es:ES, A, B:Type, Ia:AbsInterface(A), Ib:AbsInterface(B), f:(E(Ia)B), g:(E(Ib)E).
glues(es; B; g; f; Ia; Ib)  (g  E(Ib)E(Ia)) 

latex

Definitions

f(a), EState(T), Id, , x:AB(x), t  T, x:A. B(x), pred!(e;e'), SWellFounded(R(x;y)), Unit, Void, x:A.B(x), Top, S  T, left + right, Type, suptype(S; T), first(e), b, A, loc(e), <a, b>, s = t, P  Q, constant_function(f;A;B), IdLnk, x,y. t(x;y), x. t(x), kindcase(k; a.f(a); l,t.g(l;t) ), Knd, x:A  B(x), P & Q, , r  s, e < e', val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), , Msg(M), type List, kind(e), EOrderAxioms(E; pred?; info), EqDecider(T), ES, E, AbsInterface(A), e  X, {x:A| B(x)} , E(X), let x,y = A in B(x;y), glues(es; B; g; f; Ia; Ib), e loc e' , x.A(x), Inj(A;B;f), f is Q-R-pre-preserving on P, Q = f== P, g glues Ia:Qa f Ib:Rb

Lemmas

Q-R-glues-property, es-le wf, es-E-interface wf, es-is-interface 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, assert wf, first wf, top wf, unit wf