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Yiyun Liu 2024-12-25 18:09:20 -05:00
parent efc3662f31
commit 22c7eff954
1 changed files with 18 additions and 2 deletions
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theories/fp_red.v
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@ -1296,6 +1296,12 @@ Module ERPar.
- sfirstorder use:EPar.PairCong, @rtc_once.
Qed.
Lemma renaming n m (a b : Tm n) (ξ : fin n -> fin m) :
R a b -> R (ren_Tm ξ a) (ren_Tm ξ b).
Proof.
sfirstorder use:EPar.renaming, RPar.renaming.
Qed.
End ERPar.
Hint Resolve ERPar.AppCong ERPar.refl ERPar.AbsCong ERPar.PairCong ERPar.ProjCong ERPar.PiCong : erpar.
@ -1335,6 +1341,15 @@ Module ERPars.
rtc ERPar.R (Pi a0 b0) (Pi a1 b1).
Proof. solve_s. Qed.
Lemma renaming n (a0 a1 : Tm n) m (ξ : fin n -> fin m) :
rtc ERPar.R a0 a1 ->
rtc ERPar.R (ren_Tm ξ a0) (ren_Tm ξ a1).
Proof.
induction 1.
- apply rtc_refl.
- eauto using ERPar.renaming, rtc_l.
Qed.
End ERPars.
Lemma ERPar_Par n (a b : Tm n) : ERPar.R a b -> Par.R a b.
@ -1368,7 +1383,8 @@ Proof.
hauto lq:on.
- move => n a0 a1 ha iha.
apply : rtc_l. apply ERPar.EPar. apply EPar.AppEta; eauto using EPar.refl.
admit.
hauto lq:on ctrs:rtc
use:ERPars.AppCong, ERPars.AbsCong, ERPars.renaming.
- move => n a0 a1 ha iha.
apply : rtc_l. apply ERPar.EPar. apply EPar.PairEta; eauto using EPar.refl.
sfirstorder use:ERPars.PairCong, ERPars.ProjCong.
@ -1379,7 +1395,7 @@ Proof.
- sfirstorder use:ERPars.ProjCong.
- sfirstorder use:ERPars.PiCong.
- sfirstorder.
Admitted.
Qed.
Lemma Pars_ERPar n (a b : Tm n) : rtc Par.R a b -> rtc ERPar.R a b.
Proof.