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Proof step 46 from proof truncate-empty (previous step)

# fill(content0[m0], zero, n1, n0) = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ content0, ino0 ∈ files1 ⊦ [asynced := ?] ( ( (content0.stream to m0 * VFS_PAGE_SIZE) + ⌜fill(content0[m0], zero, n1, n0)⌝ + (content0.stream from (m0 + 1) * VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE + n1 = σ⊥), n0 = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 ≠ 0, n1 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino0 ∈ files1, m0 ∈ content0 ⊦ [asynced := ?] ( ( (content0.stream to m0 * VFS_PAGE_SIZE) + ⌜fill(content0[m0], zero, n1, n0)⌝ + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) to VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE + n1 = σ⊥)

Rule argument

Additional information

Used simplifier rules: append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%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)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ # fill(buf, d, m, n) = # buf; (s)