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Make progress on par epar

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Yiyun Liu 2024-12-25 13:49:45 -05:00
parent a34afed3d5
commit ce29464f08
1 changed files with 21 additions and 2 deletions
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23
theories/fp_red.v
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@ -1215,12 +1215,19 @@ Proof.
sfirstorder inv:ERPar.R use:EPar_Par, RPar_Par. sfirstorder inv:ERPar.R use:EPar_Par, RPar_Par.
Qed. Qed.
Lemma rtc_idem n (a b : Tm n) : rtc (rtc EPar.R) a b -> rtc EPar.R a b.
Proof.
induction 1; hauto l:on use:@relations.rtc_transitive, @rtc_r.
Qed.
Lemma Par_ERPar n (a b : Tm n) : Par.R a b -> rtc ERPar.R a b. Lemma Par_ERPar n (a b : Tm n) : Par.R a b -> rtc ERPar.R a b.
Proof. Proof.
move => h. elim : n a b /h. move => h. elim : n a b /h.
- move => n a0 a1 b0 b1 ha iha hb ihb. - move => n a0 a1 b0 b1 ha iha hb ihb.
apply : rtc_l. apply ERPar.RPar. suff ? : rtc ERPar.R (App (Abs a0) b0) (App (Abs a1) b1).
apply RPar.AppAbs; eauto using RPar.refl. apply : relations.rtc_transitive; eauto.
apply rtc_once. apply ERPar.RPar.
by apply RPar.AppAbs; eauto using RPar.refl.
(* congruence *) (* congruence *)
admit. admit.
- move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc. - move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc.
@ -1248,6 +1255,18 @@ Proof.
- sfirstorder. - sfirstorder.
Admitted. Admitted.
Lemma Pars_ERPar n (a b : Tm n) : rtc Par.R a b -> rtc ERPar.R a b.
Proof.
induction 1; hauto l:on use:Par_ERPar, @relations.rtc_transitive.
Qed.
Lemma Par_ERPar_iff n (a b : Tm n) : rtc Par.R a b <-> rtc ERPar.R a b.
Proof.
split.
sfirstorder use:Pars_ERPar, @relations.rtc_subrel.
sfirstorder use:ERPar_Par, @relations.rtc_subrel.
Qed.
Lemma Par_confluent n (c a1 b1 : Tm n) : Lemma Par_confluent n (c a1 b1 : Tm n) :
rtc Par.R c a1 -> rtc Par.R c a1 ->
rtc Par.R c b1 -> rtc Par.R c b1 ->