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Proof step 12 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), afs-cons(dirs, files1), write-inv(n0, n1, buf, n, content0, content), 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))]), 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 ⊦ afs-cons (dirs, files1 [ino, mkfile (m, md1, # links(ino, dirs), 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))]) ]) ∧ n0 + n + min(n1 - n0 + n, n2) ≤ n1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
files1 -- ino = files0 -- ino, files1[ino] = mkfile(m, md1, # links(ino, dirs), content), files0[ino] = mkfile(m, md1, m5, content0), n1 = n3 + n0 + n, afs-cons(dirs, files1), write-inv (n0, n1, buf, n + min(n3, n2), content0, content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n3, n2))]), write-inv(n0, n1, buf, n, content0, content), ino ∈ files1, ino ∈ files0, (n0 + n) % VFS_PAGE_SIZE + min(n3, n2) ≤ VFS_PAGE_SIZE, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ afs-cons (dirs, files1 [ino, mkfile (m, md1, # links(ino, dirs), content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n3, n2))]) ]) ∧ n0 + n + min(n3, n2) ≤ n1

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: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n1, n0 + n, n3