Nuprl Lemma : es-interface-history-first 11,40

es:ES, A:Type, X:AbsInterface(A List), e:E.
(first(e))  (es-interface-history(es;X;e) = if e  X then X(e) else [] fi   (A List)) 
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Definitionss = t, x:AB(x), x:AB(x), x:A  B(x), a:A fp B(a), type List, X(e), [], if b then t else f fi , E, {x:AB(x)} , [car / cdr], as @ bs, mapfilter(f;P;L), concat(ll), <ab>, t  T, strong-subtype(A;B), P  Q, ES, Type, AbsInterface(A), b, es-le-before(es;e), es-interface-history(es;X;e), False, A, ff, first(e), , , b, P & Q, P  Q, p =b q, i <z j, i j, (i = j), x =a y, null(as), a < b, f(a), x f y, a < b, [d], eq_atom$n(x;y), q_le(r;s), q_less(a;b), qeq(r;s), a = b, a = b, deq-member(eq;x;L), p  q, p  q, p q, tt, , Unit, left + right, map(f;as), e  X, E(X), let x,y = A in B(x;y), t.1, case b of inl(x) => s(x) | inr(y) => t(y), Top, Void, x:A.B(x), f  g, f(x)?z, loc(e), vartype(i;x), state@i, P  Q, State(ds), State(ds), x  dom(f), {T}, EqDecider(T), IdLnk, Id, EOrderAxioms(Epred?info), EState(T), Knd, xt(x), x,yt(x;y), kindcase(ka.f(a); l,t.g(l;t) ), Msg(M), , , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), e < e', r  s, constant_function(f;A;B), s ~ t
Lemmasappend nil sq, subtype rel function, constant function wf, qle wf, cless wf, val-axiom wf, rationals wf, nat wf, Msg wf, kindcase wf, Knd wf, EState wf, EOrderAxioms wf, Id wf, IdLnk wf, unit wf, deq wf, subtype rel sum, subtype rel list, top wf, es-interface-val wf2, member wf, es-E-interface wf, subtype rel wf, es-is-interface wf, map wf, eqtt to assert, iff transitivity, eqff to assert, assert of bnot, bool wf, bnot wf, not wf, event system wf, es-interface wf, assert wf, append wf, es-E wf, mapfilter wf, concat wf, es-interface-val wf, ifthenelse wf

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