End CaseEQ.
Section CaseEXT.
Section EXTEQ.

Lemma exteq: forall
(SimExt12 : Forward_simulation_extends Sem1 Sem2 g1 g2 epts12)
(SimEq23 : Forward_simulation_equals Sem2 Sem3 g2 g3 epts23),
Forward_simulation_extends Sem1 Sem3 g1 g3 epts13.