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Proof step 52 from proof writepage-prepost (previous step)

# σ = ∞, # buf0 = n4 + n0 + n1, VFS_PAGE_SIZE = n5 + n0 + n1, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, m + n1 ≤ # buf1, n0 + n1 ≤ # buf0, n0 ≤ VFS_PAGE_SIZE, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ #((⌜buf1⌝ from m) to n1) = ∞, ((σ from n3 * VFS_PAGE_SIZE from n0 + n1) to n5) + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) = σ from n3 * VFS_PAGE_SIZE + n0 + n1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ ¬ # σ0 < ⌜m + n⌝ → σ0 from m from n = σ0 from m + n
Proof step 54:
# buf0 = n4 + n0 + n1, # σ = ∞, VFS_PAGE_SIZE = n5 + n0 + n1, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ VFS_PAGE_SIZE, n0 + n1 ≤ # buf0, m + n1 ≤ # buf1 ⊦ #((⌜buf1⌝ from m) to n1) = ∞, ((σ from n3 * VFS_PAGE_SIZE + n0 + n1) to n5) + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) = σ from n3 * VFS_PAGE_SIZE + n0 + n1, # σ < ⌜n3 * VFS_PAGE_SIZE + n0 + n1⌝

Rule argument

spec: stream, inst: buffer-inf name: from-from seq: ⊦ ¬ # σ0 < ⌜m + n⌝ → σ0 from m from n = σ0 from m + n subst: [n, m, σ0] → [n0 + n1, n3 * VFS_PAGE_SIZE, σ] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ ∞ < n∞; (s) Used terms: n0 + n1, n3 * VFS_PAGE_SIZE, σ