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Proof step 28 from proof write-inv-strong-rec (previous step)

files1[ino] = mkfile(m2, md0, m3, content), files0[ino] = mkfile(m, md1, m5, content0), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1), ino ∈ files1, (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE ⊦ write-inv (n0, n1, buf, n + min(n1 - n0 + n, n2), content0, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n1 - n0 + n, n2))]), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1) ∧ files0[ino].content = content0 ∧ files1[ino].content = content ∧ n + min(n1 - n0 + n, n2) ≤ # buf ∧ min(n1 - n0 + n, n2) + (n0 + n) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
files0[ino] = mkfile(m, md1, m5, content0), files1[ino] = mkfile(m2, md0, m3, content), # buf < n + min(n1 - n0 + n, n2), write-inv(n0, n1, mkinode(ino, md, boolvar, m0, m4, m1), buf, n, dirs, files0, files1), ino ∈ files1, (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE ⊦ write-inv (n0, n1, buf, n + min(n1 - n0 + n, n2), content0, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n1 - n0 + n, n2))])

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ mkfile(m, md, m0, content).content = content; (s)%c: ⊦ m + n = n + m; from specification nat-basic