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Finish all cases of subtyping

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Yiyun Liu 2025-02-17 22:50:25 -05:00
parent 735c7f2046
commit 9c5eb31edf
2 changed files with 89 additions and 4 deletions
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32
theories/fp_red.v
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@ -2337,6 +2337,17 @@ Module DJoin.
case : c => //=.
Qed.
Lemma hne_bind_noconf n (a b : PTm n) :
R a b -> ishne a -> isbind b -> False.
Proof.
move => [c [h0 h1]] h2 h3.
have {h0 h1 h2 h3} : ishne c /\ isbind c by
hauto l:on use:REReds.hne_preservation,
REReds.bind_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.
@ -2797,4 +2808,25 @@ End Sub.
Module ESub.
Definition R {n} (a b : PTm n) := exists c0 c1, rtc ERed.R a c0 /\ rtc ERed.R b c1 /\ Sub1.R c0 c1.
Lemma pi_inj n (A0 A1 : PTm n) B0 B1 :
R (PBind PPi A0 B0) (PBind PPi A1 B1) ->
R A1 A0 /\ R B0 B1.
Proof.
move => [u0 [u1 [h0 [h1 h2]]]].
move /EReds.bind_inv : h0 => [A2][B2][?][h3]h4. subst.
move /EReds.bind_inv : h1 => [A3][B3][?][h5]h6. subst.
sauto lq:on rew:off inv:Sub1.R.
Qed.
Lemma sig_inj n (A0 A1 : PTm n) B0 B1 :
R (PBind PSig A0 B0) (PBind PSig A1 B1) ->
R A0 A1 /\ R B0 B1.
Proof.
move => [u0 [u1 [h0 [h1 h2]]]].
move /EReds.bind_inv : h0 => [A2][B2][?][h3]h4. subst.
move /EReds.bind_inv : h1 => [A3][B3][?][h5]h6. subst.
sauto lq:on rew:off inv:Sub1.R.
Qed.
End ESub.