Nuprl Lemma : es-E-interfaces-strong-subtype 11,40

es:ES, XY:AbsInterface(Top). (E(Xr E(Y))  strong-subtype(E(X);E(Y)) 
latex


Definitionss = t, t  T, x:AB(x), x:AB(x), E(X), strong-subtype(A;B), ES, AbsInterface(A), x:A  B(x), b, left + right, Top, P  Q, P  Q, Type, , P & Q, P  Q, e  X, E, {x:AB(x)} , x:AB(x), a:A fp B(a), let x,y = A in B(x;y), t.1, case b of inl(x) => s(x) | inr(y) => t(y), if b then t else f fi , , True, T, Dec(P), b | a, a ~ b, a  b, a <p b, a < b, A c B, f(a), x f y, xLP(x), (xL.P(x)), r  s, r < s, q-rel(r;x), Outcome, (x  l), l_disjoint(T;l1;l2), (e <loc e'), e loc e' , (e < e'), e c e', e<e'.P(e), ee'.P(e), e<e'P(e), ee'.P(e), 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), SqStable(P), A, a =!x:TQ(x), InvFuns(A;B;f;g), Inj(A;B;f), IsEqFun(T;eq), Refl(T;x,y.E(x;y)), Sym(T;x,y.E(x;y)), Trans(T;x,y.E(x;y)), AntiSym(T;x,y.R(x;y)), Connex(T;x,y.R(x;y)), CoPrime(a,b), Ident(T;op;id), Assoc(T;op), Comm(T;op), Inverse(T;op;id;inv), BiLinear(T;pl;tm), IsBilinear(A;B;C;+a;+b;+c;f), IsAction(A;x;e;S;f), Dist1op2opLR(A;1op;2op), fun_thru_1op(A;B;opa;opb;f), FunThru2op(A;B;opa;opb;f), Cancel(T;S;op), monot(T;x,y.R(x;y);f), IsMonoid(T;op;id), IsGroup(T;op;id;inv), IsMonHom{M1,M2}(f), a  b, IsIntegDom(r), IsPrimeIdeal(R;P), f  g, type List, f(x)?z, Unit, ff, inr x , tt, inl x , False, <ab>, IdLnk, Knd, Id, locl(a), loc(e), vartype(i;x), state@i, EqDecider(T), State(ds), State(ds), xt(x)
Lemmasfalse wf, subtype rel set, true wf, btrue wf, bfalse wf, unit wf, bool wf, sq stable from decidable, decidable assert, member wf, es-E wf, assert wf, es-is-interface wf, event system wf, top wf, es-interface wf, iff wf, rev implies wf, subtype rel wf, es-E-interface wf, strong-subtype wf

origin