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Side step the need for join subst

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Yiyun Liu 2025-02-05 20:36:39 -05:00
parent 7cc6435ea3
commit 1997e8bc12
2 changed files with 39 additions and 1 deletions
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28
theories/logrel.v
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@ -324,7 +324,33 @@ Proof.
case : H h1 h => //=.
move => p0 A0 B0 h0 /DJoin.bind_inj.
move => [? [hA hB]] _. subst.
admit.
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.
have hj0 : DJoin.R (PAbs B) (PAbs B0) by eauto using DJoin.AbsCong.
have {}hj0 : DJoin.R (PApp (PAbs B) a) (PApp (PAbs B0) a) by eauto using DJoin.AppCong, DJoin.refl.
have ? : SN (PApp (PAbs B) a)
by hauto lq:on rew:off use:N_Exp, N_β, adequacy.
have ? : SN (PApp (PAbs B0) a)
by hauto lq:on rew:off use:N_Exp, N_β, adequacy.
have : DJoin.R (PApp (PAbs B0) a) (subst_PTm (scons a VarPTm) B0)
by hauto lq:on ctrs:RRed.R use:DJoin.FromRRed0.
have : DJoin.R (subst_PTm (scons a VarPTm) B) (PApp (PAbs B) a)
by hauto lq:on ctrs:RRed.R use:DJoin.FromRRed1.
eauto using DJoin.transitive.
move => hI.
case : p0 => //=.
+ rewrite /ProdSpace.
extensionality b.
apply propositional_extensionality.
split.
move => hPF a PB.
move => a PB hPB.
- 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]]].