es:ES, P1, P2:(E), Q1, R1, Q2, R2:(EE), f:({e:E| P1(e)} E).
P1  P2
 Q1  Q2
 R1 => R2
 {f is Q1-R1-pre-preserving on P1  f is Q2-R2-pre-preserving on P2} 

latex

Definitions

ES, t  T, Type, , x:A. B(x), E, x:AB(x), f(a), {x:A| B(x)} , P  Q, s = t, x:A  B(x), x:A. B(x), x f y, R1 => R2, P1  P2, {T}, f is Q-R-pre-preserving on P, R1  R2, P1  P2, t.1, b, let x,y = A in B(x;y), EqDecider(T), Unit, left + right, IdLnk, Id, EOrderAxioms(E; pred?; info), 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, Top, <a, b>

Lemmas

es-E wf, event system wf