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Show that sne and bind are not joinable

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Yiyun Liu 2025-02-05 16:52:25 -05:00
parent 0e254c5ac3
commit e444c8408f
2 changed files with 62 additions and 6 deletions
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12
theories/logrel.v
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@ -215,9 +215,6 @@ Proof.
induction 2; hauto lq:on ctrs:rtc use:InterpUniv_back_clos.
Qed.
Definition isbind {n} (a : PTm n) := if a is PBind _ _ _ then true else false.
Definition isuniv {n} (a : PTm n) := if a is PUniv _ then true else false.
Lemma InterpUniv_case n i (A : PTm n) PA :
⟦ A ⟧ i ↘ PA ->
@ -237,6 +234,11 @@ Qed.
Lemma redsns_preservation : forall n a b, @SN n a -> rtc TRedSN a b -> SN b.
Proof. induction 2; sfirstorder use:redsn_preservation_mutual ctrs:rtc. Qed.
Lemma sne_bind_noconf n (a b : PTm n) :
SNe a -> isbind b -> DJoin.R a b -> False.
Proof.
Lemma InterpUniv_Join n i (A B : PTm n) PA PB :
⟦ A ⟧ i ↘ PA ->
⟦ B ⟧ i ↘ PB ->
@ -249,5 +251,5 @@ Proof.
- move => i A hA B PB hPB hAB.
have [*] : SN B /\ SN A by hauto l:on use:adequacy.
move /InterpUniv_case : hPB.
move => [H [h ?]].
(* have ? : SN H by sfirstorder use:redsns_preservation. *)
move => [H [/DJoin.FromRedSNs h ?]].
have ? : DJoin.R A H by eauto using DJoin.transitive.