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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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5
theories/algorithmic.v
View file

@ -5,7 +5,6 @@ Require Import ssreflect ssrbool.
Require Import Psatz.
From stdpp Require Import relations (rtc(..), nsteps(..)).
Require Import Coq.Logic.FunctionalExtensionality.
Require Import Cdcl.Itauto.
Module HRed.
Lemma ToRRed (a b : PTm) : HRed.R a b -> RRed.R a b.
@ -98,7 +97,7 @@ Proof.
- move => u v hC /andP [h0 h1] /synsub_to_usub ?.
exfalso.
suff : SNe (PApp u v) by hauto l:on use:Sub.bind_sne_noconf.
eapply ne_nf_embed => //=. itauto.
eapply ne_nf_embed => //=. sfirstorder b:on.
- move => p0 p1 hC h ?. exfalso.
have {hC} : Γ ⊢ PPair p0 p1 ∈ PUniv i by hauto l:on use:regularity.
hauto lq:on use:Sub.bind_univ_noconf, synsub_to_usub, Pair_Inv.
@ -199,7 +198,7 @@ Proof.
- move => u v hC /andP [h0 h1] /synsub_to_usub ?.
exfalso.
suff : SNe (PApp u v) by hauto l:on use:Sub.sne_bind_noconf.
eapply ne_nf_embed => //=. itauto.
eapply ne_nf_embed => //=. sfirstorder b:on.
- move => p0 p1 hC h ?. exfalso.
have {hC} : Γ ⊢ PPair p0 p1 ∈ PUniv i by hauto l:on use:regularity.
hauto lq:on use:Sub.bind_univ_noconf, synsub_to_usub, Pair_Inv.

14
theories/fp_red.v
View file

@ -10,7 +10,7 @@ From stdpp Require Import relations (rtc (..), rtc_once, rtc_r, sn).
From Hammer Require Import Tactics.
Require Import Autosubst2.core Autosubst2.unscoped Autosubst2.syntax common.
Require Import Btauto.
Require Import Cdcl.Itauto.
Ltac2 spec_refl () :=
List.iter
@ -2575,7 +2575,7 @@ Module LoReds.
~~ ishf a.
Proof.
move : hf_preservation. repeat move/[apply].
case : a; case : b => //=; itauto.
case : a; case : b => //=; sfirstorder b:on.
Qed.
#[local]Ltac solve_s_rec :=
@ -2633,7 +2633,7 @@ Module LoReds.
rtc LoRed.R (PSuc a0) (PSuc a1).
Proof. solve_s. Qed.
Local Ltac triv := simpl in *; itauto.
Local Ltac triv := simpl in *; sfirstorder b:on.
Lemma FromSN_mutual :
(forall (a : PTm) (_ : SNe a), exists v, rtc LoRed.R a v /\ ne v) /\
@ -3048,7 +3048,7 @@ Module DJoin.
have {h0 h1 h2 h3} : isbind c /\ isuniv c by
hauto l:on use:REReds.bind_preservation,
REReds.univ_preservation.
case : c => //=; itauto.
case : c => //=; sfirstorder b:on.
Qed.
Lemma hne_univ_noconf (a b : PTm) :
@ -3078,7 +3078,7 @@ Module DJoin.
Proof.
move => [c [h0 h1]] h2 h3.
have : ishne c /\ isnat c by sfirstorder use:REReds.hne_preservation, REReds.nat_preservation.
clear. case : c => //=; itauto.
clear. case : c => //=; sfirstorder b:on.
Qed.
Lemma bind_inj p0 p1 (A0 A1 : PTm) B0 B1 :
@ -3594,7 +3594,7 @@ Module Sub.
hauto l:on use:REReds.bind_preservation,
REReds.univ_preservation, Sub1.bind_preservation, Sub1.univ_preservation.
move : h2 h3. clear.
case : c => //=; itauto.
case : c => //=; sfirstorder b:on.
Qed.
Lemma univ_bind_noconf (a b : PTm) :
@ -3605,7 +3605,7 @@ Module Sub.
hauto l:on use:REReds.bind_preservation,
REReds.univ_preservation, Sub1.bind_preservation, Sub1.univ_preservation.
move : h2 h3. clear.
case : c => //=; itauto.
case : c => //=; sfirstorder b:on.
Qed.
Lemma bind_inj p0 p1 (A0 A1 : PTm) B0 B1 :

16
theories/logrel.v
View file

@ -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 ->