include('Axioms/basis_emit+2.ax').
fof(mem_c_2Ereal_2E_2F,axiom,( mem(c_2Ereal_2E_2F,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2ENUM__CEILING,axiom,( mem(c_2Ereal_2ENUM__CEILING,arr(ty_2Erealax_2Ereal,ty_2Enum_2Enum)) )).
fof(mem_c_2Ereal_2ENUM__FLOOR,axiom,( mem(c_2Ereal_2ENUM__FLOOR,arr(ty_2Erealax_2Ereal,ty_2Enum_2Enum)) )).
fof(mem_c_2Ereal_2Eabs,axiom,( mem(c_2Ereal_2Eabs,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Ereal_2Einf,axiom,( mem(c_2Ereal_2Einf,arr(arr(ty_2Erealax_2Ereal,bool),ty_2Erealax_2Ereal)) )).
fof(mem_c_2Ereal_2Emax,axiom,( mem(c_2Ereal_2Emax,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Emin,axiom,( mem(c_2Ereal_2Emin,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Epos,axiom,( mem(c_2Ereal_2Epos,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Ereal_2Epow,axiom,( mem(c_2Ereal_2Epow,arr(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Ereal__ge,axiom,( mem(c_2Ereal_2Ereal__ge,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Ereal_2Ereal__gt,axiom,( mem(c_2Ereal_2Ereal__gt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Ereal_2Ereal__lte,axiom,( mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Ereal_2Ereal__of__num,axiom,( mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Ereal_2Ereal__sub,axiom,( mem(c_2Ereal_2Ereal__sub,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Esum,axiom,( mem(c_2Ereal_2Esum,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Esup,axiom,( mem(c_2Ereal_2Esup,arr(arr(ty_2Erealax_2Ereal,bool),ty_2Erealax_2Ereal)) )).
fof(ax_thm_2Ereal_2Ereal__of__num,axiom, ( ( ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) = c_2Erealax_2Ereal__0 ) & ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,V0n)) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,V0n)),c_2Erealax_2Ereal__1) ) ) )).
fof(conj_thm_2Ereal_2EREAL__0,lemma,(( c_2Erealax_2Ereal__0 = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ))).
fof(conj_thm_2Ereal_2EREAL__1,lemma,(( c_2Erealax_2Ereal__1 = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ))).
fof(conj_thm_2Ereal_2EREAL__10,lemma,(( ~~ ( ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__SYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__COMM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__ASSOC,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,V0x)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__LDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__TOTAL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( V0x = V1y ) | ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) | p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ~~ p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__IADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__add,V0x),V2z))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUP__ALLPOS,lemma,(! [V0P] : ( mem(V0P,arr(ty_2Erealax_2Ereal,bool)) => ( ( ( ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ( p(ap(V0P,V1x)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x)) ) ) ) & ( ( ? [V2x] : ( mem(V2x,ty_2Erealax_2Ereal) & p(ap(V0P,V2x)) ) ) & ? [V3z] : ( mem(V3z,ty_2Erealax_2Ereal) & ! [V4x] : ( mem(V4x,ty_2Erealax_2Ereal) => ( p(ap(V0P,V4x)) => p(ap(ap(c_2Erealax_2Ereal__lt,V4x),V3z)) ) ) ) ) ) => ? [V5s] : ( mem(V5s,ty_2Erealax_2Ereal) & ! [V6y] : ( mem(V6y,ty_2Erealax_2Ereal) => ( ( ? [V7x] : ( mem(V7x,ty_2Erealax_2Ereal) & ( p(ap(V0P,V7x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V6y),V7x)) ) ) ) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V6y),V5s)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__SYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__COMM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__ASSOC,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),V2z) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,V0x)),V0x) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__MUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__0,lemma,(( ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ))).
fof(ax_thm_2Ereal_2Ereal__sub,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V1y)) ) ) )).
fof(ax_thm_2Ereal_2Ereal__lte,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) <=> ( ~~ p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ) )).
fof(ax_thm_2Ereal_2Ereal__gt,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__gt,V0x),V1y)) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) )).
fof(ax_thm_2Ereal_2Ereal__ge,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__ge,V0x),V1y)) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) )).
fof(ax_thm_2Ereal_2Ereal__div,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2E_2F,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Erealax_2Einv,V1y)) ) ) )).
fof(conj_thm_2Ereal_2EREAL__ADD__RID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__RINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__RID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__RINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Erealax_2Einv,V0x)) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__RDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V0x),V2z) ) <=> ( V1y = V2z ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__RADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,V0x),V2z) = ap(ap(c_2Erealax_2Ereal__add,V1y),V2z) ) <=> ( V0x = V1y ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LID__UNIQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = V1y ) <=> ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__RID__UNIQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = V0x ) <=> ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LNEG__UNIQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( V0x = ap(c_2Erealax_2Ereal__neg,V1y) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__RNEG__UNIQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( V1y = ap(c_2Erealax_2Ereal__neg,V0x) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__RZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__LMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,V0x)),V1y) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__RMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Erealax_2Ereal__neg,V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEGNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Ereal__neg,V0x)) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__MUL2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y)) = ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ENTIRE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) | ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__add,V0x),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__RADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NOT__LT,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ~~ p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ANTISYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ~~ ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__GT,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) => ( ~~ p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NOT__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ~~ p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__TOTAL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) | p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LET__TOTAL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) | p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LTE__TOTAL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) | p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V0x)) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LT,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) <=> ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) | ( V0x = V1y ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) <=> ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & ( ~~ ( V0x = V1y ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__IMP__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LTE__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LET__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__ANTISYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) <=> ( V0x = V1y ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LET__ANTISYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ~~ ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LTE__ANTISYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ~~ ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LTE__ANTSYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ~~ ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__LT0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__GT0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Ereal__neg,V0x))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__LE0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__GE0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Ereal__neg,V0x))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__NEGTOTAL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) | ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) | p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Ereal__neg,V0x))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__NEGTOTAL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) | p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Ereal__neg,V0x))) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__MUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__SQUARE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V0x))) ))).
fof(conj_thm_2Ereal_2EREAL__LE__01,lemma,(p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))).
fof(conj_thm_2Ereal_2EREAL__LT__01,lemma,(p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))).
fof(conj_thm_2Ereal_2EREAL__LE__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__add,V0x),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__RADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADD2,lemma,(! [V0w] : ( mem(V0w,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ! [V3z] : ( mem(V3z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0w),V1x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V2y),V3z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0w),V2y)),ap(ap(c_2Erealax_2Ereal__add,V1x),V3z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__ADD2,lemma,(! [V0w] : ( mem(V0w,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ! [V3z] : ( mem(V3z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0w),V1x)) & p(ap(ap(c_2Ereal_2Ereal__lte,V2y),V3z)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0w),V2y)),ap(ap(c_2Erealax_2Ereal__add,V1x),V3z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADDNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V1y),ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V2z)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADDNEG2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V1y))),V2z)) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Erealax_2Ereal__add,V2z),V1y))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADD1,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)),V1y) = V0x ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__ADD2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V1y),ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)) = V0x ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( V0x = V1y ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__DOUBLE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__add,V0x),V0x))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__NEGL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V0x)),V0x)) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__NEGR,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(c_2Erealax_2Ereal__neg,V0x))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__EQ0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ap(c_2Erealax_2Ereal__neg,V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__0,lemma,(( ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__SUB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)) = ap(ap(c_2Ereal_2Ereal__sub,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__LT,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__SUB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V0x) = V1y ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__LMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z) ) <=> ( ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) | ( V1y = V2z ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__RMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z) = ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z) ) <=> ( ( V2z = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) | ( V0x = V1y ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__LDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Ereal_2Ereal__sub,V1y),V2z)) = ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__RDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)),V2z) = ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__EQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(c_2Erealax_2Ereal__neg,V0x) = V1y ) <=> ( V0x = ap(c_2Erealax_2Ereal__neg,V1y) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__MINUS1,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,V0x) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0x) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__NZ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ~~ ( ap(c_2Erealax_2Einv,V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INVINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(c_2Erealax_2Einv,ap(c_2Erealax_2Einv,V0x)) = V0x ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__IMP__NE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) => ( ~~ ( V0x = V1y ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__POS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Einv,V0x))) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LMUL__0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__RMUL__0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__RMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__RMUL__IMP,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LMUL__IMP,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LINV__UNIQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) => ( V0x = ap(c_2Erealax_2Einv,V1y) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__RINV__UNIQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) => ( V1y = ap(c_2Erealax_2Einv,V0x) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__INV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Einv,ap(c_2Erealax_2Einv,V0x)) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__EQ__0,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ap(c_2Erealax_2Einv,V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__INV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Einv,V0x)) = ap(c_2Erealax_2Einv,ap(c_2Erealax_2Ereal__neg,V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__1OVER,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Einv,V0x) = ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__INV__EQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Einv,V0x))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__INV__EQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Einv,V0x))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__INV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Einv,V0x))) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__ADDR,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__ADDL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V1y),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADDR,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADDL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V1y),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Ereal_2Ereal__of__num,ap(c_2Enum_2ESUC,V0n)) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,V0n)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ))).
fof(conj_thm_2Ereal_2EREAL__POS,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Ereal__of__num,V0n))) ))).
fof(conj_thm_2Ereal_2EREAL__LE,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INJ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(c_2Ereal_2Ereal__of__num,V0m) = ap(c_2Ereal_2Ereal__of__num,V1n) ) <=> ( V0m = V1n ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n)) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n)) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV1,lemma,(( ap(c_2Erealax_2Einv,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ))).
fof(conj_thm_2Ereal_2EREAL__OVER1,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2E_2F,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(ap(c_2Ereal_2E_2F,V0x),V0x) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__LZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__NZ,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ~~ ( ap(c_2Ereal_2Ereal__of__num,V0n) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Ereal__of__num,V0n))) ) ))).
fof(conj_thm_2Ereal_2EREAL__NZ__IMP__LT,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ~~ ( V0n = c_2Enum_2E0 ) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Ereal__of__num,V0n))) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__RDIV__0,lemma,(! [V0y] : ( mem(V0y,ty_2Erealax_2Ereal) => ! [V1z] : ( mem(V1z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1z)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V0y),V1z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__RDIV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,V0x),V2z)),ap(ap(c_2Ereal_2E_2F,V1y),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__FRACTION__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1d] : ( mem(V1d,ty_2Erealax_2Ereal) => ( ( ~~ ( V0n = c_2Enum_2E0 ) ) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V1d),ap(c_2Ereal_2Ereal__of__num,V0n)))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1d)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__MULTIPLE,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1d] : ( mem(V1d,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V1d),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0n)),V1d))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1d)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__FRACTION,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1d] : ( mem(V1d,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,V1d),ap(c_2Ereal_2Ereal__of__num,V0n))),V1d)) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1d)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__HALF1,lemma,(! [V0d] : ( mem(V0d,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V0d),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0d)) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__HALF2,lemma,(! [V0d] : ( mem(V0d,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,V0d),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),V0d)) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0d)) ) ))).
fof(conj_thm_2Ereal_2EREAL__DOUBLE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),V0x) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0x) ) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__LMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ~~ ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(ap(c_2Erealax_2Ereal__mul,V1y),ap(ap(c_2Ereal_2E_2F,V0x),V1y)) = V0x ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__RMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ~~ ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,V0x),V1y)),V1y) = V0x ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__HALF__DOUBLE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2E_2F,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__DOWN,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ? [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) & ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__DOWN2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => ? [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) & ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) & ( p(ap(ap(c_2Erealax_2Ereal__lt,V2z),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V2z),V1y)) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__SUB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)),V0x) = ap(c_2Erealax_2Ereal__neg,V1y) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADD__SUB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z)) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2Ereal__sub,V2z),V1y))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__SUB__RADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)),V2z)) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Erealax_2Ereal__add,V2z),V1y))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__SUB__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2Ereal__sub,V1y),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0x),V2z)),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__SUB__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Ereal_2Ereal__sub,V1y),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V2z)),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__SUB__RADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)),V2z)) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Erealax_2Ereal__add,V2z),V1y))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD2__SUB2,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2c] : ( mem(V2c,ty_2Erealax_2Ereal) => ! [V3d] : ( mem(V3d,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__add,V0a),V1b)),ap(ap(c_2Erealax_2Ereal__add,V2c),V3d)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,V0a),V2c)),ap(ap(c_2Ereal_2Ereal__sub,V1b),V3d)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__LZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Erealax_2Ereal__neg,V0x) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__RZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__LET__ADD2,lemma,(! [V0w] : ( mem(V0w,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ! [V3z] : ( mem(V3z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0w),V1x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V2y),V3z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0w),V2y)),ap(ap(c_2Erealax_2Ereal__add,V1x),V3z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LTE__ADD2,lemma,(! [V0w] : ( mem(V0w,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ! [V3z] : ( mem(V3z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0w),V1x)) & p(ap(ap(c_2Ereal_2Ereal__lte,V2y),V3z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0w),V2y)),ap(ap(c_2Erealax_2Ereal__add,V1x),V3z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LET__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LTE__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__MUL2,lemma,(! [V0x1] : ( mem(V0x1,ty_2Erealax_2Ereal) => ! [V1x2] : ( mem(V1x2,ty_2Erealax_2Ereal) => ! [V2y1] : ( mem(V2y1,ty_2Erealax_2Ereal) => ! [V3y2] : ( mem(V3y2,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x1)) & ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2y1)) & ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x1),V1x2)) & p(ap(ap(c_2Erealax_2Ereal__lt,V2y1),V3y2)) ) ) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x1),V2y1)),ap(ap(c_2Erealax_2Ereal__mul,V1x2),V3y2))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__INV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Einv,V1y)),ap(c_2Erealax_2Einv,V0x))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__LNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Erealax_2Ereal__neg,V0x)),V1y) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__RNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),ap(c_2Erealax_2Ereal__neg,V1y)) = ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__NEG2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y)) = ap(ap(c_2Ereal_2Ereal__sub,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__TRIANGLE,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2c] : ( mem(V2c,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,V0a),V1b)),ap(ap(c_2Ereal_2Ereal__sub,V1b),V2c)) = ap(ap(c_2Ereal_2Ereal__sub,V0a),V2c) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__SUB__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( V0x = ap(ap(c_2Ereal_2Ereal__sub,V1y),V2z) ) <=> ( ap(ap(c_2Erealax_2Ereal__add,V0x),V2z) = V1y ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__SUB__RADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y) = V2z ) <=> ( V0x = ap(ap(c_2Erealax_2Ereal__add,V2z),V1y) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__MUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) & ( ~~ ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) => ( ap(c_2Erealax_2Einv,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Einv,V0x)),ap(c_2Erealax_2Einv,V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__RMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__INV2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) & ( ~~ ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) => ( ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Erealax_2Einv,V0x)),ap(c_2Erealax_2Einv,V1y)) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,V1y),V0x)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__SUB2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)) = V1y ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__SUB2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(c_2Erealax_2Ereal__neg,V1y) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MEAN,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) => ? [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) & ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) & p(ap(ap(c_2Erealax_2Ereal__lt,V2z),V1y)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__LMUL2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ( V1y = V2z ) <=> ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__MUL2,lemma,(! [V0x1] : ( mem(V0x1,ty_2Erealax_2Ereal) => ! [V1x2] : ( mem(V1x2,ty_2Erealax_2Ereal) => ! [V2y1] : ( mem(V2y1,ty_2Erealax_2Ereal) => ! [V3y2] : ( mem(V3y2,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x1)) & ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2y1)) & ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x1),V1x2)) & p(ap(ap(c_2Ereal_2Ereal__lte,V2y1),V3y2)) ) ) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V0x1),V2y1)),ap(ap(c_2Erealax_2Ereal__mul,V1x2),V3y2))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LDIV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),ap(ap(c_2Erealax_2Ereal__mul,V2z),V0x))) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,V1y),V0x)),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__RDIV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V1y),V0x)),V2z)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,V1y),ap(ap(c_2Ereal_2E_2F,V2z),V0x))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__DIV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__DIV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__1,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,V0x),V1y)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LMUL__IMP,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__RMUL__IMP,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V1y),V0x)),ap(ap(c_2Erealax_2Ereal__mul,V2z),V0x))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__IMP__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( V0x = V1y ) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__LT1,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Erealax_2Einv,V0x))) ) ))).
fof(conj_thm_2Ereal_2EREAL__POS__NZ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__RMUL__IMP,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ( ~~ ( V2z = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) & ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z) = ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z) ) ) => ( V0x = V1y ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__LMUL__IMP,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) & ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z) ) ) => ( V1y = V2z ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__FACT__NZ,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ~~ ( ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2EFACT,V0n)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__DIFFSQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)) = ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,V0x),V0x)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__POASQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V0x))) <=> ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUMSQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V0x)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V1y)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) & ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(c_2Erealax_2Ereal__neg,V0x) = ap(c_2Erealax_2Ereal__neg,V1y) ) <=> ( V0x = V1y ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__MUL2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1z] : ( mem(V1z,ty_2Erealax_2Ereal) => ( ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) & ( ~~ ( V1z = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2E_2F,V2y),V1z) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1z)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MIDDLE1,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0a),V1b)) => p(ap(ap(c_2Ereal_2Ereal__lte,V0a),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,V0a),V1b)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MIDDLE2,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0a),V1b)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,V0a),V1b)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),V1b)) ) ) ))).
fof(ax_thm_2Ereal_2Eabs,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,V0x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)),V0x),ap(c_2Erealax_2Ereal__neg,V0x)) ) )).
fof(conj_thm_2Ereal_2EABS__ZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ap(c_2Ereal_2Eabs,V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ))).
fof(conj_thm_2Ereal_2EABS__0,lemma,(( ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ))).
fof(conj_thm_2Ereal_2EABS__1,lemma,(( ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ))).
fof(conj_thm_2Ereal_2EABS__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Ereal_2Eabs,V0x) ) ))).
fof(conj_thm_2Ereal_2EABS__TRIANGLE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Ereal_2Eabs,V1y)))) ) ))).
fof(conj_thm_2Ereal_2EABS__TRIANGLE__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Ereal_2Eabs,V1y)))) ) ))).
fof(conj_thm_2Ereal_2EABS__TRIANGLE__SUB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V0x)),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,V1y)),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))))) ) ))).
fof(conj_thm_2Ereal_2EABS__TRIANGLE__LT,lemma,(! [V0e] : ( mem(V0e,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,V1x)),ap(c_2Ereal_2Eabs,V2y))),V0e)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,V1x),V2y))),V0e)) ) ) ) ))).
fof(conj_thm_2Ereal_2EABS__POS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Eabs,V0x))) ))).
fof(conj_thm_2Ereal_2EABS__MUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Ereal_2Eabs,V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EABS__LT__MUL2,lemma,(! [V0w] : ( mem(V0w,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ! [V3z] : ( mem(V3z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0w)),V2y)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V1x)),V3z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,V0w),V1x))),ap(ap(c_2Erealax_2Ereal__mul,V2y),V3z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EABS__SUB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)) = ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EABS__NZ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Eabs,V0x))) ) ))).
fof(conj_thm_2Ereal_2EABS__INV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(c_2Ereal_2Eabs,ap(c_2Erealax_2Einv,V0x)) = ap(c_2Erealax_2Einv,ap(c_2Ereal_2Eabs,V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EABS__ABS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Eabs,V0x)) = ap(c_2Ereal_2Eabs,V0x) ) ))).
fof(conj_thm_2Ereal_2EABS__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(c_2Ereal_2Eabs,V0x))) ))).
fof(conj_thm_2Ereal_2EABS__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ap(c_2Ereal_2Eabs,V0x) = V0x ) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ))).
fof(conj_thm_2Ereal_2EABS__N,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Ereal__of__num,V0n)) = ap(c_2Ereal_2Ereal__of__num,V0n) ) ))).
fof(conj_thm_2Ereal_2EABS__BETWEEN,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2d] : ( mem(V2d,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2d)) & ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Ereal__sub,V0x),V2d)),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),ap(ap(c_2Erealax_2Ereal__add,V0x),V2d))) ) ) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V1y),V0x))),V2d)) ) ) ) ))).
fof(conj_thm_2Ereal_2EABS__BOUND,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2d] : ( mem(V2d,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))),V2d)) => p(ap(ap(c_2Erealax_2Ereal__lt,V1y),ap(ap(c_2Erealax_2Ereal__add,V0x),V2d))) ) ) ) ))).
fof(conj_thm_2Ereal_2EABS__STILLNZ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))),ap(c_2Ereal_2Eabs,V1y))) => ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EABS__CASES,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) | p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Eabs,V0x))) ) ))).
fof(conj_thm_2Ereal_2EABS__BETWEEN1,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V1y),V0x))),ap(ap(c_2Ereal_2Ereal__sub,V2z),V0x))) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EABS__SIGN,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))),V1y)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EABS__SIGN2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))),ap(c_2Erealax_2Ereal__neg,V1y))) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ) ))).
fof(conj_thm_2Ereal_2EABS__DIV,lemma,(! [V0y] : ( mem(V0y,ty_2Erealax_2Ereal) => ( ( ~~ ( V0y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2E_2F,V1x),V0y)) = ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Eabs,V1x)),ap(c_2Ereal_2Eabs,V0y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EABS__CIRCLE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2h] : ( mem(V2h,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V2h)),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Eabs,V1y)),ap(c_2Ereal_2Eabs,V0x)))) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,V0x),V2h))),ap(c_2Ereal_2Eabs,V1y))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__ABS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Ereal_2Eabs,V1y))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)))) ) ))).
fof(conj_thm_2Ereal_2EABS__SUB__ABS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Ereal_2Eabs,V1y)))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)))) ) ))).
fof(conj_thm_2Ereal_2EABS__BETWEEN2,lemma,(! [V0x0] : ( mem(V0x0,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y0] : ( mem(V2y0,ty_2Erealax_2Ereal) => ! [V3y] : ( mem(V3y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x0),V2y0)) & ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V1x),V0x0))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,V2y0),V0x0)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V3y),V2y0))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Ereal__sub,V2y0),V0x0)),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V1x),V3y)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EABS__BOUNDS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1k] : ( mem(V1k,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V0x)),V1k)) <=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V1k)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1k)) ) ) ) ))).
fof(ax_thm_2Ereal_2Epow,axiom, ( ( ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Epow,V0x),c_2Enum_2E0) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) & ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Epow,V1x),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Erealax_2Ereal__mul,V1x),ap(ap(c_2Ereal_2Epow,V1x),V2n)) ) ) ) )).
fof(conj_thm_2Ereal_2EPOW__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Enum_2ESUC,V0n)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EPOW__NZ,lemma,(! [V0c] : ( mem(V0c,ty_2Erealax_2Ereal) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ ( V0c = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ~~ ( ap(ap(c_2Ereal_2Epow,V0c),V1n) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EPOW__INV,lemma,(! [V0c] : ( mem(V0c,ty_2Erealax_2Ereal) => ( ( ~~ ( V0c = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,V0c),V1n)) = ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Einv,V0c)),V1n) ) ) ) ))).
fof(conj_thm_2Ereal_2EPOW__ABS,lemma,(! [V0c] : ( mem(V0c,ty_2Erealax_2Ereal) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Eabs,V0c)),V1n) = ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Epow,V0c),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EPOW__PLUS1,lemma,(! [V0e] : ( mem(V0e,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0e)) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V1n)),V0e))),ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0e)),V1n))) ) ) ))).
fof(conj_thm_2Ereal_2EPOW__ADD,lemma,(! [V0c] : ( mem(V0c,ty_2Erealax_2Ereal) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Epow,V0c),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,V0c),V1m)),ap(ap(c_2Ereal_2Epow,V0c),V2n)) ) ) ) ))).
fof(conj_thm_2Ereal_2EPOW__1,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0x ) ))).
fof(conj_thm_2Ereal_2EPOW__2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(c_2Erealax_2Ereal__mul,V0x),V0x) ) ))).
fof(conj_thm_2Ereal_2EPOW__ONE,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ))).
fof(conj_thm_2Ereal_2EPOW__POS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2Epow,V0x),V1n))) ) ) ))).
fof(conj_thm_2Ereal_2EPOW__LE,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1x)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1x),V2y)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Epow,V1x),V0n)),ap(ap(c_2Ereal_2Epow,V2y),V0n))) ) ) ) ))).
fof(conj_thm_2Ereal_2EPOW__M1,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V0n)) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ))).
fof(conj_thm_2Ereal_2EPOW__MUL,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Epow,ap(ap(c_2Erealax_2Ereal__mul,V1x),V2y)),V0n) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,V1x),V0n)),ap(ap(c_2Ereal_2Epow,V2y),V0n)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__POW2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ))).
fof(conj_thm_2Ereal_2EABS__POW2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) ))).
fof(conj_thm_2Ereal_2EREAL__POW2__ABS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE1__POW2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT1__POW2,conjecture,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) ) ))).
