es:ES, Qa, Rb, Sc:(EE), A, B, C:Type, Ia:AbsInterface(A), Ib:AbsInterface(B),
Ic:AbsInterface(C), f1:(E(Ia)B), f2:(BC), g1:(E(Ib)E), g2:(E(Ic)E).
(g1 glues Ia:Qa f1 Ib:Rb & g2 glues Ib:Rb e.f2(Ib(e)) Ic:Sc)
 g1 o g2 glues Ia:Qa f2 o f1 Ic:Sc 

latex

Definitions

P & Q, t  T, True, T, x:A. B(x), P  Q, b, x:AB(x), SqStable(P), {x:A| B(x)} , E(X), x:A  B(x), ES, Type, AbsInterface(A), s = t, 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), t.1, E, X(e), f(a), x.A(x), Top, S  T, suptype(S; T), EqDecider(T), Unit, left + right, IdLnk, Id, EOrderAxioms(E; pred?; info), 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, , constant_function(f;A;B), e  X, pred!(e;e'), SWellFounded(R(x;y)), loc(e), <a, b>, A, {I}, , A c B

Lemmas

weak-antecedent-surjection wf, Q-R-pre-preserving wf, inject wf, Q-R-glues wf, val-axiom wf, constant function wf, Q-R-glues-composes, assert wf, es-is-interface wf, subtype rel function, subtype rel weakening, ext-eq weakening, Q-R-glues-property, es-E-interface wf, es-interface-val wf, sq stable from decidable, decidable assert