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Proof step 15 from proof writepage-prepost (previous step)

# buf = VFS_PAGE_SIZE, files[m0] = mkfile(m1, md0, # links(m0, dirs), content), ((m0 =>mkfile(n0, md, m, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files ⊦ [asynced := ?] ∃ content0. ((m0 => mkfile(n0, md, m, content0) * F))(files[m0, mkfile(m1, md0, # links(m0, dirs), content[n, buf])]) ∧ content0.stream = (σ to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (σ from VFS_PAGE_SIZE * n + VFS_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ ((ino =>mkfile(n, md, m, σ) * F))(files) ↔ (∃ content. ((ino => mkfile(n, md, m, content) * F))(files) ∧ content.stream = σ)
Proof step 17:
# buf = VFS_PAGE_SIZE, files[m0] = mkfile(m1, md0, # links(m0, dirs), content), afs-cons(dirs, files), m0 ∈ files, ∃ content. ((m0 => mkfile(n0, md, m, content) * F))(files) ∧ content.stream = σ ⊦ [asynced := ?] ∃ content0. ((m0 => mkfile(n0, md, m, content0) * F))(files[m0, mkfile(m1, md0, # links(m0, dirs), content[n, buf])]) ∧ content0.stream = (σ to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (σ from VFS_PAGE_SIZE * n + VFS_PAGE_SIZE)

Rule argument

spec: <toplevel> name: mkfile-stream seq: ⊦ ((ino =>mkfile(n, md, m, σ) * F))(files) ↔ (∃ content. ((ino => mkfile(n, md, m, content) * F))(files) ∧ content.stream = σ) subst: [files, F, σ, m, md, n, ino] → [files, F, σ, m, md, n0, m0] flags: <all paths>

Additional information

Used terms: files, F, σ, m, md, n0, m0