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Proof step 11 from proof crash-neutral-writepage (previous step)

# buf = VFS_PAGE_SIZE, afs-cons(dirs, files), m ∈ files ⊦ ⟨asynced := ?⟩ ( asynced ∧ dirs \ orphans(dirs, files) = dirs \ orphans(dirs, files[m, files[m].content:= files[m].content[pageno, buf]]) ∧ files \ orphans(dirs, files) = files[m, files[m].content:= files[m].content[pageno, buf]] \ orphans(dirs, files[m, files[m].content:= files[m].content[pageno, buf]])), ⟨fail#(; ; err); asynced := ?⟩ asynced

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, m1, content), afs-cons(dirs, files), m ∈ files ⊦ ⟨asynced := ?⟩ ( asynced ∧ dirs \ orphans(dirs, files) = dirs \ orphans(dirs, files[m, files[m].content:= content[pageno, buf]]) ∧ files \ orphans(dirs, files) = files[m, files[m].content:= content[pageno, buf]] \ orphans(dirs, files[m, files[m].content:= content[pageno, buf]])), ⟨fail#(; ; err); asynced := ?⟩ asynced

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m], m0, md, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m], m0, md, m1, content