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Prove most of the confluence results for eta reduction

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Yiyun Liu 2025-01-09 20:21:38 -05:00
parent e75d7745fe
commit 34a0c2856e
2 changed files with 137 additions and 5 deletions
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10
theories/fp_red.v
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@ -766,6 +766,8 @@ Module ERed.
R B0 B1 ->
R (TBind p A B0) (TBind p A B1).
Derive Dependent Inversion inv with (forall n (a b : Tm n), R a b) Sort Prop.
Lemma AppEta' n a (u : Tm n) :
u = (Abs (App (ren_Tm shift a) (VarTm var_zero))) ->
R a u.
@ -1764,15 +1766,13 @@ Qed.
Lemma prov_pair n (u : Tm n) a : prov u a <-> prov u (Pair (Proj PL a) (Proj PR a)).
Proof. hauto lq:on inv:prov ctrs:prov. Qed.
Derive Dependent Inversion inv with (forall n (a b : Tm n), ERed.R a b) Sort Prop.
Lemma prov_ered n (u : Tm n) a b : prov u a -> ERed.R a b -> prov u b.
Proof.
move => h.
move : b.
elim : u a / h.
- move => p A A0 B B0 hA hB b.
elim /inv => // _.
elim /ERed.inv => // _.
+ move => a0 *. subst.
rewrite -prov_lam.
by constructor.
@ -1782,7 +1782,7 @@ Proof.
+ qauto l:on ctrs:prov use:@rtc_r, ERed_EPar, EPar_Par.
+ qauto l:on ctrs:prov use:@rtc_r, ERed_EPar, EPar_Par.
- move => h a ha iha b.
elim /inv => // _.
elim /ERed.inv => // _.
+ move => a0 *. subst.
rewrite -prov_lam.
by constructor.
@ -1792,7 +1792,7 @@ Proof.
+ hauto lq:on ctrs:prov use:ERed.substing.
- hauto lq:on inv:ERed.R, prov ctrs:prov.
- move => h a b ha iha hb ihb b0.
elim /inv => //_.
elim /ERed.inv => //_.
+ move => a0 *. subst.
rewrite -prov_lam.
by constructor.