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Proof step 9 from proof write-inv-rec (previous step)

files1 -- mkinode(ino, md, boolvar, m0, m3, m1).ino = files0 -- mkinode(ino, md, boolvar, m0, m3, m1).ino, files1[mkinode(ino, md, boolvar, m0, m3, m1).ino].meta = files0[mkinode(ino, md, boolvar, m0, m3, m1).ino].meta, files0[mkinode(ino, md, boolvar, m0, m3, m1).ino].size = mkinode(ino, md, boolvar, m0, m3, m1).size, files1[mkinode(ino, md, boolvar, m0, m3, m1).ino].size = files0[mkinode(ino, md, boolvar, m0, m3, m1).ino].size, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m5, md1, m6, content0), afs-cons(dirs, files1), write-inv(n0, n1, buf, n, files0[mkinode(ino, md, boolvar, m0, m3, m1).ino].content, files1[mkinode(ino, md, boolvar, m0, m3, m1).ino].content), mkinode(ino, md, boolvar, m0, m3, m1).ino ∈ files0, mkinode(ino, md, boolvar, m0, m3, m1).ino ∈ files1, n + m ≤ # buf, m + (n0 + n) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, n0 + n ≤ n1, n1 - n0 ≤ # buf ⊦ content0[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content0), (n0 + n) % VFS_PAGE_SIZE, m)].stream = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
files1 -- ino = files0 -- ino, files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), files0[ino] = mkfile(m2, md0, m4, content), afs-cons(dirs, files1), write-inv(n0, n1, buf, n, content, content0), ino ∈ files1, ino ∈ files0, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m + (n0 + n) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, n + m ≤ # buf ⊦ content0[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content0), (n0 + n) % VFS_PAGE_SIZE, m)].stream = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m < n → n ≠ 0; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)