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Proof step 55 from proof write-inv-rec (previous step)

VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE = n3 + n0 + n, n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), files0[ino] = mkfile(m2, md0, m4, content), n2 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n2 + m ≤ VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE ≤ n1, m0 * VFS_PAGE_SIZE ≤ n + n0, n + m ≤ # buf, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m + n2 ≤ VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE ≤ # buf + n0, m0 * VFS_PAGE_SIZE ≤ n3 + n0 + n ⊦ ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + ((((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE) to n2) + ((⌜buf⌝ from n) to m) + ((((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE + n2 + m) to n4) + (content.stream from n0 + n from n3) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m), n4 + m = 0, #(((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE) < ⌜VFS_PAGE_SIZE⌝ , #(((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE + n2 + m) < ⌜n4⌝ , #(((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n)) < ⌜m0 * VFS_PAGE_SIZE + n2 + m⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
n0 + n = m0 * VFS_PAGE_SIZE + n2, VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE = n3 + n0 + n, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n2 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), n2 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m0 * VFS_PAGE_SIZE ≤ n3 + n0 + n, m0 * VFS_PAGE_SIZE ≤ # buf + n0, m + n2 ≤ VFS_PAGE_SIZE, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf, m0 * VFS_PAGE_SIZE ≤ n + n0, m0 * VFS_PAGE_SIZE ≤ n1, n2 + m ≤ VFS_PAGE_SIZE ⊦ n4 + m = 0, ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + ((((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE) to n2) + ((⌜buf⌝ from n) to m) + ((((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE + n2 + m) to n4) + (content.stream from n0 + n from n3) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m), #(((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE + n2 + m) < ⌜n4⌝ , #(((content.stream to n0) + (⌜buf⌝ to n)) + (content.stream from n0 + n) from m0 * VFS_PAGE_SIZE) < ⌜VFS_PAGE_SIZE⌝

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; 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⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%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)% ⊦ #(content.stream from n) = ∞; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ # ⌜buf⌝ = ⌜# buf⌝ ; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ # content.stream = ∞; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)