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Recover diamond property

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Yiyun Liu 2025-01-12 23:49:31 -05:00
parent 4d40dcf8d4
commit 2de1e5fa74
1 changed files with 43 additions and 6 deletions
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49
theories/fp_red.v
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@ -2409,6 +2409,36 @@ Lemma Univ_EPar' n i (u : Tm n) :
- hauto l:on ctrs:OExp.R. - hauto l:on ctrs:OExp.R.
Qed. Qed.
Lemma BVal_EPar' n i (u : Tm n) :
EPar.R (BVal i) u ->
rtc OExp.R (BVal i) u.
move E : (BVal i) => t h.
move : E. elim : n t u /h => //=.
- move => n a0 a1 h ih ?. subst.
specialize ih with (1 := eq_refl).
hauto lq:on ctrs:OExp.R use:rtc_r.
- move => n a0 a1 h ih ?. subst.
specialize ih with (1 := eq_refl).
hauto lq:on ctrs:OExp.R use:rtc_r.
- hauto l:on ctrs:OExp.R.
Qed.
Lemma If_EPar' n (a b c u : Tm n) :
EPar.R (If a b c) u ->
(exists a0 b0 c0, EPar.R a a0 /\ EPar.R b b0 /\ EPar.R c c0 /\ rtc OExp.R (If a0 b0 c0) u).
Proof.
move E : (If a b c) => t h.
move : a b c E. elim : n t u /h => //= n.
- move => a0 a1 ha iha a b c ?. subst.
specialize iha with (1 := eq_refl).
hauto lq:on ctrs:OExp.R use:rtc_r.
- move => a0 a1 ha iha a b c ?. subst.
specialize iha with (1 := eq_refl).
hauto lq:on ctrs:OExp.R use:rtc_r.
- hauto l:on ctrs:OExp.R.
Qed.
Lemma EPar_diamond n (c a1 b1 : Tm n) : Lemma EPar_diamond n (c a1 b1 : Tm n) :
EPar.R c a1 -> EPar.R c a1 ->
EPar.R c b1 -> EPar.R c b1 ->
@ -2456,12 +2486,19 @@ Proof.
move : OExp.commutativity0 h2; repeat move/[apply]. move : OExp.commutativity0 h2; repeat move/[apply].
move => [d h]. move => [d h].
exists d. hauto lq:on rew:off ctrs:EPar.R use:OExp.merge. exists d. hauto lq:on rew:off ctrs:EPar.R use:OExp.merge.
- qauto use:Bot_EPar', EPar.refl. - qauto use:EPar.refl.
- qauto use:Univ_EPar', EPar.refl. - qauto use:EPar.refl.
- admit. - hauto lq:on use:EPar.refl.
- admit. - hauto lq:on use:EPar.refl.
- admit. - move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc u.
Admitted. move /If_EPar' => [a2 [b2 [c2 [h0 [h1 [h2 h3]]]]]].
have {}/iha := h0. have {}/ihb := h1. have {}/ihc := h2.
move => [c hc0]. move => [b hb0]. move => [a ha0].
have : EPar.R (If a2 b2 c2) (If a b c) by hauto lq:on ctrs:EPar.R.
move : OExp.commutativity0 h3. repeat move/[apply].
move => [d ?].
exists d. hauto lq:on rew:off ctrs:EPar.R use:OExp.merge.
Qed.
(* Function tstar' {n} (a : Tm n) := *) (* Function tstar' {n} (a : Tm n) := *)
(* match a with *) (* match a with *)