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Prove some impossible cases

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Yiyun Liu 2025-02-16 01:13:41 -05:00
parent 3fb6d411e7
commit 0f48a485be
2 changed files with 49 additions and 12 deletions
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26
theories/fp_red.v
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@ -1675,6 +1675,10 @@ Module RERed.
End RERed.
Module REReds.
Lemma hne_preservation n (a b : PTm n) :
rtc RERed.R a b -> ishne a -> ishne b.
Proof. induction 1; eauto using RERed.hne_preservation, rtc_refl, rtc. Qed.
Lemma sn_preservation n (a b : PTm n) :
rtc RERed.R a b ->
SN a ->
@ -2284,6 +2288,17 @@ Module DJoin.
case : c => //=; itauto.
Qed.
Lemma hne_univ_noconf n (a b : PTm n) :
R a b -> ishne a -> isuniv b -> False.
Proof.
move => [c [h0 h1]] h2 h3.
have {h0 h1 h2 h3} : ishne c /\ isuniv c by
hauto l:on use:REReds.hne_preservation,
REReds.univ_preservation.
move => [].
case : c => //=.
Qed.
Lemma bind_inj n p0 p1 (A0 A1 : PTm n) B0 B1 :
DJoin.R (PBind p0 A0 B0) (PBind p1 A1 B1) ->
p0 = p1 /\ DJoin.R A0 A1 /\ DJoin.R B0 B1.
@ -2564,6 +2579,17 @@ Module Sub.
qauto l:on inv:SNe.
Qed.
Lemma hne_bind_noconf n (a b : PTm n) :
R a b -> ishne a -> isbind b -> False.
Proof.
rewrite /R.
move => [c[d] [? []]] h0 h1 h2 h3.
have : ishne c by eauto using REReds.hne_preservation.
have : isbind d by eauto using REReds.bind_preservation.
move : h1. clear. inversion 1; subst => //=.
clear. case : d => //=.
Qed.
Lemma bind_sne_noconf n (a b : PTm n) :
R a b -> SNe b -> isbind a -> False.
Proof.