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Finish off the SN proof

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Yiyun Liu 2025-01-30 20:23:25 -05:00
parent 64e558f09e
commit fc666956e2
1 changed files with 21 additions and 3 deletions
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24
theories/fp_red.v
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@ -313,7 +313,25 @@ Proof.
Qed. Qed.
Lemma SN_AppInv : forall n (a b : PTm n), SN (PApp a b) -> SN a /\ SN b. Lemma SN_AppInv : forall n (a b : PTm n), SN (PApp a b) -> SN a /\ SN b.
Admitted. Proof.
move => n a b. move E : (PApp a b) => u hu. move : a b E.
elim : n u /hu=>//=.
hauto lq:on rew:off inv:SNe db:sn.
move => n a b ha hb ihb a0 b0 ?. subst.
inversion ha; subst.
move {ihb}.
hecrush use:sn_unmorphing.
hauto lq:on db:sn.
Qed.
Lemma SN_ProjInv : forall n p (a : PTm n), SN (PProj p a) -> SN a.
Proof.
move => n p a. move E : (PProj p a) => u hu.
move : p a E.
elim : n u / hu => //=.
hauto lq:on rew:off inv:SNe db:sn.
hauto lq:on rew:off inv:TRedSN db:sn.
Qed.
Lemma ered_sn_preservation n : Lemma ered_sn_preservation n :
(forall (a : PTm n) (s : SNe a), forall b, ERed.R a b -> SNe b) /\ (forall (a : PTm n) (s : SNe a), forall b, ERed.R a b -> SNe b) /\
@ -942,7 +960,7 @@ Module SN_NoForbid : NoForbid.
move : a b E. elim : n u / h; sauto lq:on rew:off. Qed. move : a b E. elim : n u / h; sauto lq:on rew:off. Qed.
Lemma P_ProjInv : forall n p (a : PTm n), P (PProj p a) -> P a. Lemma P_ProjInv : forall n p (a : PTm n), P (PProj p a) -> P a.
Admitted. Proof. sfirstorder use:SN_ProjInv. Qed.
Lemma P_AbsInv : forall n (a : PTm (S n)), P (PAbs a) -> P a. Lemma P_AbsInv : forall n (a : PTm (S n)), P (PAbs a) -> P a.
Proof. Proof.
@ -952,7 +970,7 @@ Module SN_NoForbid : NoForbid.
Qed. Qed.
Lemma P_renaming : forall n m (ξ : fin n -> fin m) a , P (ren_PTm ξ a) <-> P a. Lemma P_renaming : forall n m (ξ : fin n -> fin m) a , P (ren_PTm ξ a) <-> P a.
Admitted. Proof. hauto lq:on use:sn_antirenaming, sn_renaming. Qed.
End SN_NoForbid. End SN_NoForbid.