es:ES, A, B, C:Type, Ia:AbsInterface(A), Ib:AbsInterface(B), Ic:AbsInterface(C), f1:(E(Ia)B),
f2:(BC).
(glued(es; B; f1; Ia; Ib) & glued(es; C; (e.f2(Ib(e))); Ib; Ic))
 glued(es; C; (f2 o f1); Ia; Ic) 

latex

Definitions

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

Lemmas

glue-composes, compose wf, glues-property, glues wf, glued wf, es-interface-val wf2, es-interface wf, es-E-interface wf, es-is-interface wf, es-E wf, deq wf, EOrderAxioms wf, kind wf, Msg wf, nat wf, val-axiom wf, cless wf, qle wf, bool wf, Knd wf, kindcase wf, IdLnk wf, constant function wf, loc wf, not wf, assert wf, first wf, top wf, unit wf, pred! wf, strongwellfounded wf, member wf, rationals wf, Id wf, EState wf, subtype rel wf, event system wf