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Proof step 178 from proof refine-truncate (previous step)

VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m1 * VFS_PAGE_SIZE + n1, md0, # links(ino2, dirs), content0), root.dir?, n3 < VFS_PAGE_SIZE, dom of < ino3, n1 < VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE + n3 < n, m1 * VFS_PAGE_SIZE + n1 < n, m0 * VFS_PAGE_SIZE < m1 * VFS_PAGE_SIZE + n1, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1), afs-cons(dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons(of, dirs, files1), of-cons (of, dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), m1 ∈ content0, ino2 ∈ files1, ROOT_INO ∈ dirs, m0 ∈ content0, m1 * VFS_PAGE_SIZE + n1 ≤ m0 * VFS_PAGE_SIZE + n3, psynced0 → asynced0 ⊦ m0 = m1, n0 = 0, n1 = 0, zero = content0[m0][n3], root[path].dir?, ino2 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 179:
VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m1 * VFS_PAGE_SIZE + n1, md0, # links(ino2, dirs), content0), root.dir?, m0 * VFS_PAGE_SIZE < n, n3 < VFS_PAGE_SIZE, dom of < ino3, n1 < VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE + n3 < n, m1 * VFS_PAGE_SIZE + n1 < n, m0 * VFS_PAGE_SIZE < m1 * VFS_PAGE_SIZE + n1, m0 * VFS_PAGE_SIZE + 1 < n, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1), afs-cons(dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons(of, dirs, files1), of-cons (of, dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), m1 ∈ content0, ino2 ∈ files1, ROOT_INO ∈ dirs, m0 ∈ content0, m1 * VFS_PAGE_SIZE + n1 ≤ m0 * VFS_PAGE_SIZE + n3, psynced0 → asynced0 ⊦ m0 = m1, n0 = 0, n1 = 0, n3 = 0, zero = content0[m0][n3], root[path].dir?, ino2 ∈ dirs

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic