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Proof step 11 from proof writepage-prepost (previous step)

# buf = VFS_PAGE_SIZE, ((m0 =>mkfile(n0, md, m, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files ⊦ [asynced := ?] ((m0 =>mkfile(n0, md, m, (σ to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (σ from VFS_PAGE_SIZE * n + VFS_PAGE_SIZE)) * F) )(files[m0, files[m0].content:= files[m0].content[n, buf]])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
# buf = VFS_PAGE_SIZE, files[m0] = mkfile(m1, md0, m2, content), ((m0 =>mkfile(n0, md, m, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files ⊦ [asynced := ?] ((m0 =>mkfile(n0, md, m, (σ to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (σ from VFS_PAGE_SIZE * n + VFS_PAGE_SIZE)) * F) )(files[m0, files[m0].content:= content[n, buf]])

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[m0], m1, md0, m2, 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[m0], m1, md0, m2, content