[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 98 from proof write-inv-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 99:
n0 + n = n3 + m0 * VFS_PAGE_SIZE, files1 -- ino = files0 -- ino, VFS_PAGE_SIZE = n4 + n3 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, m0 * VFS_PAGE_SIZE ≤ n + n0, m0 * VFS_PAGE_SIZE ≤ n0 + n, m0 * VFS_PAGE_SIZE ≤ # buf + n0, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf, m0 * VFS_PAGE_SIZE ≤ n1 ⊦ ((content.stream to n0) + (⌜buf⌝ to n) to m0 * VFS_PAGE_SIZE) + (((content.stream to n0) + (⌜buf⌝ to n) to n0 + n) from m0 * VFS_PAGE_SIZE) + ((⌜buf⌝ from n) to m) = (content.stream to n0) + (⌜buf⌝ to n + m), n4 + m = 0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%c: ⊦ m + n = n + m; 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 < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ + ⌜n1⌝ ↔ n + m < n0 + n1; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ 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)