yiyunliu/sp-eta-postpone
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Remove itauto dependency as it introduces weird axioms

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Yiyun Liu 2025-03-11 16:27:31 -04:00
parent 8dbef3e29e
commit f9d3a620f4
3 changed files with 17 additions and 18 deletions
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16
theories/logrel.v
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@ -6,7 +6,7 @@ Require Import ssreflect ssrbool.
Require Import Logic.PropExtensionality (propositional_extensionality).
From stdpp Require Import relations (rtc(..), rtc_subrel).
Import Psatz.
Require Import Cdcl.Itauto.
Definition ProdSpace (PA : PTm -> Prop)
(PF : PTm -> (PTm -> Prop) -> Prop) b : Prop :=
@ -355,7 +355,7 @@ Proof.
move => [H [/DJoin.FromRedSNs h [h1 h0]]].
have {h}{}hAB : Sub.R A H by qauto l:on use:Sub.FromJoin, DJoin.symmetric, Sub.transitive.
have {}h0 : SNe H.
suff : ~ isbind H /\ ~ isuniv H /\ ~ isnat H by itauto.
suff : ~ isbind H /\ ~ isuniv H /\ ~ isnat H by sfirstorder b:on.
move : hA hAB. clear. hauto lq:on db:noconf.
move : InterpUniv_SNe_inv h1 h0. repeat move/[apply]. move => ?. subst.
tauto.
@ -365,7 +365,7 @@ Proof.
move => [H [/DJoin.FromRedSNs h [h1 h0]]].
have {h}{}hAB : Sub.R H A by qauto l:on use:Sub.FromJoin, DJoin.symmetric, Sub.transitive.
have {}h0 : SNe H.
suff : ~ isbind H /\ ~ isuniv H /\ ~ isnat H by itauto.
suff : ~ isbind H /\ ~ isuniv H /\ ~ isnat H by sfirstorder b:on.
move : hAB hA h0. clear. hauto lq:on db:noconf.
move : InterpUniv_SNe_inv h1 h0. repeat move/[apply]. move => ?. subst.
tauto.
@ -375,7 +375,7 @@ Proof.
have {hU} {}h : Sub.R (PBind p A B) H
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 /\ ~ isnat H by itauto.
suff : ~ SNe H /\ ~ isuniv H /\ ~ isnat H by sfirstorder b:on.
have : isbind (PBind p A B) by scongruence.
move : h. clear. hauto l:on db:noconf.
case : H h1 h => //=.
@ -394,7 +394,7 @@ Proof.
have {hU} {}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 /\ ~ isnat H by itauto.
suff : ~ SNe H /\ ~ isuniv H /\ ~ isnat H by sfirstorder b:on.
have : isbind (PBind p A B) by scongruence.
move : h. clear. move : (PBind p A B). hauto lq:on db:noconf.
case : H h1 h => //=.
@ -413,7 +413,7 @@ Proof.
move => [H [/DJoin.FromRedSNs h [h1 h0]]].
have {h}{}hAB : Sub.R PNat H by qauto l:on use:Sub.FromJoin, DJoin.symmetric, Sub.transitive.
have {}h0 : isnat H.
suff : ~ isbind H /\ ~ isuniv H /\ ~ SNe H by itauto.
suff : ~ isbind H /\ ~ isuniv H /\ ~ SNe H by sfirstorder b:on.
have : @isnat PNat by simpl.
move : h0 hAB. clear. qauto l:on db:noconf.
case : H h1 hAB h0 => //=.
@ -424,7 +424,7 @@ Proof.
move => [H [/DJoin.FromRedSNs h [h1 h0]]].
have {h}{}hAB : Sub.R H PNat by qauto l:on use:Sub.FromJoin, DJoin.symmetric, Sub.transitive.
have {}h0 : isnat H.
suff : ~ isbind H /\ ~ isuniv H /\ ~ SNe H by itauto.
suff : ~ isbind H /\ ~ isuniv H /\ ~ SNe H by sfirstorder b:on.
have : @isnat PNat by simpl.
move : h0 hAB. clear. qauto l:on db:noconf.
case : H h1 hAB h0 => //=.
@ -1058,7 +1058,7 @@ Definition Γ_sub' Γ Δ := forall ρ, ρ_ok Δ ρ -> ρ_ok Γ ρ.
Definition Γ_eq' Γ Δ := forall ρ, ρ_ok Δ ρ <-> ρ_ok Γ ρ.
Lemma Γ_sub'_refl Γ : Γ_sub' Γ Γ.
rewrite /Γ_sub'. itauto. Qed.
rewrite /Γ_sub'. sfirstorder b:on. Qed.
Lemma Γ_sub'_cons Γ Δ A B i j :
Sub.R B A ->