Definition evalDet_equiv(A : Set)(c1 c2 : Comp A) :=
  (forall s y, evalDet c1 s y <-> evalDet c2 s y).

Theorem evalDet_steps_bind_eof_inv_h : forall (A : Set)(x y : comp_state A), evalDet_steps x y -> forall (B : Set)(c1 : Comp B)(c2 : B -> Comp A) s, x = (cs_more (Bind c1 c2) s) -> y = (@cs_eof A) -> evalDet_steps (cs_more c1 s) (@cs_eof B) \/ exists b s', evalDet_steps (cs_more c1 s) (cs_done b s') /\ evalDet_steps (cs_more (c2 b) s') (@cs_eof A).