yiyunliu/sp-eta-postpone
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Add one interpuniv sub case

Browse source
This commit is contained in:
Yiyun Liu 2025-02-07 01:19:19 -05:00
parent 707483d401
commit 4bc08e1897
1 changed files with 21 additions and 22 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

43
theories/logrel.v
View file

@ -347,28 +347,27 @@ Proof.
move : hAB hA h0. clear. hauto lq:on db:noconf.
move : InterpUniv_SNe_inv h1 h0. repeat move/[apply]. move => ?. subst.
tauto.
-
(* - move => i p A B PA PF hPA ihPA hTot hRes ihPF U PU hU. *)
(* have hU' : SN U by hauto l:on use:adequacy. *)
(* move /InterpUniv_case : hU => [H [/DJoin.FromRedSNs h [h1 h0]]] hU. *)
(* have {hU} {}h : Sub.R (PBind p A B) H \/ Sub.R H (PBind p A B) *)
(* by move : hU hU' h; clear; hauto q:on use:Sub.FromJoin, DJoin.symmetric, Sub.transitive. *)
(* have{h0} : isbind H. *)
(* suff : ~ SNe H /\ ~ isuniv H by itauto. *)
(* have : isbind (PBind p A B) by scongruence. *)
(* (* hauto l:on use: DJoin.sne_bind_noconf, DJoin.bind_univ_noconf, DJoin.symmetric. *) *)
(* admit. *)
(* case : H h1 h => //=. *)
(* move => p0 A0 B0 h0. /DJoin.bind_inj. *)
(* move => [? [hA hB]] _. subst. *)
(* move /InterpUniv_Bind_inv : h0. *)
(* move => [PA0][PF0][hPA0][hTot0][hRes0 ?]. subst. *)
(* have ? : PA0 = PA by qauto l:on. subst. *)
(* have : forall a PB PB', PA a -> PF a PB -> PF0 a PB' -> PB = PB'. *)
(* move => a PB PB' ha hPB hPB'. apply : ihPF; eauto. *)
(* by apply DJoin.substing. *)
(* move => h. extensionality b. apply propositional_extensionality. *)
(* hauto l:on use:bindspace_iff. *)
- move => i p A B PA PF hPA ihPA hTot hRes ihPF U PU hU. split.
+ have hU' : SN U by hauto l:on use:adequacy.
move /InterpUniv_case : hU => [H [/DJoin.FromRedSNs h [h1 h0]]] hU.
have {hU} {}h : Sub.R (PBind p A B) H \/ Sub.R H (PBind p A B)
by move : hU hU' h; clear; hauto q:on use:Sub.FromJoin, DJoin.symmetric, Sub.transitive.
have{h0} : isbind H.
suff : ~ SNe H /\ ~ isuniv H by itauto.
have : isbind (PBind p A B) by scongruence.
hauto l:on db:noconf.
admit.
case : H h1 h => //=.
move => p0 A0 B0 h0. /DJoin.bind_inj.
move => [? [hA hB]] _. subst.
move /InterpUniv_Bind_inv : h0.
move => [PA0][PF0][hPA0][hTot0][hRes0 ?]. subst.
have ? : PA0 = PA by qauto l:on. subst.
have : forall a PB PB', PA a -> PF a PB -> PF0 a PB' -> PB = PB'.
move => a PB PB' ha hPB hPB'. apply : ihPF; eauto.
by apply DJoin.substing.
move => h. extensionality b. apply propositional_extensionality.
hauto l:on use:bindspace_iff.
(* - move => i j jlti ih B PB hPB. *)
(* have ? : SN B by hauto l:on use:adequacy. *)
(* move /InterpUniv_case : hPB => [H [/DJoin.FromRedSNs h [h1 h0]]]. *)