poss:(ES{i}{i'}), R:(possible-event{i:l}(poss)possible-event{i:l}(poss){i'}).
Trans(possible-event{i:l}
Trans(possible-event(poss);a,b.R(a,b))
 (P:(possible-event{i:l}(poss){i'}), e:possible-event{i:l}(poss).
 es-knows{i:l}
 es-knows(poss; R; P; e)
  es-knows{i:l}
  es-knows(poss; R; (e.es-knows{i:l}(poss; R; P; e)); e)) 

latex

Definitions	x:AB(x), x:A. B(x), Trans(T;x,y.E(x;y)), x:A  B(x), PossibleEvent(poss), f(a), t  T, P  Q, Type, , ES, x,y. t(x;y), K(P)@e
Lemmas	trans wf, possible-event wf, event system wf