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logrelnew #1

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yiyunliu merged 18 commits from logrelnew into master 2025-02-06 00:26:46 -05:00
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2 changed files with 19 additions and 2 deletions
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17
theories/fp_red.v
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@ -1707,6 +1707,15 @@ Module REReds.
elim : u C / hu; sauto lq:on rew:off.
Qed.
Lemma univ_inv n i C :
rtc (@RERed.R n) (PUniv i) C ->
C = PUniv i.
Proof.
move E : (PUniv i) => u hu.
move : i E. elim : u C / hu=>//=.
hauto lq:on rew:off ctrs:rtc inv:RERed.R.
Qed.
End REReds.
Module LoRed.
@ -2139,6 +2148,12 @@ Module DJoin.
hauto lq:on rew:off use:REReds.bind_inv.
Qed.
Lemma univ_inj n i j :
@R n (PUniv i) (PUniv j) -> i = j.
Proof.
sauto lq:on rew:off use:REReds.univ_inv.
Qed.
Lemma FromRRed0 n (a b : PTm n) :
RRed.R a b -> R a b.
Proof.
@ -2151,4 +2166,6 @@ Module DJoin.
hauto lq:on ctrs:rtc use:RERed.FromBeta unfold:R.
Qed.
End DJoin.

4
theories/logrel.v
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@ -370,7 +370,7 @@ Proof.
hauto l:on use: DJoin.sne_univ_noconf, DJoin.bind_univ_noconf, DJoin.symmetric.
case : H h1 h => //=.
move => j' hPB h _.
have {}h : j' = j by admit. subst.
have {}h : j' = j by hauto lq:on use: DJoin.univ_inj. subst.
hauto lq:on use:InterpUniv_Univ_inv.
- move => i A A0 PA hr hPA ihPA B PB hPB hAB.
have /DJoin.symmetric ? : DJoin.R A A0 by hauto lq:on rew:off ctrs:rtc use:DJoin.FromRedSNs.
@ -378,4 +378,4 @@ Proof.
have ? : SN A by eauto using N_Exp.
have : DJoin.R A0 B by eauto using DJoin.transitive.
eauto.
Admitted.
Qed.