Plain-language statement
A variant of [fupd_mask_frame] that works well for accessors: Tailored to eliminate updates of the form [|={E1,E1∖E2}=> Q] and provides a way to transform the closing view shift instead of letting you prove the same side-conditions twice.
Exact Lean statement
@[rocq_alias fupd_mask_frame_acc]
theorem fupd_mask_frame_acc {E E' E1 E2 : CoPset} {P Q : PROP}:
E1 ⊆ E → (|={E1,E1 \ E2}=> Q) ⊢
(Q -∗ |={E \ E2,E'}=> (∀ R, (|={E1 \ E2,E1}=> R) -∗ |={E \ E2,E}=> R) -∗ P) -∗
(|={E,E'}=> P)Formal artifact
Lean source
@[rocq_alias fupd_mask_frame_acc]theorem fupd_mask_frame_acc {E E' E1 E2 : CoPset} {P Q : PROP}: E1 ⊆ E → (|={E1,E1 \ E2}=> Q) ⊢ (Q -∗ |={E \ E2,E'}=> (∀ R, (|={E1 \ E2,E1}=> R) -∗ |={E \ E2,E}=> R) -∗ P) -∗ (|={E,E'}=> P) := λ hE => by have hmask : E \ E2 ⊆ (E1 \ E2) ∪ (E \ E1) := by intro x hx; rw [mem_diff] at hx by_cases hx1 : x ∈ E1 · exact mem_union.2 <| .inl <| mem_diff.2 ⟨hx1, hx.2⟩ · exact mem_union.2 <| .inr <| mem_diff.2 ⟨hx.1, hx1⟩ have hdisj : (E1 \ E2) ## (E \ E1) := disjoint_subset_left diff_subset_left disjoint_diff_right refine wand_intro <| frame_right.trans <| (BIFUpdate.mono wand_elim_right).trans ?_ refine (BIFUpdate.mono ?_).trans <| fupd_mask_frame hE refine sep_emp.2.trans <| (sep_mono_right <| fupd_mask_intro_subseteq hmask).trans ?_ refine fupd_frame_left.trans <| (BIFUpdate.mono frame_right).trans <| fupd_elim ?_ refine BIFUpdate.mono <| sep_symm.trans ?_ refine (sep_mono ?_ .rfl).trans wand_elim_right refine forall_intro λ R => wand_intro <| frame_right.trans <| fupd_elim ?_ exact emp_sep.1.trans <| (fupd_mask_frame_right hdisj).trans <| by simp [subset_union_diff hE]- Project
- Iris-Lean
- License
- Apache-2.0
- Commit
- 37f53e0ac065
- Source
- Iris/Iris/BI/Updates.lean:431-449
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