es:ES, Q1, Q2, R:(EE), A, B:Type, Ia1, Ia2:AbsInterface(A), Ib1, Ib2:AbsInterface(B),
f:(E([Ia1?Ia2])B).
Ia1  Ia2 = 0
 Ib1  Ib2 = 0
 Q-R-glued(es; B; f; Ia1; Q1; Ib1; R)
 Q-R-glued(es; B; f; Ia2; Q2; Ib2; R)
 Q-R-glued(es; B; f; [Ia1?Ia2]; (Q1|{Ia1}  Q2|{Ia2}); [Ib1?Ib2]; R) 

latex

Definitions

x:A  B(x), b, ES, x:AB(x), Type, s = t, A, X  Y = 0, Inj(A;B;f), f is Q-R-pre-preserving on P, Q = f== P, g glues Ia:Qa f Ib:Rb, P  Q, x:A. B(x), Top, S  T, suptype(S; T), x:A. B(x), Q-R-glued(es; Ib_valtype; f; Ia; Qa; Ib; Rb), E, , {I}, R|P, R1  R2, {T}, P  Q, t.1, if b then t else f fi , P  Q, P & Q, P  Q, {x:A| B(x)} , let x,y = A in B(x;y), left + right, e  X, , f(a), EState(T), Id, , pred!(e;e'), SWellFounded(R(x;y)), loc(e), <a, b>, constant_function(f;A;B), kindcase(k; a.f(a); l,t.g(l;t) ), Knd, e < e', r  s, val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), , Unit, Msg(M), type List, IdLnk, EOrderAxioms(E; pred?; info), EqDecider(T), [f?g], E(X), AbsInterface(A), t  T, X(e), bool-decider(b), x.A(x), [P? f : g]

Lemmas

Q-R-glues-conditional, conditional wf-interface2, weak-antecedent-surjection wf, Q-R-pre-preserving wf, inject wf, es-E wf, val-axiom wf, constant function wf, assert wf, p-conditional wf, es-interface-conditional, es-interface-conditional-domain-iff, Q-R-glues wf, Q-R-glued wf, Q-R-glues-property, es-E-interface wf, subtype rel function