diff --git a/theories/relations.v b/theories/relations.v index 80e6af26f1de31e6a05a2085b54421ad0a21281d..fdadac438988e9b2efad90480765211cad0b3b1f 100644 --- a/theories/relations.v +++ b/theories/relations.v @@ -280,6 +280,10 @@ Section properties. Lemma wn_step_rtc x y : wn R y → rtc R x y → wn R x. Proof. induction 2; eauto using wn_step. Qed. + (** The following theorem requires that [red R] is decidable. The intuition + for this requirement is that [wn R] is a very "positive" statement as it + points out a particular trace. In contrast, [sn R] just says "this also holds + for all successors", there is no "data"/"trace" there. *) Lemma sn_wn `{!∀ y, Decision (red R y)} x : sn R x → wn R x. Proof. induction 1 as [x _ IH]. destruct (decide (red R x)) as [[x' ?]|?].