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Proof step 19 from proof readpage-prepost (previous step)

# buf = VFS_PAGE_SIZE, files[m0] = mkfile(n0, md, # links(m0, dirs), content), F(files -- m0), afs-cons(dirs, files), m0 ∈ files, n ∈ content ⊦ ⌜content[n]⌝ = (content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n])
Proof step 21:
# buf = VFS_PAGE_SIZE, files[m0] = mkfile(n0, md, # links(m0, dirs), content), F(files -- m0), afs-cons(dirs, files), n ∈ content, m0 ∈ files ⊦ # ⌜content[n]⌝ = #((content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) ∧ (∀ n0. ⌜n0⌝ < # ⌜content[n]⌝ → ⌜content[n]⌝ [n0] = ((content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE)[n0])

Rule argument

spec: stream, inst: buffer-inf name: extensionality seq: ⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n]) subst: [σ2, σ] → [(content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE, ⌜content[n]⌝ ] flags: <all paths>

Additional information

Used terms: (content.stream from n * VFS_PAGE_SIZE) to VFS_PAGE_SIZE, ⌜content[n]⌝