Nuprl Lemma : es-interface-sum-cases 11,40

es:ES, X:AbsInterface(), e:E.
e(X)
=
if e  X
ifthen if e  prior(X) then prior(X)(e)(X) else 0 fi +X(e)
if e  prior(X) then prior(X)(e)(X) else 0 fi 
  
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Definitionstt, ff, p q, p  q, p  q, b, e = e', deq-member(eq;x;L), a = b, a = b, qeq(r;s), q_less(a;b), q_le(r;s), eq_atom$n(x;y), [d], a < b, x f y, a < b, null(as), x =a y, (i = j), i j, i <z j, p =b q, X(e), E(X), f(x)?z, P  Q, P  Q, {x:AB(x)} , prior(X), e  X, case b of inl(x) => s(x) | inr(y) => t(y), False, e(X), t.1, local-state(f;base;X;e), n+m, if b then t else f fi , #$n, let x,y = A in B(x;y), AbsInterface(A), E, , P & Q, xt(x), x.A(x), pred(e), <ab>, A, first(e), suptype(ST), S  T, Top, x:A.B(x), Void, x,yt(x;y), pred!(e;e'), , SWellFounded(R(x;y)), constant_function(f;A;B), b, , e < e', r  s, val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), , type List, Msg(M), kind(e), loc(e), Knd, kindcase(ka.f(a); l,t.g(l;t) ), EOrderAxioms(Epred?info), x:A  B(x), IdLnk, left + right, Unit, EqDecider(T), Type, P  Q, strong-subtype(A;B), , Id, f(a), a:A fp B(a), EState(T), ES, x:AB(x), x:AB(x), t  T, s = t
Lemmasevent system wf, subtype rel wf, EState wf, Id wf, rationals wf, member wf, strongwellfounded wf, pred! wf, unit wf, top wf, first wf, assert wf, not wf, loc wf, constant function wf, IdLnk wf, kindcase wf, Knd wf, bool wf, qle wf, cless wf, val-axiom wf, nat wf, Msg wf, kind wf, EOrderAxioms wf, deq wf, es-E wf, ifthenelse wf, es-interface-local-state wf, es-interface wf, es-interface-subtype rel, es-E-interface-subtype rel, es-E-interface wf, es-prior-interface wf, es-interface-val wf, es-interface-val wf2, es-is-interface wf, assert of bnot, eqff to assert, iff transitivity, eqtt to assert, es-interface-local-state-cases, rev implies wf, iff wf

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