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Proof step 32 from proof write-inv-strong-rec (previous step)

files1 -- ino = files0 -- ino, files0[ino] = mkfile(m, md1, m5, content0), files1[ino] = mkfile(m, md1, # links(ino, dirs), content), # buf < n + min(n1 - n0 + n, n2), afs-cons(dirs, files1), write-inv(n0, n1, buf, n, content0, content), ino ∈ files0, ino ∈ files1, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, (n0 + n) % VFS_PAGE_SIZE + min(n1 - n0 + n, n2) ≤ VFS_PAGE_SIZE ⊦ min(n1 - n0 + n, n2) = 0, 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))])

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n1, n0 + n, n3]

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < min(n, m); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n1, n0 + n, n3