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Finish SE_Pair

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Yiyun Liu 2025-02-06 15:20:40 -05:00
parent 435c0e037e
commit 733e86c611
2 changed files with 78 additions and 22 deletions
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26
theories/fp_red.v
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@ -1756,6 +1756,24 @@ Module REReds.
induction 1; hauto lq:on ctrs:rtc use:RERed.substing.
Qed.
Lemma cong_up n m (ρ0 ρ1 : fin n -> PTm m) :
(forall i, rtc RERed.R (ρ0 i) (ρ1 i)) ->
(forall i, rtc RERed.R (up_PTm_PTm ρ0 i) (up_PTm_PTm ρ1 i)).
Proof. move => h i. destruct i as [i|].
simpl. rewrite /funcomp.
substify. by apply substing.
apply rtc_refl.
Qed.
Lemma cong n m (a : PTm n) (ρ0 ρ1 : fin n -> PTm m) :
(forall i, rtc RERed.R (ρ0 i) (ρ1 i)) ->
rtc RERed.R (subst_PTm ρ0 a) (subst_PTm ρ1 a).
Proof.
move : m ρ0 ρ1. elim : n / a;
eauto using AppCong, AbsCong, BindCong, ProjCong, PairCong, cong_up, rtc_refl.
Qed.
End REReds.
Module LoRed.
@ -2259,4 +2277,12 @@ Module DJoin.
hauto lq:on rew:off ctrs:rtc unfold:R use:REReds.substing.
Qed.
Lemma cong n m (a : PTm (S n)) c d (ρ : fin n -> PTm m) :
R c d -> R (subst_PTm (scons c ρ) a) (subst_PTm (scons d ρ) a).
Proof.
rewrite /R. move => [cd [h0 h1]].
exists (subst_PTm (scons cd ρ) a).
hauto q:on ctrs:rtc inv:option use:REReds.cong.
Qed.
End DJoin.