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Finish most of the preservation proof

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Yiyun Liu 2025-01-25 23:10:29 -05:00
parent 8463b4067f
commit 263fbf7fb6
1 changed files with 10 additions and 5 deletions
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15
theories/fp_red.v
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@ -153,12 +153,17 @@ Scheme sne_ind := Induction for SNe Sort Prop
Combined Scheme sn_mutual from sne_ind, sn_ind, sred_ind. Combined Scheme sn_mutual from sne_ind, sn_ind, sred_ind.
Check sn_mutual. Inductive TRedSN' {n} (a : PTm n) : PTm n -> Prop :=
| T_Refl :
TRedSN' a a
| T_Once b :
TRedSN a b ->
TRedSN' a b.
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) /\
(forall (a : PTm n) (s : SN a), forall b, ERed.R a b -> SN b) /\ (forall (a : PTm n) (s : SN a), forall b, ERed.R a b -> SN b) /\
(forall (a b : PTm n) (_ : TRedSN a b), forall c, ERed.R a c -> exists d, TRedSN c d /\ ERed.R b d). (forall (a b : PTm n) (_ : TRedSN a b), forall c, ERed.R a c -> exists d, TRedSN' c d /\ ERed.R b d).
Proof. Proof.
move : n. apply sn_mutual => n. move : n. apply sn_mutual => n.
- sauto lq:on. - sauto lq:on.
@ -182,7 +187,7 @@ Proof.
- move => A a b ha iha c h0. - move => A a b ha iha c h0.
inversion h0; subst. inversion h0; subst.
inversion H1; subst. inversion H1; subst.
+ exists (PApp a1 b1). split. admit. + exists (PApp a1 b1). split.sfirstorder.
asimpl. asimpl.
sauto lq:on. sauto lq:on.
+ have {}/iha := H3 => iha. + have {}/iha := H3 => iha.
@ -197,7 +202,7 @@ Proof.
elim /ERed.inv : ha => //= _. elim /ERed.inv : ha => //= _.
+ move => a0 a2 ha [*]. subst. + move => a0 a2 ha [*]. subst.
exists (PProj PL a1). exists (PProj PL a1).
split. admit. split. sauto.
sauto lq:on. sauto lq:on.
+ sauto lq:on rew:off. + sauto lq:on rew:off.
- move => a b ha iha c. - move => a b ha iha c.
@ -206,7 +211,7 @@ Proof.
elim /ERed.inv => //=_. elim /ERed.inv => //=_.
+ move => a0 a2 h [*]. subst. + move => a0 a2 h [*]. subst.
exists (PProj PR a1). exists (PProj PR a1).
split. admit. split. sauto.
sauto lq:on. sauto lq:on.
+ sauto lq:on. + sauto lq:on.
- sauto lq:on. - sauto lq:on.