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Yiyun Liu 2025-03-10 15:35:43 -04:00
parent 849d19708e
commit 4cbd2ac0fd
2 changed files with 22 additions and 12 deletions
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16
theories/algorithmic.v
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@ -737,8 +737,6 @@ Lemma A_Conf' a b :
algo_dom_r a b.
Proof.
move => ha hb.
have {}ha : HRed.nf a by sfirstorder use:hf_no_hred, hne_no_hred.
have {}hb : HRed.nf b by sfirstorder use:hf_no_hred, hne_no_hred.
move => ?.
apply A_NfNf.
by apply A_Conf.
@ -1234,6 +1232,11 @@ Qed.
Lemma algo_dom_r_algo_dom : forall a b, HRed.nf a -> HRed.nf b -> algo_dom_r a b -> algo_dom a b.
Proof. hauto l:on use:algo_dom_r_inv, hreds_nf_refl. Qed.
Lemma algo_dom_algo_dom_neu : forall a b, ishne a -> ishne b -> algo_dom a b -> algo_dom_neu a b \/ tm_conf a b.
Proof.
inversion 3; subst => //=; tauto.
Qed.
Lemma term_metric_algo_dom : forall k a b, term_metric k a b -> algo_dom_r a b.
Proof.
move => [:hneL].
@ -1268,9 +1271,12 @@ Proof.
case : b hfa hfb h => //=; case a => //=; eauto 5 using A_Conf' with adom.
+ move => a0 b0 a1 b1 nfa0 nfa1.
move /term_metric_app /(_ nfa0 nfa1) => [j][hj][ha]hb.
apply A_NfNf. apply A_AppCong => //; eauto.
have {}nfa0 : HRed.nf a0 by sfirstorder use:hne_no_hred.
have {}nfb0 : HRed.nf a1 by sfirstorder use:hne_no_hred.
apply A_NfNf.
(* apply A_NfNf. apply A_NeuNeu. apply A_AppCong => //; eauto. *)
have nfa0' : HRed.nf a0 by sfirstorder use:hne_no_hred.
have nfb0' : HRed.nf a1 by sfirstorder use:hne_no_hred.
have ha0 : algo_dom a0 a1 by eauto using algo_dom_r_algo_dom.
apply A_Conf. admit. admit. rewrite /tm_conf. simpl.
eauto using algo_dom_r_algo_dom.
+ move => p0 A0 p1 A1 neA0 neA1.
have {}nfa0 : HRed.nf A0 by sfirstorder use:hne_no_hred.