(fo__c_2Ebinary__ieee_2Eflags__size:(tp__ty_2Ebinary__ieee_2Eflags > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Ebinary__ieee_2Eflags__size,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Eflags] : ((inj__ty_2Enum_2Enum @ (fo__c_2Ebinary__ieee_2Eflags__size @ X0)) = (ap @ c_2Ebinary__ieee_2Eflags__size @ (inj__ty_2Ebinary__ieee_2Eflags @ X0))))).
thf(tp_c_2Ebinary__ieee_2Efloat__CASE,type,(c_2Ebinary__ieee_2Efloat__CASE:(del>(del>(del>$i))))).
thf(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))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Exponent,type,(c_2Ebinary__ieee_2Efloat__Exponent:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__Exponent,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Efcp_2Ecart@bool@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Exponent__fupd,type,(c_2Ebinary__ieee_2Efloat__Exponent__fupd:(del>(del>(del>$i))))).
thf(mem_c_2Ebinary__ieee_2Efloat__Exponent__fupd,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : ( ! [A_27x:del] : (mem@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@(arr@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27x)))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Sign,type,(c_2Ebinary__ieee_2Efloat__Sign:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__Sign,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Sign__fupd,type,(c_2Ebinary__ieee_2Efloat__Sign__fupd:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__Sign__fupd,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@(arr@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Significand,type,(c_2Ebinary__ieee_2Efloat__Significand:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__Significand,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__Significand__fupd,type,(c_2Ebinary__ieee_2Efloat__Significand__fupd:(del>(del>(del>$i))))).
thf(mem_c_2Ebinary__ieee_2Efloat__Significand__fupd,axiom,( ! [A_27t:del] : ( ! [A_27u:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@(arr@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27u@A_27w)))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__abs,type,(c_2Ebinary__ieee_2Efloat__abs:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__abs,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__abs@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__add,type,(c_2Ebinary__ieee_2Efloat__add:(del>(del>$i)))).
thf(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))))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__bottom,type,(c_2Ebinary__ieee_2Efloat__bottom:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__bottom,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__bottom@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__compare,type,(c_2Ebinary__ieee_2Efloat__compare:(del>(del>$i)))).
thf(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)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__compare2num,type,(c_2Ebinary__ieee_2Efloat__compare2num:$i)).
thf(mem_c_2Ebinary__ieee_2Efloat__compare2num,axiom,(mem@c_2Ebinary__ieee_2Efloat__compare2num@(arr@ty_2Ebinary__ieee_2Efloat__compare@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ebinary__ieee_2Efloat__compare2num,type,(fo__c_2Ebinary__ieee_2Efloat__compare2num:(tp__ty_2Ebinary__ieee_2Efloat__compare > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Ebinary__ieee_2Efloat__compare2num,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Efloat__compare] : ((inj__ty_2Enum_2Enum @ (fo__c_2Ebinary__ieee_2Efloat__compare2num @ X0)) = (ap @ c_2Ebinary__ieee_2Efloat__compare2num @ (inj__ty_2Ebinary__ieee_2Efloat__compare @ X0))))).
thf(tp_c_2Ebinary__ieee_2Efloat__compare__CASE,type,(c_2Ebinary__ieee_2Efloat__compare__CASE:(del>$i))).
thf(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)))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__compare__size,type,(c_2Ebinary__ieee_2Efloat__compare__size:$i)).
thf(mem_c_2Ebinary__ieee_2Efloat__compare__size,axiom,(mem@c_2Ebinary__ieee_2Efloat__compare__size@(arr@ty_2Ebinary__ieee_2Efloat__compare@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ebinary__ieee_2Efloat__compare__size,type,(fo__c_2Ebinary__ieee_2Efloat__compare__size:(tp__ty_2Ebinary__ieee_2Efloat__compare > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Ebinary__ieee_2Efloat__compare__size,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Efloat__compare] : ((inj__ty_2Enum_2Enum @ (fo__c_2Ebinary__ieee_2Efloat__compare__size @ X0)) = (ap @ c_2Ebinary__ieee_2Efloat__compare__size @ (inj__ty_2Ebinary__ieee_2Efloat__compare @ X0))))).
thf(tp_c_2Ebinary__ieee_2Efloat__div,type,(c_2Ebinary__ieee_2Efloat__div:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__div,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__div@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__equal,type,(c_2Ebinary__ieee_2Efloat__equal:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__equal,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__equal@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__greater__equal,type,(c_2Ebinary__ieee_2Efloat__greater__equal:(del>(del>$i)))).
thf(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)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__greater__than,type,(c_2Ebinary__ieee_2Efloat__greater__than:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__greater__than,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__greater__than@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__finite,type,(c_2Ebinary__ieee_2Efloat__is__finite:(del>(del>$i)))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__infinite,type,(c_2Ebinary__ieee_2Efloat__is__infinite:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__is__infinite,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__is__infinite@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__integral,type,(c_2Ebinary__ieee_2Efloat__is__integral:(del>(del>$i)))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__nan,type,(c_2Ebinary__ieee_2Efloat__is__nan:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__is__nan,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__is__nan@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__normal,type,(c_2Ebinary__ieee_2Efloat__is__normal:(del>(del>$i)))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__signalling,type,(c_2Ebinary__ieee_2Efloat__is__signalling:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__is__signalling,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__is__signalling@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__subnormal,type,(c_2Ebinary__ieee_2Efloat__is__subnormal:(del>(del>$i)))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__zero,type,(c_2Ebinary__ieee_2Efloat__is__zero:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__is__zero,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__is__zero@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool))))).
thf(tp_c_2Ebinary__ieee_2Efloat__less__equal,type,(c_2Ebinary__ieee_2Efloat__less__equal:(del>(del>$i)))).
thf(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)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__less__than,type,(c_2Ebinary__ieee_2Efloat__less__than:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__less__than,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__less__than@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__minus__infinity,type,(c_2Ebinary__ieee_2Efloat__minus__infinity:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__minus__infinity,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__minus__infinity@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__minus__min,type,(c_2Ebinary__ieee_2Efloat__minus__min:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__minus__min,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__minus__min@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__minus__zero,type,(c_2Ebinary__ieee_2Efloat__minus__zero:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__minus__zero,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__minus__zero@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__mul,type,(c_2Ebinary__ieee_2Efloat__mul:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__mul,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__mul@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__mul__add,type,(c_2Ebinary__ieee_2Efloat__mul__add:(del>(del>$i)))).
thf(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)))))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__mul__sub,type,(c_2Ebinary__ieee_2Efloat__mul__sub:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__mul__sub,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__mul__sub@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__negate,type,(c_2Ebinary__ieee_2Efloat__negate:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__negate,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__negate@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__infinity,type,(c_2Ebinary__ieee_2Efloat__plus__infinity:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__plus__infinity,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__min,type,(c_2Ebinary__ieee_2Efloat__plus__min:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__plus__min,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__plus__min@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__zero,type,(c_2Ebinary__ieee_2Efloat__plus__zero:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__plus__zero,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__plus__zero@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__round,type,(c_2Ebinary__ieee_2Efloat__round:(del>(del>$i)))).
thf(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)))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__round__to__integral,type,(c_2Ebinary__ieee_2Efloat__round__to__integral:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__round__to__integral,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__round__to__integral@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__round__with__flags,type,(c_2Ebinary__ieee_2Efloat__round__with__flags:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__round__with__flags,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__round__with__flags@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@bool@(arr@ty_2Erealax_2Ereal@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__size,type,(c_2Ebinary__ieee_2Efloat__size:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__size,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__size@A_27t@A_27w)@(arr@(arr@A_27t@ty_2Enum_2Enum)@(arr@(arr@A_27w@ty_2Enum_2Enum)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@ty_2Enum_2Enum))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__some__qnan,type,(c_2Ebinary__ieee_2Efloat__some__qnan:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__some__qnan,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__some__qnan@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efp__op@A_27t@A_27w)@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__sqrt,type,(c_2Ebinary__ieee_2Efloat__sqrt:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__sqrt,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__sqrt@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__sub,type,(c_2Ebinary__ieee_2Efloat__sub:(del>(del>$i)))).
thf(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))))))))).
thf(stp_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,type,(tp__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint : $tType)).
thf(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 > $i))).
thf(stp_surj_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,type,(surj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint : ($i > tp__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint))).
thf(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))).
thf(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)))).
thf(stp_iso_mem_c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Eoption_2Eoption@ty_2Einteger_2Eint)) => (X = (inj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint @ (surj__c_ty_2Eoption_2Eoption_ty_2Einteger_2Eint @ X)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__to__int,type,(c_2Ebinary__ieee_2Efloat__to__int:(del>(del>$i)))).
thf(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))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__to__real,type,(c_2Ebinary__ieee_2Efloat__to__real:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__to__real,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__to__real@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@ty_2Erealax_2Ereal))))).
thf(tp_c_2Ebinary__ieee_2Efloat__top,type,(c_2Ebinary__ieee_2Efloat__top:(del>(del>$i)))).
thf(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)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__value,type,(c_2Ebinary__ieee_2Efloat__value:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__value,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@ty_2Ebinary__ieee_2Efloat__value))))).
thf(tp_c_2Ebinary__ieee_2Efloat__value__CASE,type,(c_2Ebinary__ieee_2Efloat__value__CASE:(del>$i))).
thf(mem_c_2Ebinary__ieee_2Efloat__value__CASE,axiom,( ! [A_27a:del] : (mem@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(arr@ty_2Ebinary__ieee_2Efloat__value@(arr@(arr@ty_2Erealax_2Ereal@A_27a)@(arr@A_27a@(arr@A_27a@A_27a))))))).
thf(tp_c_2Ebinary__ieee_2Efloat__value__size,type,(c_2Ebinary__ieee_2Efloat__value__size:$i)).
thf(mem_c_2Ebinary__ieee_2Efloat__value__size,axiom,(mem@c_2Ebinary__ieee_2Efloat__value__size@(arr@ty_2Ebinary__ieee_2Efloat__value@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ebinary__ieee_2Efloat__value__size,type,(fo__c_2Ebinary__ieee_2Efloat__value__size:(tp__ty_2Ebinary__ieee_2Efloat__value > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Ebinary__ieee_2Efloat__value__size,axiom,( ! [X0:tp__ty_2Ebinary__ieee_2Efloat__value] : ((inj__ty_2Enum_2Enum @ (fo__c_2Ebinary__ieee_2Efloat__value__size @ X0)) = (ap @ c_2Ebinary__ieee_2Efloat__value__size @ (inj__ty_2Ebinary__ieee_2Efloat__value @ X0))))).
thf(tp_c_2Ebinary__ieee_2Efp__op__CASE,type,(c_2Ebinary__ieee_2Efp__op__CASE:(del>(del>(del>$i))))).
thf(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))))))))))))).
thf(tp_c_2Ebinary__ieee_2Efp__op__size,type,(c_2Ebinary__ieee_2Efp__op__size:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efp__op__size,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efp__op__size@A_27t@A_27w)@(arr@(arr@A_27t@ty_2Enum_2Enum)@(arr@(arr@A_27w@ty_2Enum_2Enum)@(arr@(ty_2Ebinary__ieee_2Efp__op@A_27t@A_27w)@ty_2Enum_2Enum))))))).
thf(tp_c_2Ebinary__ieee_2Eintegral__round,type,(c_2Ebinary__ieee_2Eintegral__round:(del>(del>$i)))).
thf(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))))))).
thf(tp_c_2Ebinary__ieee_2Einvalidop__flags,type,(c_2Ebinary__ieee_2Einvalidop__flags:$i)).
thf(mem_c_2Ebinary__ieee_2Einvalidop__flags,axiom,(mem@c_2Ebinary__ieee_2Einvalidop__flags@ty_2Ebinary__ieee_2Eflags)).
thf(stp_fo_c_2Ebinary__ieee_2Einvalidop__flags,type,(fo__c_2Ebinary__ieee_2Einvalidop__flags:tp__ty_2Ebinary__ieee_2Eflags)).
thf(stp_eq_fo_c_2Ebinary__ieee_2Einvalidop__flags,axiom,((inj__ty_2Ebinary__ieee_2Eflags @ fo__c_2Ebinary__ieee_2Einvalidop__flags) = c_2Ebinary__ieee_2Einvalidop__flags)).
thf(tp_c_2Ebinary__ieee_2Eis__closest,type,(c_2Ebinary__ieee_2Eis__closest:(del>(del>$i)))).
thf(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))))))).
thf(tp_c_2Ebinary__ieee_2Eis__integral,type,(c_2Ebinary__ieee_2Eis__integral:$i)).
thf(mem_c_2Ebinary__ieee_2Eis__integral,axiom,(mem@c_2Ebinary__ieee_2Eis__integral@(arr@ty_2Erealax_2Ereal@bool))).
thf(tp_c_2Ebinary__ieee_2Elargest,type,(c_2Ebinary__ieee_2Elargest:(del>(del>$i)))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Enum2float__compare,type,(c_2Ebinary__ieee_2Enum2float__compare:$i)).
thf(mem_c_2Ebinary__ieee_2Enum2float__compare,axiom,(mem@c_2Ebinary__ieee_2Enum2float__compare@(arr@ty_2Enum_2Enum@ty_2Ebinary__ieee_2Efloat__compare))).
thf(stp_fo_c_2Ebinary__ieee_2Enum2float__compare,type,(fo__c_2Ebinary__ieee_2Enum2float__compare:(tp__ty_2Enum_2Enum > tp__ty_2Ebinary__ieee_2Efloat__compare))).
thf(stp_eq_fo_c_2Ebinary__ieee_2Enum2float__compare,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Ebinary__ieee_2Efloat__compare @ (fo__c_2Ebinary__ieee_2Enum2float__compare @ X0)) = (ap @ c_2Ebinary__ieee_2Enum2float__compare @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ebinary__ieee_2Enum2rounding,type,(c_2Ebinary__ieee_2Enum2rounding:$i)).
thf(mem_c_2Ebinary__ieee_2Enum2rounding,axiom,(mem@c_2Ebinary__ieee_2Enum2rounding@(arr@ty_2Enum_2Enum@ty_2Ebinary__ieee_2Erounding))).
thf(stp_fo_c_2Ebinary__ieee_2Enum2rounding,type,(fo__c_2Ebinary__ieee_2Enum2rounding:(tp__ty_2Enum_2Enum > tp__ty_2Ebinary__ieee_2Erounding))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Ereal__to__float,type,(c_2Ebinary__ieee_2Ereal__to__float:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Ereal__to__float,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ebinary__ieee_2Ereal__to__float@A_27a@A_27b)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@ty_2Erealax_2Ereal@(ty_2Ebinary__ieee_2Efloat@A_27a@A_27b))))))).
thf(tp_c_2Ebinary__ieee_2Ereal__to__float__with__flags,type,(c_2Ebinary__ieee_2Ereal__to__float__with__flags:(del>(del>$i)))).
thf(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)))))))).
thf(tp_c_2Ebinary__ieee_2Erecordtype_2Eflags,type,(c_2Ebinary__ieee_2Erecordtype_2Eflags:$i)).
thf(mem_c_2Ebinary__ieee_2Erecordtype_2Eflags,axiom,(mem@c_2Ebinary__ieee_2Erecordtype_2Eflags@(arr@bool@(arr@bool@(arr@bool@(arr@bool@(arr@bool@(arr@bool@ty_2Ebinary__ieee_2Eflags)))))))).
thf(tp_c_2Ebinary__ieee_2Erecordtype_2Efloat,type,(c_2Ebinary__ieee_2Erecordtype_2Efloat:(del>(del>$i)))).
thf(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)))))))).
thf(tp_c_2Ebinary__ieee_2Eround,type,(c_2Ebinary__ieee_2Eround:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Eround,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Eround@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@ty_2Erealax_2Ereal@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))).
thf(tp_c_2Ebinary__ieee_2EroundTiesToEven,type,(c_2Ebinary__ieee_2EroundTiesToEven:$i)).
thf(mem_c_2Ebinary__ieee_2EroundTiesToEven,axiom,(mem@c_2Ebinary__ieee_2EroundTiesToEven@ty_2Ebinary__ieee_2Erounding)).
thf(stp_fo_c_2Ebinary__ieee_2EroundTiesToEven,type,(fo__c_2Ebinary__ieee_2EroundTiesToEven:tp__ty_2Ebinary__ieee_2Erounding)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EroundTiesToEven,axiom,((inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTiesToEven) = c_2Ebinary__ieee_2EroundTiesToEven)).
thf(tp_c_2Ebinary__ieee_2EroundTowardNegative,type,(c_2Ebinary__ieee_2EroundTowardNegative:$i)).
thf(mem_c_2Ebinary__ieee_2EroundTowardNegative,axiom,(mem@c_2Ebinary__ieee_2EroundTowardNegative@ty_2Ebinary__ieee_2Erounding)).
thf(stp_fo_c_2Ebinary__ieee_2EroundTowardNegative,type,(fo__c_2Ebinary__ieee_2EroundTowardNegative:tp__ty_2Ebinary__ieee_2Erounding)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EroundTowardNegative,axiom,((inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTowardNegative) = c_2Ebinary__ieee_2EroundTowardNegative)).
thf(tp_c_2Ebinary__ieee_2EroundTowardPositive,type,(c_2Ebinary__ieee_2EroundTowardPositive:$i)).
thf(mem_c_2Ebinary__ieee_2EroundTowardPositive,axiom,(mem@c_2Ebinary__ieee_2EroundTowardPositive@ty_2Ebinary__ieee_2Erounding)).
thf(stp_fo_c_2Ebinary__ieee_2EroundTowardPositive,type,(fo__c_2Ebinary__ieee_2EroundTowardPositive:tp__ty_2Ebinary__ieee_2Erounding)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EroundTowardPositive,axiom,((inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTowardPositive) = c_2Ebinary__ieee_2EroundTowardPositive)).
thf(tp_c_2Ebinary__ieee_2EroundTowardZero,type,(c_2Ebinary__ieee_2EroundTowardZero:$i)).
thf(mem_c_2Ebinary__ieee_2EroundTowardZero,axiom,(mem@c_2Ebinary__ieee_2EroundTowardZero@ty_2Ebinary__ieee_2Erounding)).
thf(stp_fo_c_2Ebinary__ieee_2EroundTowardZero,type,(fo__c_2Ebinary__ieee_2EroundTowardZero:tp__ty_2Ebinary__ieee_2Erounding)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EroundTowardZero,axiom,((inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTowardZero) = c_2Ebinary__ieee_2EroundTowardZero)).
thf(tp_c_2Ebinary__ieee_2Erounding2num,type,(c_2Ebinary__ieee_2Erounding2num:$i)).
thf(mem_c_2Ebinary__ieee_2Erounding2num,axiom,(mem@c_2Ebinary__ieee_2Erounding2num@(arr@ty_2Ebinary__ieee_2Erounding@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ebinary__ieee_2Erounding2num,type,(fo__c_2Ebinary__ieee_2Erounding2num:(tp__ty_2Ebinary__ieee_2Erounding > tp__ty_2Enum_2Enum))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Erounding__CASE,type,(c_2Ebinary__ieee_2Erounding__CASE:(del>$i))).
thf(mem_c_2Ebinary__ieee_2Erounding__CASE,axiom,( ! [A_27a:del] : (mem@(c_2Ebinary__ieee_2Erounding__CASE@A_27a)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@A_27a@(arr@A_27a@(arr@A_27a@(arr@A_27a@A_27a)))))))).
thf(tp_c_2Ebinary__ieee_2Erounding__size,type,(c_2Ebinary__ieee_2Erounding__size:$i)).
thf(mem_c_2Ebinary__ieee_2Erounding__size,axiom,(mem@c_2Ebinary__ieee_2Erounding__size@(arr@ty_2Ebinary__ieee_2Erounding@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ebinary__ieee_2Erounding__size,type,(fo__c_2Ebinary__ieee_2Erounding__size:(tp__ty_2Ebinary__ieee_2Erounding > tp__ty_2Enum_2Enum))).
thf(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))))).
thf(tp_c_2Ebinary__ieee_2Ethreshold,type,(c_2Ebinary__ieee_2Ethreshold:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Ethreshold,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Ethreshold@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@ty_2Erealax_2Ereal))))).
thf(tp_c_2Ebinary__ieee_2Eulp,type,(c_2Ebinary__ieee_2Eulp:(del>(del>$i)))).
thf(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))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__TY__DEF,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: (? [V0rep:$i] : ((mem@V0rep@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t)))))) & (p@(ap@(ap@(c_2Ebool_2ETYPE__DEFINITION@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t))))@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(lam@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t))))@(^ [V1a0_27:$i] : (ap@(c_2Ebool_2E_21@(arr@(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))))@bool))@(lam@(arr@(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))))@bool)@(^ [V2_27float_27:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(c_2Ebool_2E_21@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t)))))@(lam@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t))))@(^ [V3a0_27:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(c_2Ebool_2E_3F@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(lam@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(^ [V4a0:$i] : (ap@(c_2Ebool_2E_3F@(ty_2Efcp_2Ecart@bool@A_27w))@(lam@(ty_2Efcp_2Ecart@bool@A_27w)@(^ [V5a1:$i] : (ap@(c_2Ebool_2E_3F@(ty_2Efcp_2Ecart@bool@A_27t))@(lam@(ty_2Efcp_2Ecart@bool@A_27t)@(^ [V6a2:$i] : (ap@(ap@(c_2Emin_2E_3D@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t)))))@V3a0_27)@(ap@(ap@(ap@(lam@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(^ [V7a0:$i] : (lam@(ty_2Efcp_2Ecart@bool@A_27w)@(^ [V8a1:$i] : (lam@(ty_2Efcp_2Ecart@bool@A_27t)@(^ [V9a2:$i] : (ap@(ap@(ap@(c_2Eind__type_2ECONSTR@(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))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(ap@(c_2Epair_2E_2C@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t)))@V7a0)@(ap@(ap@(c_2Epair_2E_2C@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t))@V8a1)@V9a2)))@(lam@ty_2Enum_2Enum@(^ [V10n:$i] : (c_2Eind__type_2EBOTTOM@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Epair_2Eprod@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27t)))))))))))))@V4a0)@V5a1)@V6a2))))))))))))@(ap@V2_27float_27@V3a0_27))))))@(ap@V2_27float_27@V1a0_27))))))))@V0rep))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__case__def,axiom,( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0a0:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1a1:$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))))))))))))).
thf(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))))))))))))))))).
thf(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))))))))).
thf(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))))))))).
thf(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))))))))).
thf(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))))))))))).
thf(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:$i] : ((mem@V3c1@(ty_2Efcp_2Ecart@bool@A_27t)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V0f)@(ap@(ap@(ap@(c_2Ebinary__ieee_2Erecordtype_2Efloat@A_27t@A_27w)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1c))@V2c0)@V3c1)) = (ap@(ap@(ap@(c_2Ebinary__ieee_2Erecordtype_2Efloat@A_27t@A_27w)@(ap@V0f@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1c)))@V2c0)@V3c1)))))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__Exponent__fupd,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [V0f:$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))))))))))))).
thf(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:$i] : ((mem@V3c1@(ty_2Efcp_2Ecart@bool@A_27t)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V0f)@(ap@(ap@(ap@(c_2Ebinary__ieee_2Erecordtype_2Efloat@A_27t@A_27w)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1c))@V2c0)@V3c1)) = (ap@(ap@(ap@(c_2Ebinary__ieee_2Erecordtype_2Efloat@A_27u@A_27w)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1c))@V2c0)@(ap@V0f@V3c1)))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__fn__updates,lemma,( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: (( ! [V0f:$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))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__accfupds,lemma,( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: (( ! [V0f0:$i] : ((mem@V0f0@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))) => ( ! [V1f:$i] : ((mem@V1f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27x)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V0f0)@V1f))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V1f))))))) & (( ! [V2f0:$i] : ((mem@V2f0@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))) => ( ! [V3f:$i] : ((mem@V3f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27u@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V2f0)@V3f))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V3f))))))) & (( ! [V4f0:$i] : ((mem@V4f0@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V5f:$i] : ((mem@V5f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V4f0)@V5f)) = (ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V5f)))))) & (( ! [V6f0:$i] : ((mem@V6f0@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))) => ( ! [V7f:$i] : ((mem@V7f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27u@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V6f0)@V7f)) = (ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V7f)))))) & (( ! [V8f0:$i] : ((mem@V8f0@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V9f:$i] : ((mem@V9f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V8f0)@V9f)) = (ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@V9f)))))) & (( ! [V10f0:$i] : ((mem@V10f0@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))) => ( ! [V11f:$i] : ((mem@V11f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27x)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V10f0)@V11f)) = (ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@V11f)))))) & (( ! [V12f0:$i] : ((mem@V12f0@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V13f:$i] : ((mem@V13f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V12f0)@V13f))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@V12f0@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V13f)))))))) & (( ! [V14f0:$i] : ((mem@V14f0@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))) => ( ! [V15f:$i] : ((mem@V15f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27x)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V14f0)@V15f)) = (ap@V14f0@(ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V15f))))))) & ( ! [V16f0:$i] : ((mem@V16f0@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))) => ( ! [V17f:$i] : ((mem@V17f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27u@A_27w)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V16f0)@V17f)) = (ap@V16f0@(ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@V17f)))))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__fupdfupds,lemma,( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27v:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [A_27y:del]: (( ! [V0g:$i] : ((mem@V0g@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V1f0:$i] : ((mem@V1f0@(arr@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))) => ( ! [V2f:$i] : ((mem@V2f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V1f0)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@V0g)@V2f)) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@(ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@V1f0)@V0g))@V2f)))))))) & (( ! [V3g:$i] : ((mem@V3g@(arr@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27x))) => ( ! [V4f0:$i] : ((mem@V4f0@(arr@(ty_2Efcp_2Ecart@bool@A_27x)@(ty_2Efcp_2Ecart@bool@A_27y))) => ( ! [V5f:$i] : ((mem@V5f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27x@A_27y)@V4f0)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V3g)@V5f)) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27y)@(ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27y)@(ty_2Efcp_2Ecart@bool@A_27x))@V4f0)@V3g))@V5f)))))))) & ( ! [V6g:$i] : ((mem@V6g@(arr@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27u))) => ( ! [V7f0:$i] : ((mem@V7f0@(arr@(ty_2Efcp_2Ecart@bool@A_27u)@(ty_2Efcp_2Ecart@bool@A_27v))) => ( ! [V8f:$i] : ((mem@V8f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27u@A_27v@A_27w)@V7f0)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V6g)@V8f)) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27v@A_27w)@(ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27v)@(ty_2Efcp_2Ecart@bool@A_27u))@V7f0)@V6g))@V8f))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__fupdfupds__comp,lemma,( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27v:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [A_27y:del]: ((( ! [V0g:$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))))))))))))))))))).
thf(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:$i] : ((mem@V8f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27x)@V7f0)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27x)@V6g)@V8f)) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27u@A_27w@A_27x)@V6g)@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@V7f0)@V8f)))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__fupdcanon__comp,lemma,( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ((( ! [V0g:$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)))))))))))))))))).
thf(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)))))))))))).
thf(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:$i] : ((mem@V3c@(ty_2Efcp_2Ecart@bool@A_27u)) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27u@A_27x)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1c1)))@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27u@A_27w@A_27x)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@A_27x)@(ty_2Efcp_2Ecart@bool@A_27w))@V2c0))@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@A_27u)@(ty_2Efcp_2Ecart@bool@A_27t))@V3c))@V0f))) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27u@A_27x)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1c1)))@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27u@A_27w@A_27x)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@A_27x)@(ty_2Efcp_2Ecart@bool@A_27w))@V2c0))@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27u@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@A_27u)@(ty_2Efcp_2Ecart@bool@A_27t))@V3c))@(c_2Ebool_2EARB@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__literal__nchotomy,lemma,( ! [A_27t:del]: ( ! [A_27u:del]: ( ! [A_27w:del]: ( ! [A_27x:del]: ( ! [V0f:$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)))))))))))))))))).
thf(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)))))))))))))))))))).
thf(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)))))))))))))))))))).
thf(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))))))))))))))))))).
thf(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))))))))))))))).
thf(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))))))))))))))))).
thf(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:$i] : ((mem@V3c1@(ty_2Efcp_2Ecart@bool@A_27t)) & (V0ff = (ap@(ap@(ap@(c_2Ebinary__ieee_2Erecordtype_2Efloat@A_27t@A_27w)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1c))@V2c0)@V3c1)))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__Axiom,lemma,( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f:$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:$i] : ((mem@V4a2@(ty_2Efcp_2Ecart@bool@A_27t)) => ((ap@V1fn@(ap@(ap@(ap@(c_2Ebinary__ieee_2Erecordtype_2Efloat@A_27t@A_27w)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V2a0))@V3a1)@V4a2)) = (ap@(ap@(ap@V0f@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V2a0))@V3a1)@V4a2))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__induction,lemma,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0P:$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:$i] : ((mem@V4f@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => (p@(ap@V0P@V4f)))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__case__cong,lemma,( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0f_27:$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:$i] : ((mem@V6a2@(ty_2Efcp_2Ecart@bool@A_27t)) => ((V2M_27 = (ap@(ap@(ap@(c_2Ebinary__ieee_2Erecordtype_2Efloat@A_27t@A_27w)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V4a0))@V5a1)@V6a2)) => ((ap@(ap@(ap@V3f@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V4a0))@V5a1)@V6a2) = (ap@(ap@(ap@V0f_27@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V4a0))@V5a1)@V6a2))))))))) => ((ap@(ap@(c_2Ebinary__ieee_2Efloat__CASE@A_27a@A_27t@A_27w)@V1M)@V3f) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__CASE@A_27a@A_27t@A_27w)@V2M_27)@V0f_27))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__case__eq,lemma,( ! [A_27a:del]: ( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$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)))))))))))))))))).
thf(stp_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,type,(tp__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal : $tType)).
thf(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 > $i))).
thf(stp_surj_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,type,(surj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal : ($i > tp__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal))).
thf(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))).
thf(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)))).
thf(stp_iso_mem_c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal)) => (X = (inj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal @ (surj__c_ty_2Eind__type_2Erecspace_ty_2Erealax_2Ereal @ X)))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__value__TY__DEF,axiom,(? [V0rep:$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)@(lam@(ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal)@(^ [V1a0:$i] : (ap@(c_2Ebool_2E_21@(arr@(ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal)@bool))@(lam@(arr@(ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal)@bool)@(^ [V2_27float__value_27:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(c_2Ebool_2E_21@(ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal))@(lam@(ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal)@(^ [V3a0:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(ap@c_2Ebool_2E_5C_2F@(ap@(c_2Ebool_2E_3F@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V4a:$i] : (ap@(ap@(c_2Emin_2E_3D@(ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal))@V3a0)@(ap@(lam@ty_2Erealax_2Ereal@(^ [V5a:$i] : (ap@(ap@(ap@(c_2Eind__type_2ECONSTR@ty_2Erealax_2Ereal)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@V5a)@(lam@ty_2Enum_2Enum@(^ [V6n:$i] : (c_2Eind__type_2EBOTTOM@ty_2Erealax_2Ereal))))))@V4a))))))@(ap@(ap@c_2Ebool_2E_5C_2F@(ap@(ap@(c_2Emin_2E_3D@(ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal))@V3a0)@(ap@(ap@(ap@(c_2Eind__type_2ECONSTR@ty_2Erealax_2Ereal)@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(c_2Ebool_2EARB@ty_2Erealax_2Ereal))@(lam@ty_2Enum_2Enum@(^ [V7n:$i] : (c_2Eind__type_2EBOTTOM@ty_2Erealax_2Ereal))))))@(ap@(ap@(c_2Emin_2E_3D@(ty_2Eind__type_2Erecspace@ty_2Erealax_2Ereal))@V3a0)@(ap@(ap@(ap@(c_2Eind__type_2ECONSTR@ty_2Erealax_2Ereal)@(ap@c_2Enum_2ESUC@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(c_2Ebool_2EARB@ty_2Erealax_2Ereal))@(lam@ty_2Enum_2Enum@(^ [V8n:$i] : (c_2Eind__type_2EBOTTOM@ty_2Erealax_2Ereal))))))))@(ap@V2_27float__value_27@V3a0))))))@(ap@V2_27float__value_27@V1a0))))))))@V0rep))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__value__case__def,axiom,( ! [A_27a:del]: (( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1f:$i] : ((mem@V1f@(arr@ty_2Erealax_2Ereal@A_27a)) => ( ! [V2v:$i] : ((mem@V2v@A_27a) => ( ! [V3v1:$i] : ((mem@V3v1@A_27a) => ((ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(ap@c_2Ebinary__ieee_2EFloat@(inj__ty_2Erealax_2Ereal @ V0a)))@V1f)@V2v)@V3v1) = (ap@V1f@(inj__ty_2Erealax_2Ereal @ V0a)))))))))) & (( ! [V4f:$i] : ((mem@V4f@(arr@ty_2Erealax_2Ereal@A_27a)) => ( ! [V5v:$i] : ((mem@V5v@A_27a) => ( ! [V6v1:$i] : ((mem@V6v1@A_27a) => ((ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2EInfinity))@V4f)@V5v)@V6v1) = V5v))))))) & ( ! [V7f:$i] : ((mem@V7f@(arr@ty_2Erealax_2Ereal@A_27a)) => ( ! [V8v:$i] : ((mem@V8v@A_27a) => ( ! [V9v1:$i] : ((mem@V9v1@A_27a) => ((ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2ENaN))@V7f)@V8v)@V9v1) = V9v1))))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__value__size__def,axiom,(( ! [V0a:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Enum_2Enum @ (ap@c_2Ebinary__ieee_2Efloat__value__size@(ap@c_2Ebinary__ieee_2EFloat@(inj__ty_2Erealax_2Ereal @ V0a)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Ebinary__ieee_2Efloat__value__size@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2EInfinity))) = fo__c_2Enum_2E0) & ((surj__ty_2Enum_2Enum @ (ap@c_2Ebinary__ieee_2Efloat__value__size@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2ENaN))) = fo__c_2Enum_2E0)))).
thf(conj_thm_2Ebinary__ieee_2Edatatype__float__value,lemma,( ! [V0float__value:$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))))))).
thf(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))))).
thf(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))))).
thf(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))))).
thf(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))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__value__induction,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Ebinary__ieee_2Efloat__value@bool)) => ((( ! [V1r:tp__ty_2Erealax_2Ereal] : (p@(ap@V0P@(ap@c_2Ebinary__ieee_2EFloat@(inj__ty_2Erealax_2Ereal @ V1r))))) & ((p@(ap@V0P@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2EInfinity))) & (p@(ap@V0P@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2ENaN))))) => ( ! [V2f:tp__ty_2Ebinary__ieee_2Efloat__value] : (p@(ap@V0P@(inj__ty_2Ebinary__ieee_2Efloat__value @ V2f)))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__value__case__cong,lemma,( ! [A_27a:del]: ( ! [V0f_27:$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:$i] : ((mem@V7v1@A_27a) => (((V3M = V4M_27) & (( ! [V8a:tp__ty_2Erealax_2Ereal] : ((V4M_27 = (surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@c_2Ebinary__ieee_2EFloat@(inj__ty_2Erealax_2Ereal @ V8a)))) => ((ap@V5f@(inj__ty_2Erealax_2Ereal @ V8a)) = (ap@V0f_27@(inj__ty_2Erealax_2Ereal @ V8a))))) & (((V4M_27 = fo__c_2Ebinary__ieee_2EInfinity) => (V6v = V1v_27)) & ((V4M_27 = fo__c_2Ebinary__ieee_2ENaN) => (V7v1 = V2v1_27))))) => ((ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(inj__ty_2Ebinary__ieee_2Efloat__value @ V3M))@V5f)@V6v)@V7v1) = (ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(inj__ty_2Ebinary__ieee_2Efloat__value @ V4M_27))@V0f_27)@V1v_27)@V2v1_27))))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Efloat__value__case__eq,lemma,( ! [A_27a:del]: ( ! [V0x:tp__ty_2Ebinary__ieee_2Efloat__value] : ( ! [V1f:$i] : ((mem@V1f@(arr@ty_2Erealax_2Ereal@A_27a)) => ( ! [V2v:$i] : ((mem@V2v@A_27a) => ( ! [V3v1:$i] : ((mem@V3v1@A_27a) => ( ! [V4v_27:$i] : ((mem@V4v_27@A_27a) => (((ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@A_27a)@(inj__ty_2Ebinary__ieee_2Efloat__value @ V0x))@V1f)@V2v)@V3v1) = V4v_27) <=> ((? [V5r:tp__ty_2Erealax_2Ereal] : ((V0x = (surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@c_2Ebinary__ieee_2EFloat@(inj__ty_2Erealax_2Ereal @ V5r)))) & ((ap@V1f@(inj__ty_2Erealax_2Ereal @ V5r)) = V4v_27))) | (((V0x = fo__c_2Ebinary__ieee_2EInfinity) & (V2v = V4v_27)) | ((V0x = fo__c_2Ebinary__ieee_2ENaN) & (V3v1 = V4v_27)))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__to__real__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$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)))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__value__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@V0x)) = (surj__ty_2Ebinary__ieee_2Efloat__value @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Ebinary__ieee_2Efloat__value)@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@A_27w))@(ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V0x))@(c_2Ewords_2Eword__T@A_27w)))@(ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Ebinary__ieee_2Efloat__value)@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@A_27t))@(ap@(c_2Ebinary__ieee_2Efloat__Significand@A_27t@A_27w)@V0x))@(ap@(c_2Ewords_2En2w@A_27t)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2EInfinity))@(inj__ty_2Ebinary__ieee_2Efloat__value @ fo__c_2Ebinary__ieee_2ENaN)))@(ap@c_2Ebinary__ieee_2EFloat@(ap@(c_2Ebinary__ieee_2Efloat__to__real@A_27t@A_27w)@V0x)))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__is__nan__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$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))@(lam@ty_2Erealax_2Ereal@(^ [V1v1:$i] : c_2Ebool_2EF)))@c_2Ebool_2EF)@c_2Ebool_2ET)))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__is__signalling__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$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))))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__is__infinite__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((p@(ap@(c_2Ebinary__ieee_2Efloat__is__infinite@A_27t@A_27w)@V0x)) <=> (p@(ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@bool)@(ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@V0x))@(lam@ty_2Erealax_2Ereal@(^ [V1v1:$i] : c_2Ebool_2EF)))@c_2Ebool_2ET)@c_2Ebool_2EF)))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__is__normal__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((p@(ap@(c_2Ebinary__ieee_2Efloat__is__normal@A_27t@A_27w)@V0x)) <=> ((~ ((ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V0x) = (ap@(c_2Ewords_2En2w@A_27w)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (~ ((ap@(c_2Ebinary__ieee_2Efloat__Exponent@A_27t@A_27w)@V0x) = (c_2Ewords_2Eword__T@A_27w)))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__is__subnormal__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$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))))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__is__zero__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((p@(ap@(c_2Ebinary__ieee_2Efloat__is__zero@A_27t@A_27w)@V0x)) <=> (p@(ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@bool)@(ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@V0x))@(lam@ty_2Erealax_2Ereal@(^ [V1r:$i] : (ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@V1r)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))@c_2Ebool_2EF)@c_2Ebool_2EF)))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__is__finite__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((p@(ap@(c_2Ebinary__ieee_2Efloat__is__finite@A_27t@A_27w)@V0x)) <=> (p@(ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@bool)@(ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@V0x))@(lam@ty_2Erealax_2Ereal@(^ [V1v1:$i] : c_2Ebool_2ET)))@c_2Ebool_2EF)@c_2Ebool_2EF)))))))).
thf(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)))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__is__integral__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((p@(ap@(c_2Ebinary__ieee_2Efloat__is__integral@A_27t@A_27w)@V0x)) <=> (p@(ap@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__value__CASE@bool)@(ap@(c_2Ebinary__ieee_2Efloat__value@A_27t@A_27w)@V0x))@(lam@ty_2Erealax_2Ereal@(^ [V1r:$i] : (ap@c_2Ebinary__ieee_2Eis__integral@V1r))))@c_2Ebool_2EF)@c_2Ebool_2EF)))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__negate__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ((ap@(c_2Ebinary__ieee_2Efloat__negate@A_27t@A_27w)@V0x) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ewords_2Eword__1comp@ty_2Eone_2Eone)@(ap@(c_2Ebinary__ieee_2Efloat__Sign@A_27t@A_27w)@V0x))))@V0x))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__abs__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:$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))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__plus__infinity__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ((ap@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))) = (ap@(ap@(c_2Ebinary__ieee_2Efloat__Sign__fupd@A_27t@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone)@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Exponent__fupd@A_27t@A_27w@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@A_27w)@(ty_2Efcp_2Ecart@bool@A_27w))@(c_2Ewords_2Eword__T@A_27w)))@(ap@(ap@(c_2Ebinary__ieee_2Efloat__Significand__fupd@A_27t@A_27t@A_27w)@(ap@(c_2Ecombin_2EK@(ty_2Efcp_2Ecart@bool@A_27t)@(ty_2Efcp_2Ecart@bool@A_27t))@(ap@(c_2Ewords_2En2w@A_27t)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(c_2Ebool_2EARB@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__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))))))))).
thf(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))))))))).
thf(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))))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__minus__infinity__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ((ap@(c_2Ebinary__ieee_2Efloat__minus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w))) = (ap@(c_2Ebinary__ieee_2Efloat__negate@A_27t@A_27w)@(ap@(c_2Ebinary__ieee_2Efloat__plus__infinity@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))))))).
thf(ax_thm_2Ebinary__ieee_2Efloat__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)))))))).
thf(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)))))))).
thf(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)))))))).
thf(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)).
thf(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 > $i))).
thf(stp_surj_c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(surj__c_ty_2Eind__type_2Erecspace_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : ($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))).
thf(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))).
thf(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))))))))).
thf(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)))))).
thf(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)).
thf(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 > $i))).
thf(stp_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : ($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))).
thf(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))).
thf(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)))))))).
thf(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)))))).
thf(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)).
thf(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 > $i))).
thf(stp_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,(surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o : ($i > tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o))).
thf(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))).
thf(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))))))).
thf(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:$i] : ((mem @ X @ (ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool))))) => (X = (inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ (surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ X)))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__TY__DEF,axiom,(? [V0rep:$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)@(lam@(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))))))@(^ [V1a0_27:$i] : (ap@(c_2Ebool_2E_21@(arr@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool))))))@bool))@(lam@(arr@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool))))))@bool)@(^ [V2_27flags_27:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(c_2Ebool_2E_21@(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)))))))@(lam@(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))))))@(^ [V3a0_27:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(c_2Ebool_2E_3F@bool)@(lam@bool@(^ [V4a0:$i] : (ap@(c_2Ebool_2E_3F@bool)@(lam@bool@(^ [V5a1:$i] : (ap@(c_2Ebool_2E_3F@bool)@(lam@bool@(^ [V6a2:$i] : (ap@(c_2Ebool_2E_3F@bool)@(lam@bool@(^ [V7a3:$i] : (ap@(c_2Ebool_2E_3F@bool)@(lam@bool@(^ [V8a4:$i] : (ap@(c_2Ebool_2E_3F@bool)@(lam@bool@(^ [V9a5:$i] : (ap@(ap@(c_2Emin_2E_3D@(ty_2Eind__type_2Erecspace@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool)))))))@V3a0_27)@(ap@(ap@(ap@(ap@(ap@(ap@(lam@bool@(^ [V10a0:$i] : (lam@bool@(^ [V11a1:$i] : (lam@bool@(^ [V12a2:$i] : (lam@bool@(^ [V13a3:$i] : (lam@bool@(^ [V14a4:$i] : (lam@bool@(^ [V15a5:$i] : (ap@(ap@(ap@(c_2Eind__type_2ECONSTR@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool))))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(ap@(c_2Epair_2E_2C@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool)))))@V10a0)@(ap@(ap@(c_2Epair_2E_2C@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool))))@V11a1)@(ap@(ap@(c_2Epair_2E_2C@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool)))@V12a2)@(ap@(ap@(c_2Epair_2E_2C@bool@(ty_2Epair_2Eprod@bool@bool))@V13a3)@(ap@(ap@(c_2Epair_2E_2C@bool@bool)@V14a4)@V15a5))))))@(lam@ty_2Enum_2Enum@(^ [V16n:$i] : (c_2Eind__type_2EBOTTOM@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@(ty_2Epair_2Eprod@bool@bool)))))))))))))))))))))@V4a0)@V5a1)@V6a2)@V7a3)@V8a4)@V9a5)))))))))))))))))))))@(ap@V2_27flags_27@V3a0_27))))))@(ap@V2_27flags_27@V1a0_27))))))))@V0rep))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__case__def,axiom,( ! [A_27a:del]: ( ! [V0a0:$i] : ((mem@V0a0@bool) => ( ! [V1a1:$i] : ((mem@V1a1@bool) => ( ! [V2a2:$i] : ((mem@V2a2@bool) => ( ! [V3a3:$i] : ((mem@V3a3@bool) => ( ! [V4a4:$i] : ((mem@V4a4@bool) => ( ! [V5a5:$i] : ((mem@V5a5@bool) => ( ! [V6f:$i] : ((mem@V6f@(arr@bool@(arr@bool@(arr@bool@(arr@bool@(arr@bool@(arr@bool@A_27a))))))) => ((ap@(ap@(c_2Ebinary__ieee_2Eflags__CASE@A_27a)@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0a0)@V1a1)@V2a2)@V3a3)@V4a4)@V5a5))@V6f) = (ap@(ap@(ap@(ap@(ap@(ap@V6f@V0a0)@V1a1)@V2a2)@V3a3)@V4a4)@V5a5)))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__size__def,axiom,( ! [V0a0:$i] : ((mem@V0a0@bool) => ( ! [V1a1:$i] : ((mem@V1a1@bool) => ( ! [V2a2:$i] : ((mem@V2a2@bool) => ( ! [V3a3:$i] : ((mem@V3a3@bool) => ( ! [V4a4:$i] : ((mem@V4a4@bool) => ( ! [V5a5:$i] : ((mem@V5a5@bool) => ((surj__ty_2Enum_2Enum @ (ap@c_2Ebinary__ieee_2Eflags__size@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0a0)@V1a1)@V2a2)@V3a3)@V4a4)@V5a5))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2EbasicSize_2Ebool__size@V0a0))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2EbasicSize_2Ebool__size@V1a1))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2EbasicSize_2Ebool__size@V2a2))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2EbasicSize_2Ebool__size@V3a3))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2EbasicSize_2Ebool__size@V4a4))@(ap@c_2EbasicSize_2Ebool__size@V5a5)))))))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__DivideByZero,axiom,( ! [V0b:$i] : ((mem@V0b@bool) => ( ! [V1b0:$i] : ((mem@V1b0@bool) => ( ! [V2b1:$i] : ((mem@V2b1@bool) => ( ! [V3b2:$i] : ((mem@V3b2@bool) => ( ! [V4b3:$i] : ((mem@V4b3@bool) => ( ! [V5b4:$i] : ((mem@V5b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__DivideByZero@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0b)@V1b0)@V2b1)@V3b2)@V4b3)@V5b4))) <=> (p@V0b))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__InvalidOp,axiom,( ! [V0b:$i] : ((mem@V0b@bool) => ( ! [V1b0:$i] : ((mem@V1b0@bool) => ( ! [V2b1:$i] : ((mem@V2b1@bool) => ( ! [V3b2:$i] : ((mem@V3b2@bool) => ( ! [V4b3:$i] : ((mem@V4b3@bool) => ( ! [V5b4:$i] : ((mem@V5b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__InvalidOp@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0b)@V1b0)@V2b1)@V3b2)@V4b3)@V5b4))) <=> (p@V1b0))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__Overflow,axiom,( ! [V0b:$i] : ((mem@V0b@bool) => ( ! [V1b0:$i] : ((mem@V1b0@bool) => ( ! [V2b1:$i] : ((mem@V2b1@bool) => ( ! [V3b2:$i] : ((mem@V3b2@bool) => ( ! [V4b3:$i] : ((mem@V4b3@bool) => ( ! [V5b4:$i] : ((mem@V5b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__Overflow@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0b)@V1b0)@V2b1)@V3b2)@V4b3)@V5b4))) <=> (p@V2b1))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__Precision,axiom,( ! [V0b:$i] : ((mem@V0b@bool) => ( ! [V1b0:$i] : ((mem@V1b0@bool) => ( ! [V2b1:$i] : ((mem@V2b1@bool) => ( ! [V3b2:$i] : ((mem@V3b2@bool) => ( ! [V4b3:$i] : ((mem@V4b3@bool) => ( ! [V5b4:$i] : ((mem@V5b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__Precision@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0b)@V1b0)@V2b1)@V3b2)@V4b3)@V5b4))) <=> (p@V3b2))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,axiom,( ! [V0b:$i] : ((mem@V0b@bool) => ( ! [V1b0:$i] : ((mem@V1b0@bool) => ( ! [V2b1:$i] : ((mem@V2b1@bool) => ( ! [V3b2:$i] : ((mem@V3b2@bool) => ( ! [V4b3:$i] : ((mem@V4b3@bool) => ( ! [V5b4:$i] : ((mem@V5b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0b)@V1b0)@V2b1)@V3b2)@V4b3)@V5b4))) <=> (p@V4b3))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,axiom,( ! [V0b:$i] : ((mem@V0b@bool) => ( ! [V1b0:$i] : ((mem@V1b0@bool) => ( ! [V2b1:$i] : ((mem@V2b1@bool) => ( ! [V3b2:$i] : ((mem@V3b2@bool) => ( ! [V4b3:$i] : ((mem@V4b3@bool) => ( ! [V5b4:$i] : ((mem@V5b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0b)@V1b0)@V2b1)@V3b2)@V4b3)@V5b4))) <=> (p@V5b4))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__accessors,lemma,(( ! [V0b:$i] : ((mem@V0b@bool) => ( ! [V1b0:$i] : ((mem@V1b0@bool) => ( ! [V2b1:$i] : ((mem@V2b1@bool) => ( ! [V3b2:$i] : ((mem@V3b2@bool) => ( ! [V4b3:$i] : ((mem@V4b3@bool) => ( ! [V5b4:$i] : ((mem@V5b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__DivideByZero@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V0b)@V1b0)@V2b1)@V3b2)@V4b3)@V5b4))) <=> (p@V0b)))))))))))))) & (( ! [V6b:$i] : ((mem@V6b@bool) => ( ! [V7b0:$i] : ((mem@V7b0@bool) => ( ! [V8b1:$i] : ((mem@V8b1@bool) => ( ! [V9b2:$i] : ((mem@V9b2@bool) => ( ! [V10b3:$i] : ((mem@V10b3@bool) => ( ! [V11b4:$i] : ((mem@V11b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__InvalidOp@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V6b)@V7b0)@V8b1)@V9b2)@V10b3)@V11b4))) <=> (p@V7b0)))))))))))))) & (( ! [V12b:$i] : ((mem@V12b@bool) => ( ! [V13b0:$i] : ((mem@V13b0@bool) => ( ! [V14b1:$i] : ((mem@V14b1@bool) => ( ! [V15b2:$i] : ((mem@V15b2@bool) => ( ! [V16b3:$i] : ((mem@V16b3@bool) => ( ! [V17b4:$i] : ((mem@V17b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__Overflow@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V12b)@V13b0)@V14b1)@V15b2)@V16b3)@V17b4))) <=> (p@V14b1)))))))))))))) & (( ! [V18b:$i] : ((mem@V18b@bool) => ( ! [V19b0:$i] : ((mem@V19b0@bool) => ( ! [V20b1:$i] : ((mem@V20b1@bool) => ( ! [V21b2:$i] : ((mem@V21b2@bool) => ( ! [V22b3:$i] : ((mem@V22b3@bool) => ( ! [V23b4:$i] : ((mem@V23b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__Precision@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V18b)@V19b0)@V20b1)@V21b2)@V22b3)@V23b4))) <=> (p@V21b2)))))))))))))) & (( ! [V24b:$i] : ((mem@V24b@bool) => ( ! [V25b0:$i] : ((mem@V25b0@bool) => ( ! [V26b1:$i] : ((mem@V26b1@bool) => ( ! [V27b2:$i] : ((mem@V27b2@bool) => ( ! [V28b3:$i] : ((mem@V28b3@bool) => ( ! [V29b4:$i] : ((mem@V29b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V24b)@V25b0)@V26b1)@V27b2)@V28b3)@V29b4))) <=> (p@V28b3)))))))))))))) & ( ! [V30b:$i] : ((mem@V30b@bool) => ( ! [V31b0:$i] : ((mem@V31b0@bool) => ( ! [V32b1:$i] : ((mem@V32b1@bool) => ( ! [V33b2:$i] : ((mem@V33b2@bool) => ( ! [V34b3:$i] : ((mem@V34b3@bool) => ( ! [V35b4:$i] : ((mem@V35b4@bool) => ((p@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V30b)@V31b0)@V32b1)@V33b2)@V34b3)@V35b4))) <=> (p@V35b4)))))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__DivideByZero__fupd,axiom,( ! [V0f:$i] : ((mem@V0f@(arr@bool@bool)) => ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2b0:$i] : ((mem@V2b0@bool) => ( ! [V3b1:$i] : ((mem@V3b1@bool) => ( ! [V4b2:$i] : ((mem@V4b2@bool) => ( ! [V5b3:$i] : ((mem@V5b3@bool) => ( ! [V6b4:$i] : ((mem@V6b4@bool) => ((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@V1b)@V2b0)@V3b1)@V4b2)@V5b3)@V6b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@(ap@V0f@V1b))@V2b0)@V3b1)@V4b2)@V5b3)@V6b4)))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__InvalidOp__fupd,axiom,( ! [V0f:$i] : ((mem@V0f@(arr@bool@bool)) => ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2b0:$i] : ((mem@V2b0@bool) => ( ! [V3b1:$i] : ((mem@V3b1@bool) => ( ! [V4b2:$i] : ((mem@V4b2@bool) => ( ! [V5b3:$i] : ((mem@V5b3@bool) => ( ! [V6b4:$i] : ((mem@V6b4@bool) => ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__InvalidOp__fupd@V0f)@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V1b)@V2b0)@V3b1)@V4b2)@V5b3)@V6b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V1b)@(ap@V0f@V2b0))@V3b1)@V4b2)@V5b3)@V6b4)))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__Overflow__fupd,axiom,( ! [V0f:$i] : ((mem@V0f@(arr@bool@bool)) => ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2b0:$i] : ((mem@V2b0@bool) => ( ! [V3b1:$i] : ((mem@V3b1@bool) => ( ! [V4b2:$i] : ((mem@V4b2@bool) => ( ! [V5b3:$i] : ((mem@V5b3@bool) => ( ! [V6b4:$i] : ((mem@V6b4@bool) => ((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@V1b)@V2b0)@V3b1)@V4b2)@V5b3)@V6b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V1b)@V2b0)@(ap@V0f@V3b1))@V4b2)@V5b3)@V6b4)))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__Precision__fupd,axiom,( ! [V0f:$i] : ((mem@V0f@(arr@bool@bool)) => ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2b0:$i] : ((mem@V2b0@bool) => ( ! [V3b1:$i] : ((mem@V3b1@bool) => ( ! [V4b2:$i] : ((mem@V4b2@bool) => ( ! [V5b3:$i] : ((mem@V5b3@bool) => ( ! [V6b4:$i] : ((mem@V6b4@bool) => ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__Precision__fupd@V0f)@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V1b)@V2b0)@V3b1)@V4b2)@V5b3)@V6b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V1b)@V2b0)@V3b1)@(ap@V0f@V4b2))@V5b3)@V6b4)))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,axiom,( ! [V0f:$i] : ((mem@V0f@(arr@bool@bool)) => ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2b0:$i] : ((mem@V2b0@bool) => ( ! [V3b1:$i] : ((mem@V3b1@bool) => ( ! [V4b2:$i] : ((mem@V4b2@bool) => ( ! [V5b3:$i] : ((mem@V5b3@bool) => ( ! [V6b4:$i] : ((mem@V6b4@bool) => ((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@V1b)@V2b0)@V3b1)@V4b2)@V5b3)@V6b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V1b)@V2b0)@V3b1)@V4b2)@(ap@V0f@V5b3))@V6b4)))))))))))))))))).
thf(ax_thm_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,axiom,( ! [V0f:$i] : ((mem@V0f@(arr@bool@bool)) => ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2b0:$i] : ((mem@V2b0@bool) => ( ! [V3b1:$i] : ((mem@V3b1@bool) => ( ! [V4b2:$i] : ((mem@V4b2@bool) => ( ! [V5b3:$i] : ((mem@V5b3@bool) => ( ! [V6b4:$i] : ((mem@V6b4@bool) => ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V0f)@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V1b)@V2b0)@V3b1)@V4b2)@V5b3)@V6b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V1b)@V2b0)@V3b1)@V4b2)@V5b3)@(ap@V0f@V6b4))))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__fn__updates,lemma,(( ! [V0f:$i] : ((mem@V0f@(arr@bool@bool)) => ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2b0:$i] : ((mem@V2b0@bool) => ( ! [V3b1:$i] : ((mem@V3b1@bool) => ( ! [V4b2:$i] : ((mem@V4b2@bool) => ( ! [V5b3:$i] : ((mem@V5b3@bool) => ( ! [V6b4:$i] : ((mem@V6b4@bool) => ((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@V1b)@V2b0)@V3b1)@V4b2)@V5b3)@V6b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@(ap@V0f@V1b))@V2b0)@V3b1)@V4b2)@V5b3)@V6b4))))))))))))))))) & (( ! [V7f:$i] : ((mem@V7f@(arr@bool@bool)) => ( ! [V8b:$i] : ((mem@V8b@bool) => ( ! [V9b0:$i] : ((mem@V9b0@bool) => ( ! [V10b1:$i] : ((mem@V10b1@bool) => ( ! [V11b2:$i] : ((mem@V11b2@bool) => ( ! [V12b3:$i] : ((mem@V12b3@bool) => ( ! [V13b4:$i] : ((mem@V13b4@bool) => ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__InvalidOp__fupd@V7f)@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V8b)@V9b0)@V10b1)@V11b2)@V12b3)@V13b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V8b)@(ap@V7f@V9b0))@V10b1)@V11b2)@V12b3)@V13b4))))))))))))))))) & (( ! [V14f:$i] : ((mem@V14f@(arr@bool@bool)) => ( ! [V15b:$i] : ((mem@V15b@bool) => ( ! [V16b0:$i] : ((mem@V16b0@bool) => ( ! [V17b1:$i] : ((mem@V17b1@bool) => ( ! [V18b2:$i] : ((mem@V18b2@bool) => ( ! [V19b3:$i] : ((mem@V19b3@bool) => ( ! [V20b4:$i] : ((mem@V20b4@bool) => ((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@V15b)@V16b0)@V17b1)@V18b2)@V19b3)@V20b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V15b)@V16b0)@(ap@V14f@V17b1))@V18b2)@V19b3)@V20b4))))))))))))))))) & (( ! [V21f:$i] : ((mem@V21f@(arr@bool@bool)) => ( ! [V22b:$i] : ((mem@V22b@bool) => ( ! [V23b0:$i] : ((mem@V23b0@bool) => ( ! [V24b1:$i] : ((mem@V24b1@bool) => ( ! [V25b2:$i] : ((mem@V25b2@bool) => ( ! [V26b3:$i] : ((mem@V26b3@bool) => ( ! [V27b4:$i] : ((mem@V27b4@bool) => ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__Precision__fupd@V21f)@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V22b)@V23b0)@V24b1)@V25b2)@V26b3)@V27b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V22b)@V23b0)@V24b1)@(ap@V21f@V25b2))@V26b3)@V27b4))))))))))))))))) & (( ! [V28f:$i] : ((mem@V28f@(arr@bool@bool)) => ( ! [V29b:$i] : ((mem@V29b@bool) => ( ! [V30b0:$i] : ((mem@V30b0@bool) => ( ! [V31b1:$i] : ((mem@V31b1@bool) => ( ! [V32b2:$i] : ((mem@V32b2@bool) => ( ! [V33b3:$i] : ((mem@V33b3@bool) => ( ! [V34b4:$i] : ((mem@V34b4@bool) => ((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@V29b)@V30b0)@V31b1)@V32b2)@V33b3)@V34b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V29b)@V30b0)@V31b1)@V32b2)@(ap@V28f@V33b3))@V34b4))))))))))))))))) & ( ! [V35f:$i] : ((mem@V35f@(arr@bool@bool)) => ( ! [V36b:$i] : ((mem@V36b@bool) => ( ! [V37b0:$i] : ((mem@V37b0@bool) => ( ! [V38b1:$i] : ((mem@V38b1@bool) => ( ! [V39b2:$i] : ((mem@V39b2@bool) => ( ! [V40b3:$i] : ((mem@V40b3@bool) => ( ! [V41b4:$i] : ((mem@V41b4@bool) => ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V35f)@(ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V36b)@V37b0)@V38b1)@V39b2)@V40b3)@V41b4))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@(ap@(ap@(ap@(ap@c_2Ebinary__ieee_2Erecordtype_2Eflags@V36b)@V37b0)@V38b1)@V39b2)@V40b3)@(ap@V35f@V41b4)))))))))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__accfupds,lemma,(( ! [V0f0:$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:$i] : ((mem@V70f0@(arr@bool@bool)) => ( ! [V71f:tp__ty_2Ebinary__ieee_2Eflags] : ((p@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V70f0)@(inj__ty_2Ebinary__ieee_2Eflags @ V71f)))) <=> (p@(ap@V70f0@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding@(inj__ty_2Ebinary__ieee_2Eflags @ V71f)))))))))))))))))))))))))))))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__fupdfupds,lemma,(( ! [V0g:$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:$i] : ((mem@V16f0@(arr@bool@bool)) => ( ! [V17f:tp__ty_2Ebinary__ieee_2Eflags] : ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V16f0)@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V15g)@(inj__ty_2Ebinary__ieee_2Eflags @ V17f)))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@(ap@(ap@(c_2Ecombin_2Eo@bool@bool@bool)@V16f0)@V15g))@(inj__ty_2Ebinary__ieee_2Eflags @ V17f))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__fupdfupds__comp,lemma,( ! [A_27a:del]: ((( ! [V0g:$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:$i] : ((mem@V29f0@(arr@bool@bool)) => ((ap@(ap@(c_2Ecombin_2Eo@A_27a@ty_2Ebinary__ieee_2Eflags@ty_2Ebinary__ieee_2Eflags)@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V29f0))@(ap@(ap@(c_2Ecombin_2Eo@A_27a@ty_2Ebinary__ieee_2Eflags@ty_2Ebinary__ieee_2Eflags)@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V28g))@V27h)) = (ap@(ap@(c_2Ecombin_2Eo@A_27a@ty_2Ebinary__ieee_2Eflags@ty_2Ebinary__ieee_2Eflags)@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@(ap@(ap@(c_2Ecombin_2Eo@bool@bool@bool)@V29f0)@V28g)))@V27h)))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__fupdcanon,lemma,(( ! [V0g:$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:$i] : ((mem@V43f0@(arr@bool@bool)) => ( ! [V44f:tp__ty_2Ebinary__ieee_2Eflags] : ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V43f0)@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd@V42g)@(inj__ty_2Ebinary__ieee_2Eflags @ V44f)))) = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd@V42g)@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@V43f0)@(inj__ty_2Ebinary__ieee_2Eflags @ V44f))))))))))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__fupdcanon__comp,lemma,( ! [A_27a:del]: ((( ! [V0g:$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)))))))))))))))))))))))))).
thf(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))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__updates__eq__literal,lemma,( ! [V0f:tp__ty_2Ebinary__ieee_2Eflags] : ( ! [V1b4:$i] : ((mem@V1b4@bool) => ( ! [V2b3:$i] : ((mem@V2b3@bool) => ( ! [V3b2:$i] : ((mem@V3b2@bool) => ( ! [V4b1:$i] : ((mem@V4b1@bool) => ( ! [V5b0:$i] : ((mem@V5b0@bool) => ( ! [V6b:$i] : ((mem@V6b@bool) => ((surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__DivideByZero__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V1b4))@(ap@(ap@c_2Ebinary__ieee_2Eflags__InvalidOp__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V2b3))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Overflow__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V3b2))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Precision__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V4b1))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V5b0))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@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)@V1b4))@(ap@(ap@c_2Ebinary__ieee_2Eflags__InvalidOp__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V2b3))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Overflow__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V3b2))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Precision__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V4b1))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V5b0))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V6b))@(c_2Ebool_2EARB@ty_2Ebinary__ieee_2Eflags))))))))))))))))))))))).
thf(conj_thm_2Ebinary__ieee_2Eflags__literal__nchotomy,conjecture,( ! [V0f:tp__ty_2Ebinary__ieee_2Eflags] : (? [V1b4:$i] : ((mem@V1b4@bool) & (? [V2b3:$i] : ((mem@V2b3@bool) & (? [V3b2:$i] : ((mem@V3b2@bool) & (? [V4b1:$i] : ((mem@V4b1@bool) & (? [V5b0:$i] : ((mem@V5b0@bool) & (? [V6b:$i] : ((mem@V6b@bool) & (V0f = (surj__ty_2Ebinary__ieee_2Eflags @ (ap@(ap@c_2Ebinary__ieee_2Eflags__DivideByZero__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V1b4))@(ap@(ap@c_2Ebinary__ieee_2Eflags__InvalidOp__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V2b3))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Overflow__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V3b2))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Precision__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V4b1))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V5b0))@(ap@(ap@c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd@(ap@(c_2Ecombin_2EK@bool@bool)@V6b))@(c_2Ebool_2EARB@ty_2Ebinary__ieee_2Eflags))))))))))))))))))))))).
