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Add commutativity rules for eliminators

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Yiyun Liu 2025-01-12 16:08:56 -05:00
parent d0760cd9db
commit c9fcafb47f
1 changed files with 19 additions and 1 deletions
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20
theories/fp_red.v
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@ -100,7 +100,18 @@ Module Par.
R a0 a1 ->
R b0 b1 ->
R c0 c1 ->
R (If a0 b0 c0) (If a1 b1 c1).
R (If a0 b0 c0) (If a1 b1 c1)
| IfApp a0 a1 b0 b1 c0 c1 d0 d1 :
R a0 a1 ->
R b0 b1 ->
R c0 c1 ->
R d0 d1 ->
R (If (App a0 b0) c0 d0) (App (If a1 c1 d1) b1)
| IfProj p a0 a1 b0 b1 c0 c1 :
R a0 a1 ->
R b0 b1 ->
R c0 c1 ->
R (If (Proj p a0) b0 c0) (Proj p (If a1 b1 c1)).
Lemma refl n (a : Tm n) : R a a.
elim : n /a; hauto ctrs:R.
@ -187,6 +198,8 @@ Module Par.
- sfirstorder.
- sfirstorder.
- hauto lq:on ctrs:R.
- hauto lq:on ctrs:R.
- qauto l:on ctrs:R.
Qed.
Lemma substing n m (a b : Tm n) (ρ : fin n -> Tm m) :
@ -296,6 +309,11 @@ Module Par.
- move => n a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ξ []//= t t0 t1[*]. subst.
spec_refl.
qauto l:on ctrs:R.
- move => n a0 a1 b0 b1 c0 c1 d0 d1 ha iha hb ihb hc ihc hd ihd m ξ []//= t0 t1 t2 [h *]. subst.
case : t0 h => //= t t0 [*]. subst.
qauto l:on ctrs:R.
- move => n p a0 a1 b0 b1 c0 c1 ha iha hb ihb hc ihc m ξ []//= t0 t1 t [h *]. subst.
case : t0 h => //=. qauto l:on ctrs:R.
Qed.
End Par.