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Proof step 74 from proof truncate-empty (previous step)

VFS_PAGE_SIZE = n2 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino0 ∈ files1, m0 ∈ content0, m0 * VFS_PAGE_SIZE + n1 ≤ m0 * VFS_PAGE_SIZE + n1 ⊦ [asynced := ?] ((((content0.stream from m0 * VFS_PAGE_SIZE + n1) to (m0 * VFS_PAGE_SIZE + n1 - m0 * VFS_PAGE_SIZE + n1)) + (σ⊥ to n2)) + σ⊥ = σ⊥), n1 = 0, n2 = 0, # content0.stream < ⌜m0 * VFS_PAGE_SIZE + n1⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
VFS_PAGE_SIZE = n2 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n1 ≠ 0, n2 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ content0, ino0 ∈ files1 ⊦ [asynced := ?] ((σ⊥ to n2) + σ⊥ = σ⊥)

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ [] + σ0 = σ0; (s)% ⊦ σ0 to 0 = []; (s)% ⊦ m - m = 0; (s)% ⊦ m + n - n + n1 = m - n1; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)% ⊦ # content.stream = ∞; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)