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refactor: use step_fupd_mono more #404

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refactor: use step_fupd_mono more #404

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9 changes: 4 additions & 5 deletions Iris/Iris/BI/Updates.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -403,7 +403,7 @@ theorem step_fupd_mask_mono {Eo₁ Eo₂ Ei₁ Ei₂ : CoPset} {P : PROP}

theorem step_fupd_mono {Eo Ei : CoPset} {P Q : PROP} :
(Q ⊢ P) → (|={Eo}[Ei]▷=> Q) ⊢ |={Eo}[Ei]▷=> P :=
(BIFUpdate.mono <| later_mono <| BIFUpdate.mono ·)
(mono <| later_mono <| mono ·)

@[rocq_alias step_fupd_intro]
theorem step_fupd_intro {Ei Eo : CoPset} {P : PROP} (Ei_Eo : Ei ⊆ Eo) :
Expand All @@ -422,8 +422,7 @@ theorem step_fupdN_intro {Ei Eo : CoPset} {P : PROP} (Ei_Eo : Ei ⊆ Eo) :
simp only [Nat.repeat]
refine .trans (later_laterN n).1 ?_
refine .trans (step_fupd_intro Ei_Eo) ?_
refine mono <| later_mono <| mono ?_
exact step_fupdN_intro Ei_Eo
exact step_fupd_mono <| step_fupdN_intro Ei_Eo

@[rocq_alias step_fupdN_le]
theorem step_fupdN_le {n m : Nat} {Eo Ei : CoPset} {P : PROP} :
Expand All @@ -434,7 +433,7 @@ theorem step_fupdN_le {n m : Nat} {Eo Ei : CoPset} {P : PROP} :

@[rocq_alias step_fupd_fupd]
theorem step_fupd_fupd {Eo Ei : CoPset} {P : PROP} : (|={Eo}[Ei]▷=> P) ⊣⊢ (|={Eo}[Ei]▷=> |={Eo}=> P) :=
⟨mono <| later_mono <| mono fupd_intro, mono <| later_mono BIFUpdate.trans⟩
⟨step_fupd_mono fupd_intro, mono <| later_mono BIFUpdate.trans⟩

@[rocq_alias step_fupdN_mono]
theorem step_fupdN_mono {n : Nat} {Eo Ei : CoPset} {P Q : PROP} (H : P ⊢ Q) :
Expand Down Expand Up @@ -486,7 +485,7 @@ theorem step_fupdN_plain {E1 E2 : CoPset} {n : Nat} {P : PROP} [Plain P] :
| zero => exact except0_intro.trans fupd_intro
| succ n ih =>
simp only [Nat.repeat]
refine (mono <| later_mono <| mono ih).trans ?_
refine (step_fupd_mono ih).trans ?_
refine step_fupd_fupd.2.trans ?_
refine step_fupd_plain.trans ?_
refine (mono <| later_mono <| except0_laterN n).trans ?_
Expand Down