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Finish most of the pi pi case

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Yiyun Liu 2025-02-15 17:22:43 -05:00
parent 926c2284a5
commit 3fb6d411e7
2 changed files with 88 additions and 2 deletions
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18
theories/fp_red.v
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@ -1540,6 +1540,17 @@ Module EReds.
hauto q:on ctrs:rtc,ERed.R inv:ERed.R.
Qed.
Lemma bind_inv n p (A : PTm n) B C :
rtc ERed.R (PBind p A B) C ->
exists A0 B0, C = PBind p A0 B0 /\ rtc ERed.R A A0 /\ rtc ERed.R B B0.
Proof.
move E : (PBind p A B) => u hu.
move : p A B E.
elim : u C / hu.
hauto lq:on ctrs:rtc.
hauto lq:on rew:off ctrs:rtc, ERed.R inv:ERed.R, rtc.
Qed.
End EReds.
#[export]Hint Constructors ERed.R RRed.R EPar.R : red.
@ -1561,6 +1572,13 @@ Module EJoin.
hauto lq:on rew:off use:EReds.proj_inv.
Qed.
Lemma bind_inj n p0 p1 (A0 A1 : PTm n) B0 B1 :
R (PBind p0 A0 B0) (PBind p1 A1 B1) ->
p0 = p1 /\ R A0 A1 /\ R B0 B1.
Proof.
hauto lq:on rew:off use:EReds.bind_inv.
Qed.
End EJoin.
Module RERed.