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Finish preservation

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Yiyun Liu 2025-02-25 22:35:59 -05:00
parent bb39f157ba
commit 687d1be03f
6 changed files with 74 additions and 5 deletions
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theories/algorithmic.v
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@ -16,13 +16,22 @@ Module HRed.
| ProjPair p a b :
R (PProj p (PPair a b)) (if p is PL then a else b)
| IndZero P b c :
R (PInd P PZero b c) b
| IndSuc P a b c :
R (PInd P (PSuc a) b c) (subst_PTm (scons (PInd P a b c) (scons a VarPTm)) c)
(*************** Congruence ********************)
| AppCong a0 a1 b :
R a0 a1 ->
R (PApp a0 b) (PApp a1 b)
| ProjCong p a0 a1 :
R a0 a1 ->
R (PProj p a0) (PProj p a1).
R (PProj p a0) (PProj p a1)
| IndCong P a0 a1 b c :
R a0 a1 ->
R (PInd P a0 b c) (PInd P a1 b c).
Lemma ToRRed n (a b : PTm n) : HRed.R a b -> RRed.R a b.
Proof. induction 1; hauto lq:on ctrs:RRed.R. Qed.