es:ES, P:(E), R:(EE), f:({e:E| P(e)} E). f is R-pre-preserving on P   

latex

Definitions

ES, t  T, f(a), EState(T), Id, , x:AB(x), x:A. B(x), pred!(e;e'), SWellFounded(R(x;y)), Unit, Void, x:A.B(x), Top, S  T, left + right, Type, suptype(S; T), first(e), b, A, loc(e), <a, b>, s = t, P  Q, constant_function(f;A;B), IdLnk, x,y. t(x;y), x. t(x), kindcase(k; a.f(a); l,t.g(l;t) ), Knd, x:A  B(x), P & Q, , r  s, e < e', val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), , Msg(M), type List, kind(e), EOrderAxioms(E; pred?; info), EqDecider(T), , E, {x:A| B(x)} , f is Q-R-pre-preserving on P, f is R-pre-preserving on P

Lemmas

Q-R-pre-preserving wf, es-E wf, deq wf, EOrderAxioms wf, Id wf, kind wf, loc wf, Msg wf, nat wf, val-axiom wf, cless wf, qle wf, bool wf, rationals wf, Knd wf, kindcase wf, IdLnk wf, EState wf, constant function wf, not wf, assert wf, first wf, top wf, unit wf, event system wf