Nuprl Lemma : es-fix-equal-E-interface 11,40

es:ES, X:AbsInterface(Top), f:(E(X)E(X)).
(x:E(X). f(x) c x (e:E(X). (f**(e) = e (f(e) = e  E)) 
latex


DefinitionsP  Q, P  Q, e  X, (e < e'), e c e', {x:AB(x)} , AbsInterface(A), E(X), E, P & Q, xt(x), x.A(x), pred(e), <ab>, A, first(e), suptype(ST), S  T, Top, x:A.B(x), Void, x,yt(x;y), pred!(e;e'), , SWellFounded(R(x;y)), constant_function(f;A;B), b, , e < e', r  s, val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), , type List, Msg(M), kind(e), loc(e), Knd, kindcase(ka.f(a); l,t.g(l;t) ), EOrderAxioms(Epred?info), x:A  B(x), IdLnk, left + right, Unit, EqDecider(T), Type, P  Q, strong-subtype(A;B), , Id, f(a), a:A fp B(a), EState(T), ES, x:AB(x), x:AB(x), t  T, s = t, A c B, (x  l), locl(a), True, T, if b then t else f fi , case b of inl(x) => s(x) | inr(y) => t(y), P  Q, let x,y = A in B(x;y), f**(e), y=f*(x) via L, hd(l), x:AB(x), y is f*(x), , p q, p  q, p  q, e = e', deq-member(eq;x;L), a = b, a = b, qeq(r;s), q_less(a;b), q_le(r;s), eq_atom$n(x;y), [d], =, =, a < b, =, x f y, , a < b, null(as), x =a y, (i = j), i j, i <z j, p =b q, tt, b, ff, eqof(d), es-eq(es), False, f**(x), f(x)?z, f  g, IsPrimeIdeal(R;P), IsIntegDom(r), a  b, IsMonHom{M1,M2}(f), IsGroup(T;op;id;inv), IsMonoid(T;op;id), monot(T;x,y.R(x;y);f), Cancel(T;S;op), FunThru2op(A;B;opa;opb;f), fun_thru_1op(A;B;opa;opb;f), Dist1op2opLR(A;1op;2op), IsAction(A;x;e;S;f), IsBilinear(A;B;C;+a;+b;+c;f), BiLinear(T;pl;tm), Inverse(T;op;id;inv), Comm(T;op), Assoc(T;op), Ident(T;op;id), CoPrime(a,b), Connex(T;x,y.R(x;y)), AntiSym(T;x,y.R(x;y)), Trans(T;x,y.E(x;y)), Sym(T;x,y.E(x;y)), Refl(T;x,y.E(x;y)), IsEqFun(T;eq), Inj(A;B;f), InvFuns(A;B;f;g), a =!x:TQ(x), SqStable(P), e(e1,e2].P(e), e[e1,e2].P(e), e[e1,e2].P(e), e[e1,e2).P(e), e[e1,e2).P(e), ee'.P(e), e<e'P(e), ee'.P(e), e<e'.P(e), e loc e' , (e <loc e'), l_disjoint(T;l1;l2), Outcome, q-rel(r;x), r < s, (xL.P(x)), xLP(x), a < b, a <p b, a  b, a ~ b, b | a, Dec(P), t.1, inl x , inr x 
Lemmasbfalse wf, btrue wf, false wf, true wf, decidable assert, sq stable from decidable, es-E-interface-strong-subtype, strong-subtype wf, strong-subtype-deq-subtype, deq property, bnot wf, es-eq wf, eqof wf, assert of bnot, eqff to assert, iff transitivity, eqtt to assert, es-fix-equal, rev implies wf, iff wf, es-fix property, event system wf, subtype rel wf, EState wf, Id wf, rationals wf, member wf, strongwellfounded wf, pred! wf, unit wf, top wf, first wf, assert wf, not wf, loc wf, constant function wf, IdLnk wf, kindcase wf, Knd wf, bool wf, qle wf, cless wf, val-axiom wf, nat wf, Msg wf, kind wf, EOrderAxioms wf, deq wf, es-E wf, es-E-interface wf, es-E-interface-subtype rel, es-causle wf, es-causl wf, es-is-interface wf, es-interface wf

origin