yiyunliu/sp-eta-postpone
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Add a constant to avoid kripke LR

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This commit is contained in:
Yiyun Liu 2025-02-04 22:14:27 -05:00
parent e923194e3d
commit 38a0416b2c
3 changed files with 46 additions and 7 deletions
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24
theories/Autosubst2/syntax.v
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@ -40,7 +40,8 @@ Inductive PTm (n_PTm : nat) : Type :=
| PPair : PTm n_PTm -> PTm n_PTm -> PTm n_PTm
| PProj : PTag -> PTm n_PTm -> PTm n_PTm
| PBind : BTag -> PTm n_PTm -> PTm (S n_PTm) -> PTm n_PTm
| PUniv : nat -> PTm n_PTm.
| PUniv : nat -> PTm n_PTm
| PBot : PTm n_PTm.
Lemma congr_PAbs {m_PTm : nat} {s0 : PTm (S m_PTm)} {t0 : PTm (S m_PTm)}
(H0 : s0 = t0) : PAbs m_PTm s0 = PAbs m_PTm t0.
@ -89,6 +90,11 @@ Proof.
exact (eq_trans eq_refl (ap (fun x => PUniv m_PTm x) H0)).
Qed.
Lemma congr_PBot {m_PTm : nat} : PBot m_PTm = PBot m_PTm.
Proof.
exact (eq_refl).
Qed.
Lemma upRen_PTm_PTm {m : nat} {n : nat} (xi : fin m -> fin n) :
fin (S m) -> fin (S n).
Proof.
@ -112,6 +118,7 @@ Fixpoint ren_PTm {m_PTm : nat} {n_PTm : nat}
| PBind _ s0 s1 s2 =>
PBind n_PTm s0 (ren_PTm xi_PTm s1) (ren_PTm (upRen_PTm_PTm xi_PTm) s2)
| PUniv _ s0 => PUniv n_PTm s0
| PBot _ => PBot n_PTm
end.
Lemma up_PTm_PTm {m : nat} {n_PTm : nat} (sigma : fin m -> PTm n_PTm) :
@ -142,6 +149,7 @@ Fixpoint subst_PTm {m_PTm : nat} {n_PTm : nat}
PBind n_PTm s0 (subst_PTm sigma_PTm s1)
(subst_PTm (up_PTm_PTm sigma_PTm) s2)
| PUniv _ s0 => PUniv n_PTm s0
| PBot _ => PBot n_PTm
end.
Lemma upId_PTm_PTm {m_PTm : nat} (sigma : fin m_PTm -> PTm m_PTm)
@ -184,6 +192,7 @@ Fixpoint idSubst_PTm {m_PTm : nat} (sigma_PTm : fin m_PTm -> PTm m_PTm)
congr_PBind (eq_refl s0) (idSubst_PTm sigma_PTm Eq_PTm s1)
(idSubst_PTm (up_PTm_PTm sigma_PTm) (upId_PTm_PTm _ Eq_PTm) s2)
| PUniv _ s0 => congr_PUniv (eq_refl s0)
| PBot _ => congr_PBot
end.
Lemma upExtRen_PTm_PTm {m : nat} {n : nat} (xi : fin m -> fin n)
@ -229,6 +238,7 @@ ren_PTm xi_PTm s = ren_PTm zeta_PTm s :=
(extRen_PTm (upRen_PTm_PTm xi_PTm) (upRen_PTm_PTm zeta_PTm)
(upExtRen_PTm_PTm _ _ Eq_PTm) s2)
| PUniv _ s0 => congr_PUniv (eq_refl s0)
| PBot _ => congr_PBot
end.
Lemma upExt_PTm_PTm {m : nat} {n_PTm : nat} (sigma : fin m -> PTm n_PTm)
@ -275,6 +285,7 @@ subst_PTm sigma_PTm s = subst_PTm tau_PTm s :=
(ext_PTm (up_PTm_PTm sigma_PTm) (up_PTm_PTm tau_PTm)
(upExt_PTm_PTm _ _ Eq_PTm) s2)
| PUniv _ s0 => congr_PUniv (eq_refl s0)
| PBot _ => congr_PBot
end.
Lemma up_ren_ren_PTm_PTm {k : nat} {l : nat} {m : nat} (xi : fin k -> fin l)
@ -322,6 +333,7 @@ Fixpoint compRenRen_PTm {k_PTm : nat} {l_PTm : nat} {m_PTm : nat}
(compRenRen_PTm (upRen_PTm_PTm xi_PTm) (upRen_PTm_PTm zeta_PTm)
(upRen_PTm_PTm rho_PTm) (up_ren_ren _ _ _ Eq_PTm) s2)
| PUniv _ s0 => congr_PUniv (eq_refl s0)
| PBot _ => congr_PBot
end.
Lemma up_ren_subst_PTm_PTm {k : nat} {l : nat} {m_PTm : nat}
@ -378,6 +390,7 @@ Fixpoint compRenSubst_PTm {k_PTm : nat} {l_PTm : nat} {m_PTm : nat}
(compRenSubst_PTm (upRen_PTm_PTm xi_PTm) (up_PTm_PTm tau_PTm)
(up_PTm_PTm theta_PTm) (up_ren_subst_PTm_PTm _ _ _ Eq_PTm) s2)
| PUniv _ s0 => congr_PUniv (eq_refl s0)
| PBot _ => congr_PBot
end.
Lemma up_subst_ren_PTm_PTm {k : nat} {l_PTm : nat} {m_PTm : nat}
@ -454,6 +467,7 @@ ren_PTm zeta_PTm (subst_PTm sigma_PTm s) = subst_PTm theta_PTm s :=
(compSubstRen_PTm (up_PTm_PTm sigma_PTm) (upRen_PTm_PTm zeta_PTm)
(up_PTm_PTm theta_PTm) (up_subst_ren_PTm_PTm _ _ _ Eq_PTm) s2)
| PUniv _ s0 => congr_PUniv (eq_refl s0)
| PBot _ => congr_PBot
end.
Lemma up_subst_subst_PTm_PTm {k : nat} {l_PTm : nat} {m_PTm : nat}
@ -532,6 +546,7 @@ subst_PTm tau_PTm (subst_PTm sigma_PTm s) = subst_PTm theta_PTm s :=
(compSubstSubst_PTm (up_PTm_PTm sigma_PTm) (up_PTm_PTm tau_PTm)
(up_PTm_PTm theta_PTm) (up_subst_subst_PTm_PTm _ _ _ Eq_PTm) s2)
| PUniv _ s0 => congr_PUniv (eq_refl s0)
| PBot _ => congr_PBot
end.
Lemma renRen_PTm {k_PTm : nat} {l_PTm : nat} {m_PTm : nat}
@ -649,6 +664,7 @@ Fixpoint rinst_inst_PTm {m_PTm : nat} {n_PTm : nat}
(rinst_inst_PTm (upRen_PTm_PTm xi_PTm) (up_PTm_PTm sigma_PTm)
(rinstInst_up_PTm_PTm _ _ Eq_PTm) s2)
| PUniv _ s0 => congr_PUniv (eq_refl s0)
| PBot _ => congr_PBot
end.
Lemma rinstInst'_PTm {m_PTm : nat} {n_PTm : nat}
@ -855,6 +871,8 @@ Core.
Arguments VarPTm {n_PTm}.
Arguments PBot {n_PTm}.
Arguments PUniv {n_PTm}.
Arguments PBind {n_PTm}.
@ -867,9 +885,9 @@ Arguments PApp {n_PTm}.
Arguments PAbs {n_PTm}.
#[global]Hint Opaque subst_PTm: rewrite.
#[global] Hint Opaque subst_PTm: rewrite.
#[global]Hint Opaque ren_PTm: rewrite.
#[global] Hint Opaque ren_PTm: rewrite.
End Extra.