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Proof step 24 from proof write-inv-strong-rec (previous step)

files1 -- ino = files0 -- ino, files1[ino] = mkfile(m, md1, # links(ino, dirs), content), dirs[ino] = mkdir(m4, md2, m6, m7, entries), files0[ino] = mkfile(m, md1, m5, content0), afs-cons(dirs, files1), write-inv(n0, n3 + n0 + n, buf, n, content0, content), write-inv (n0, n3 + n0 + n, 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))]), ino ∈ files0, ino ∈ files1, ROOT_INO ∈ dirs, n1 ∈ content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n3, n2))], min(n3, n2) ≤ n3, (n0 + n) % VFS_PAGE_SIZE + min(n3, n2) ≤ VFS_PAGE_SIZE, n ≤ # buf, n3 + n ≤ # buf ⊦ # content[(n0 + n) / VFS_PAGE_SIZE, copy(buf, n, getpage((n0 + n) / VFS_PAGE_SIZE, content), (n0 + n) % VFS_PAGE_SIZE, min(n3, n2))][n1] = VFS_PAGE_SIZE, ino ∈ dirs

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: n1 = (n0 + n) / VFS_PAGE_SIZE

Additional information

Used simplifier rules: ⊦ n ≠ n0 → content[n0, buf][n] = content[n]; (s)% ⊦ n ≠ n0 → (n ∈ content[n0, buf] ↔ n ∈ content); (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ content[n, buf][n] = buf; (s)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, m0, content) → # getpage(n, content) = VFS_PAGE_SIZE; (s) Used formulas: n1 = (n0 + n) / VFS_PAGE_SIZE