Commit 2407263c authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Optimize proof of step_is_head.

parent 05c16632
......@@ -88,15 +88,14 @@ Section ectxi_language.
Proof. change (LanguageCtx _ (fill [Ki])). apply _. Qed.
Lemma step_is_head K e σ :
to_val e = None ( Ki K e', e = fill (Ki::K) e' ¬head_reducible e' σ)
to_val e = None
( Ki K e', e = fill (Ki :: K) e' ¬head_reducible e' σ)
reducible (fill K e) σ head_reducible e σ.
intros Hnonval Hnondecomp (e'&σ''&ef&Hstep).
change fill with ectx_language.fill in Hstep.
apply fill_step_inv in Hstep; last done. destruct Hstep as (e2'&_&Hstep).
clear K. destruct Hstep as [K e1' e2'' ?? Hstep]. subst.
destruct K as [|K0 K].
{ rewrite fill_empty in Hnonval. subst. eexists; eauto. }
exfalso. eapply Hnondecomp; first done. do 3 eexists. done.
apply fill_step_inv in Hstep as (e2'&_&Hstep); last done.
clear K. destruct Hstep as [[|Ki K] e1' e2'' -> -> Hstep]; [red; eauto|].
destruct (Hnondecomp Ki K e1'); unfold head_reducible; eauto.
End ectxi_language.
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