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Add one interpuniv sub case

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Yiyun Liu 2025-02-07 01:19:19 -05:00
parent 707483d401
commit 4bc08e1897
1 changed files with 21 additions and 22 deletions
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43
theories/logrel.v
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@ -347,28 +347,27 @@ Proof.
move : hAB hA h0. clear. hauto lq:on db:noconf. move : hAB hA h0. clear. hauto lq:on db:noconf.
move : InterpUniv_SNe_inv h1 h0. repeat move/[apply]. move => ?. subst. move : InterpUniv_SNe_inv h1 h0. repeat move/[apply]. move => ?. subst.
tauto. tauto.
- - move => i p A B PA PF hPA ihPA hTot hRes ihPF U PU hU. split.
(* - 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.
(* have hU' : SN U by hauto l:on use:adequacy. *) move /InterpUniv_case : hU => [H [/DJoin.FromRedSNs h [h1 h0]]] hU.
(* 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)
(* 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.
(* by move : hU hU' h; clear; hauto q:on use:Sub.FromJoin, DJoin.symmetric, Sub.transitive. *) have{h0} : isbind H.
(* have{h0} : isbind H. *) suff : ~ SNe H /\ ~ isuniv H by itauto.
(* suff : ~ SNe H /\ ~ isuniv H by itauto. *) have : isbind (PBind p A B) by scongruence.
(* have : isbind (PBind p A B) by scongruence. *) hauto l:on db:noconf.
(* (* hauto l:on use: DJoin.sne_bind_noconf, DJoin.bind_univ_noconf, DJoin.symmetric. *) *) admit.
(* admit. *) case : H h1 h => //=.
(* case : H h1 h => //=. *) move => p0 A0 B0 h0. /DJoin.bind_inj.
(* move => p0 A0 B0 h0. /DJoin.bind_inj. *) move => [? [hA hB]] _. subst.
(* move => [? [hA hB]] _. subst. *) move /InterpUniv_Bind_inv : h0.
(* move /InterpUniv_Bind_inv : h0. *) move => [PA0][PF0][hPA0][hTot0][hRes0 ?]. subst.
(* move => [PA0][PF0][hPA0][hTot0][hRes0 ?]. subst. *) have ? : PA0 = PA by qauto l:on. subst.
(* have ? : PA0 = PA by qauto l:on. subst. *) have : forall a PB PB', PA a -> PF a PB -> PF0 a PB' -> PB = PB'.
(* 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.
(* move => a PB PB' ha hPB hPB'. apply : ihPF; eauto. *) by apply DJoin.substing.
(* by apply DJoin.substing. *) move => h. extensionality b. apply propositional_extensionality.
(* move => h. extensionality b. apply propositional_extensionality. *) hauto l:on use:bindspace_iff.
(* hauto l:on use:bindspace_iff. *)
(* - move => i j jlti ih B PB hPB. *) (* - move => i j jlti ih B PB hPB. *)
(* have ? : SN B by hauto l:on use:adequacy. *) (* have ? : SN B by hauto l:on use:adequacy. *)
(* move /InterpUniv_case : hPB => [H [/DJoin.FromRedSNs h [h1 h0]]]. *) (* move /InterpUniv_case : hPB => [H [/DJoin.FromRedSNs h [h1 h0]]]. *)