es:ES, Q1, Q2, R:(EE), A, B:Type, Ia1, Ia2:AbsInterface(A), Ib1, Ib2:AbsInterface(B),
f:(E([Ia1?Ia2])B), g1:(E(Ib1)E), g2:(E(Ib2)E).
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|{Ia2} f [Ib1?Ib2]:R 

latex

Definitions

x:A  B(x), b, ES, x:AB(x), Type, s = t, Top, Void, x:A.B(x), P  Q, x:A. B(x), <a, b>, left + right, EqDecider(T), Unit, IdLnk, 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, , constant_function(f;A;B), P & Q, let x,y = A in B(x;y), E, True, T, A, X  Y = 0, e  X, P  Q, {x:A| B(x)} , E(X), t.1, if b then t else f fi , P  Q, P  Q, case b of inl(x) => s(x) | inr(y) => t(y), S  T, Inj(A;B;f), f is Q-R-pre-preserving on P, Q = f== P, g glues Ia:Qa f Ib:Rb, {T}, {I}, R|P, R1  R2, suptype(S; T), , [f?g], AbsInterface(A), t  T

Lemmas

Q-R-glues-property, Q-R-glues-conditional, es-interface-conditional, Q-R-glues wf, es-E-interface wf, es-E-interface functionality, p-conditional wf, es-interface-conditional-domain-iff, assert wf, es-is-interface wf, es-interface wf, subtype rel function, subtype rel sum