End InductiveInv.
(* Proving by the rule of consequence *)
Definition conseq (W : world) A this (e : DT this W A) (s : spec A) :=
forall i, s.1 i -> verify i e (s.2 i).

(* The specification implies itself *)
Lemma conseq_refl (W : world) A this (e : DT this W A) :
conseq e (spec_of e).