Commit fa3141d2 authored by Ralf Jung's avatar Ralf Jung
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add lemma about readucing ectxi-languages

parent 6f093ff9
......@@ -86,4 +86,17 @@ Section ectxi_language.
Global Instance ectxi_lang_ctx_item Ki :
LanguageCtx (ectx_lang expr) (fill_item Ki).
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)
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.
End ectxi_language.
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