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Proof step 104 from proof truncate-empty (previous step)

files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((content0 upto (m0 * VFS_PAGE_SIZE + n0)).stream from m0 * VFS_PAGE_SIZE + n0 = σ⊥), n0 ≠ 0 ∧ m0 ∈ content0, (m0 * VFS_PAGE_SIZE + n0 = m0 * VFS_PAGE_SIZE + n0 ∧ n0 ≠ 0 ∧ n0 < VFS_PAGE_SIZE) ∧ (true ↔ finp(content0.stream) → ⌜(m0 + 1) * VFS_PAGE_SIZE⌝ < # content0.stream ∨ ⌜(m0 + 1) * VFS_PAGE_SIZE⌝ = # content0.stream)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 105:
files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((content0 upto m0 * VFS_PAGE_SIZE).stream from m0 * VFS_PAGE_SIZE = σ⊥)

Rule argument

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%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)% ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; (s)% ⊦ # content.stream = ∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)