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

es:ES, Q1Q2R:(EE), AB:Type, Ia1Ia2:AbsInterface(A), Ib1Ib2:AbsInterface(B),
f:(E([Ia1?Ia2])B), g1:(E(Ib1)E(Ia1)), g2:(E(Ib2)E(Ia2)).
Ia1  Ia2 = 0
 Ib1  Ib2 = 0
 g1 glues Ia1:Q1 f Ib1:R
 g2 glues Ia2:Q2 f Ib2:R
 [{Ib1}? g1 : g2] glues [Ia1?Ia2]:Q1|{Ia1 Q2|{Ia2f [Ib1?Ib2]:R 
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Definitionss = t, ES, Type, , x:AB(x), Top, x:A  B(x), b, left + right, E, , Void, x:A.B(x), {x:AB(x)} , P  Q, x:AB(x), E(X), X  Y = 0, False, A, P  Q, P & Q, P  Q, type List, f(x)?z, strong-subtype(A;B), a:A fp B(a), S  T, e  X, P  Q, 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 , EqDecider(T), Unit, 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), , , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), e < e', r  s, constant_function(f;A;B), loc(e), kind(e), (x  l), x  dom(f), True, T, Dec(P), x:AB(x), b | a, a ~ b, a  b, a <p b, a < b, A c B, x f y, xLP(x), (xL.P(x)), y is f*(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), 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, loc(e), vartype(i;x), state@i, State(ds), State(ds), g glues Ia:Qa f Ib:Rb, <ab>, Q ==f== P, f is Q-R-pre-preserving on P, Q f== P, {T}, {I}, R|P, R1  R2, suptype(ST), bool-decider(b), x.A(x), [Pf : g], [f?g], AbsInterface(A), t  T, X(e), P1  P2, , P1  P2, R1  R2, tt, ff, R1  R2, if p:P then A(p) else B fi , SQType(T), s ~ t, inr x , inl x , b
Lemmasbnot wf, assert of bnot, eqff to assert, iff transitivity, eqtt to assert, iff wf, rev implies wf, es-interface-val-conditional, assert of bor, es-interface-conditional-domain, conditional wf2, es-interface-conditional-domain-member, decidable wf, rel-restriction-implies, ext-eq weakening, subtype rel weakening, Q-R-pre-preserving-conditional, subtype rel sum, predicate equivalent weakening, false wf, rel or idempotent, bfalse wf, btrue wf, subtype rel set, subtype rel function, not wf, conditional wf, rel equivalent weakening, rel equivalent inversion, rel implies weakening, predicate implies weakening, Q-R-pre-preserving functionality wrt implies, bool-decider wf, weak-antecedent-surjection-conditional2, conditional wf-interface, predicate or wf, es-interface-conditional-predicate-equivalent, weak-antecedent-surjection functionality wrt pred equiv, weak-antecedent-function wf, es-interface-val wf, es-interface-conditional, es-interface-disjoint wf, Q-R-glues wf, inject wf, rel-restriction wf, rel or wf, Q-R-pre-preserving wf, es-interface-predicate wf, weak-antecedent-surjection wf, true wf, squash wf, sq stable from decidable, decidable assert, es-E-interface functionality, p-conditional wf, constant function 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, es-interface-conditional-domain-iff, assert wf, es-is-interface wf, es-E wf, es-E-interface wf, es-E-interface-subtype rel, member wf, es-interface wf, es-interface-subtype rel, top wf, subtype rel wf

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