yiyunliu/sp-eta-postpone
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Fix the broken pair eta rule

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Yiyun Liu 2025-01-27 16:48:38 -05:00
parent 9f80013df6
commit b8d7ebfaa2
1 changed files with 15 additions and 7 deletions
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22
theories/fp_red.v
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@ -25,10 +25,9 @@ Module ERed.
| AppEta a0 a1 : | AppEta a0 a1 :
R a0 a1 -> R a0 a1 ->
R (PAbs (PApp (ren_PTm shift a0) (VarPTm var_zero))) a1 R (PAbs (PApp (ren_PTm shift a0) (VarPTm var_zero))) a1
| PairEta a0 b0 a1 : | PairEta a0 a1 :
R a0 a1 -> R a0 a1 ->
R b0 a1 -> R (PPair (PProj PL a0) (PProj PR a0)) a1
R (PPair (PProj PL a0) (PProj PR b0)) a1
(*************** Congruence ********************) (*************** Congruence ********************)
| AbsCong a0 a1 : | AbsCong a0 a1 :
R a0 a1 -> R a0 a1 ->
@ -230,7 +229,7 @@ Proof.
elim /ERed.inv => //= _. elim /ERed.inv => //= _.
move => p a0 a1 ha [*]. subst. move => p a0 a1 ha [*]. subst.
elim /ERed.inv : ha => //= _. elim /ERed.inv : ha => //= _.
+ move => a0 b0 a2 ha ha' [*]. subst. + move => a0 a2 ha' [*]. subst.
exists (PProj PL a1). exists (PProj PL a1).
split. sauto. split. sauto.
sauto lq:on. sauto lq:on.
@ -239,7 +238,7 @@ Proof.
elim /ERed.inv => //=_. elim /ERed.inv => //=_.
move => p a0 a1 + [*]. subst. move => p a0 a1 + [*]. subst.
elim /ERed.inv => //=_. elim /ERed.inv => //=_.
+ move => a0 b0 a2 h0 h1 [*]. subst. + move => a0 a2 h1 [*]. subst.
exists (PProj PR a1). exists (PProj PR a1).
split. sauto. split. sauto.
sauto lq:on. sauto lq:on.
@ -319,8 +318,17 @@ Function tstar {n} (a : PTm n) :=
| PProj p a => PProj p (tstar a) | PProj p a => PProj p (tstar a)
end. end.
Lemma η_nf n (a b c : PTm n) : ERed.R a b -> nf b -> Lemma η_nf n (a b : PTm n) : ERed.R a b -> nf b -> ERed.R (tstar a) b.
ERed.R c b. Proof.
move => h.
elim : n a b /h => n.
- move => a0 a1 ha iha.
move : ha. clear. best.
clear.
- sfirstorder.
-
Lemma η_nf n (a b c : PTm n) : ERed.R a b -> nf b -> RRed.R a c -> Lemma η_nf n (a b c : PTm n) : ERed.R a b -> nf b -> RRed.R a c ->
ERed.R c b. ERed.R c b.