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Add ERPar

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Yiyun Liu 2024-12-25 13:40:51 -05:00
parent 2b26735fff
commit a34afed3d5
1 changed files with 54 additions and 5 deletions
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59
theories/fp_red.v
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@ -1114,11 +1114,6 @@ Proof.
- qauto rew:db:prov. - qauto rew:db:prov.
Qed. Qed.
Lemma EPar_Par n (a b : Tm n) : EPar.R a b -> Par.R a b.
Proof.
move => h. elim : n a b /h; qauto ctrs:Par.R.
Qed.
Lemma prov_par n (A : Tm n) B a b : prov A B a -> Par.R a b -> prov A B b. Lemma prov_par n (A : Tm n) B a b : prov A B a -> Par.R a b -> prov A B b.
Proof. Proof.
move => + h. move : A B. move => + h. move : A B.
@ -1199,6 +1194,60 @@ Proof.
exists A2, B2. hauto l:on. exists A2, B2. hauto l:on.
Qed. Qed.
Lemma EPar_Par n (a b : Tm n) : EPar.R a b -> Par.R a b.
Proof.
move => h. elim : n a b /h; qauto ctrs:Par.R.
Qed.
Lemma RPar_Par n (a b : Tm n) : RPar.R a b -> Par.R a b.
Proof.
move => h. elim : n a b /h; hauto lq:on ctrs:Par.R.
Qed.
Module ERPar.
Inductive R {n} (a b : Tm n) : Prop :=
| RPar : RPar.R a b -> R a b
| EPar : EPar.R a b -> R a b.
End ERPar.
Lemma ERPar_Par n (a b : Tm n) : ERPar.R a b -> Par.R a b.
Proof.
sfirstorder inv:ERPar.R use:EPar_Par, RPar_Par.
Qed.
Lemma Par_ERPar n (a b : Tm n) : Par.R a b -> rtc ERPar.R a b.
Proof.
move => h. elim : n a b /h.
- move => n a0 a1 b0 b1 ha iha hb ihb.
apply : rtc_l. apply ERPar.RPar.
apply RPar.AppAbs; eauto using RPar.refl.
(* congruence *)
admit.
- move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc.
apply : rtc_l. apply ERPar.RPar.
apply RPar.AppPair; eauto using RPar.refl.
admit.
- move => n p a0 a1 ha iha.
apply : rtc_l. apply ERPar.RPar. apply RPar.ProjAbs; eauto using RPar.refl.
admit.
- move => n p a0 a1 b0 b1 ha iha hb ihb.
apply : rtc_l. apply ERPar.RPar. apply RPar.ProjPair; eauto using RPar.refl.
admit.
- move => n a0 a1 ha iha.
apply : rtc_l. apply ERPar.EPar. apply EPar.AppEta; eauto using EPar.refl.
admit.
- move => n a0 a1 ha iha.
apply : rtc_l. apply ERPar.EPar. apply EPar.PairEta; eauto using EPar.refl.
admit.
- sfirstorder.
- admit.
- admit.
- admit.
- admit.
- admit.
- sfirstorder.
Admitted.
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 ->