Nuprl Lemma : Q-R-glues-split 11,40

es:ES, P:(E), p:(e:E. Dec(P(e))), QR:(EE).
(xy:E. (Q(x,y))  (P(x P(y)))
 (AB:Type, Ia:AbsInterface(A), Ib:AbsInterface(B), f:(E(Ia)B), g1g2:(E(Ib)E),
 (q:(e:E. Dec(((e  Ib)) c P(g1(e)))).
 g1 glues (Ia|p):Q f (Ib|q):R
  g2 glues (Ia|p):Q f (Ib|q):R
  [e.P(g1(e))? g1 : g2] glues Ia:Q f Ib:R
latex


Definitionss = t, t  T, x:AB(x), x:AB(x), ES, a:A fp B(a), x:A  B(x), Type, EqDecider(T), Unit, left + right, IdLnk, Id, EOrderAxioms(Epred?info), f(a), EState(T), Knd, xt(x), x,yt(x;y), kindcase(ka.f(a); l,t.g(l;t) ), Msg(M), type List, , , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), e < e', r  s, P  Q, , b, constant_function(f;A;B), Top, strong-subtype(A;B), AbsInterface(A), let x,y = A in B(x;y), , Dec(P), x(s), P  Q, P  Q, E, P  Q, A, e  X, A c B, t.1, case b of inl(x) => s(x) | inr(y) => t(y), if b then t else f fi , {x:AB(x)} , ff, inr x , tt, inl x , True, x.A(x), Void, x:A.B(x), f  g, f(x)?z, loc(e), vartype(i;x), state@i, State(ds), State(ds), <ab>, x  dom(f), False, {T}, S  T, suptype(ST), g glues Ia:Qa f Ib:Rb, f o g, [Pf : g], x:AB(x), Q ==f== P, Inj(A;B;f), f is Q-R-pre-preserving on P, Q f== P, {I}, X(e), (x  l), T, b | a, a ~ b, a  b, a <p b, a < b, x f y, xLP(x), (xL.P(x)), r < s, q-rel(r;x), Outcome, 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 =!x:TQ(x), InvFuns(A;B;f;g), 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), loc(e), kind(e), SWellFounded(R(x;y)), pred!(e;e'), first(e), pred(e), E(X), (I|p), P & Q, (I|p), X  Y = 0, [f?g], R|P, R1  R2, R1  R2, bool-decider(b), |g|, MonHom(M1,M2), p-filter(f), do-apply(f;x), if p:P then A(p) else B fi , t  ...$L, SQType(T), s ~ t
LemmasQ-R-glues functionality, conditional wf, subtype rel set, bool-decider wf, es-is-interface-co-restrict, and functionality wrt iff, or functionality wrt iff, iff functionality wrt iff, es-is-interface-restrict, es-interface-restrict-conditional, ext-eq weakening, subtype rel weakening, es-interface-conditional, Q-R-glues-conditional2, p-conditional wf, es-interface-disjoint wf, es-interface-restrict-disjoint, kind wf, loc wf, first wf, pred! wf, strongwellfounded wf, iff wf, not wf, decidable wf, squash wf, sq stable from decidable, decidable assert, es-E-interface-restrict, es-E-interface-co-restrict, es-interface-co-restrict wf, es-interface-val wf2, Q-R-pre-preserving wf, es-interface-predicate wf, weak-antecedent-surjection wf, inject wf, Q-R-glues wf, false wf, es-interface-restrict wf, subtype rel function, subtype rel sum, es-is-interface wf, true wf, es-interface wf, btrue wf, bfalse wf, es-E-interface wf, es-E wf, member wf, top wf, constant function wf, assert wf, bool wf, qle wf, cless wf, val-axiom wf, rationals wf, nat wf, Msg wf, kindcase wf, Knd wf, EState wf, EOrderAxioms wf, Id wf, IdLnk wf, unit wf, deq wf, event system wf, subtype rel wf

origin