es:ES, P:(E), p:(e:E. Dec(P(e))), Q, R:(EE), A, B:Type, Ia:AbsInterface(A),
Ib:AbsInterface(B), f:(E(Ia)B), g:(E(Ib)E), q:(e:E. Dec(((e  Ib)) c P(g(e)))).
(e:E. ((e  Ib))  P(g(e)))
 g glues (Ia|p):Q f (Ib|q):R
 g glues (Ia|p):Q f Ib:R 

latex

Definitions

t  T, ES, Type, EqDecider(T), Unit, left + right, x:AB(x), IdLnk, x:A  B(x), Id, EOrderAxioms(E; pred?; info), f(a), EState(T), Knd, kindcase(k; a.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, x:A. B(x), , b, constant_function(f;A;B), P & Q, Top, let x,y = A in B(x;y), A, x(s), Dec(P), AbsInterface(A), t.1, E, if b then t else f fi , s = t, {x:A| B(x)} , E(X), , ff, tt, case b of inl(x) => s(x) | inr(y) => t(y), True, A c B, x.A(x), e  X, x. t(x), Inj(A;B;f), f is Q-R-pre-preserving on P, Q = f== P, g glues Ia:Qa f Ib:Rb, T, (I|p), S  T, suptype(S; T), False, pred!(e;e'), SWellFounded(R(x;y)), Void, x:A.B(x), first(e), loc(e), <a, b>, x,y. t(x;y), kind(e), {I}, X(e)

Lemmas

weak-antecedent-surjection wf, Q-R-pre-preserving wf, inject wf, es-interface-val wf, es-interface-predicate wf, Q-R-glues wf, squash wf, es-interface wf, event system wf, subtype rel sum, decidable wf, es-E wf, deq wf, EOrderAxioms wf, Id wf, kind wf, loc wf, Msg wf, nat wf, val-axiom wf, cless wf, qle wf, bool wf, rationals wf, Knd wf, kindcase wf, IdLnk wf, EState wf, constant function wf, not wf, first wf, top wf, unit wf, Q-R-glues-trivial-restrict, true wf, false wf, es-interface-restrict wf, subtype rel function, es-E-interface wf, es-E-interface-restrict, assert wf, es-is-interface wf, btrue wf, bfalse wf