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Proof step 47 from proof writepage-prepost (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
# buf0 = n4 + n0 + n1, # σ = ∞, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 ≤ VFS_PAGE_SIZE, n0 + n1 ≤ # buf0, m + n1 ≤ # buf1, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ #((⌜buf1⌝ from m) to n1) = ∞, (((σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from n0 + n1) + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE) = σ from n3 * VFS_PAGE_SIZE + n0 + n1

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ ⌜m⌝ + n∞ = ∞ ↔ n∞ = ∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)% ⊦ σ0 + σ3 = σ0 + σ4 ↔ σ3 = σ4 ∨ # σ0 = ∞; (ws)