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Proof step 263 from proof refine-truncate (previous step)

files0[ino2] = mkfile(m2 * VFS_PAGE_SIZE + n0, md0, # links(ino2, dirs), content0), root.dir?, m1 * VFS_PAGE_SIZE + n1 < m2 * VFS_PAGE_SIZE + n0, n0 < VFS_PAGE_SIZE, m1 * VFS_PAGE_SIZE + n1 < n, dom of < ino3, n1 < VFS_PAGE_SIZE, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto (n < m2 * VFS_PAGE_SIZE + n0 ⊃ n;m2 * VFS_PAGE_SIZE + n0))]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0), of-cons(of, dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto (n < m2 * VFS_PAGE_SIZE + n0 ⊃ n;m2 * VFS_PAGE_SIZE + n0))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ino2 ∈ files0, ROOT_INO ∈ dirs, psynced0 → asynced0 ⊦ (m1 ∈ content0 ⊃ content0[m1];zeropage)[n1] = (m1 * VFS_PAGE_SIZE < (n < m2 * VFS_PAGE_SIZE + n0 ⊃ n;m2 * VFS_PAGE_SIZE + n0) ∧ m1 ∈ content0 ⊃ content0[m1];zeropage)[n1], root[path].dir?, ino2 ∈ dirs, m2 * VFS_PAGE_SIZE + n0 ≤ n ∧ n0 ≠ 0 ∧ m2 ∈ content0

User applied rule case distinction

And obtained the following new goals

Proof step 264:
files0[ino2] = mkfile(m2 * VFS_PAGE_SIZE + n0, md0, # links(ino2, dirs), content0), root.dir?, n1 < VFS_PAGE_SIZE, dom of < ino3, m1 * VFS_PAGE_SIZE + n1 < n, n0 < VFS_PAGE_SIZE, m1 * VFS_PAGE_SIZE + n1 < m2 * VFS_PAGE_SIZE + n0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto (n < m2 * VFS_PAGE_SIZE + n0 ⊃ n;m2 * VFS_PAGE_SIZE + n0))]), afs-cons(dirs, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto (n < m2 * VFS_PAGE_SIZE + n0 ⊃ n;m2 * VFS_PAGE_SIZE + n0))]), of-cons(of, dirs, files0), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ROOT_INO ∈ dirs, ino2 ∈ files0, m1 ∈ content0, psynced0 → asynced0 ⊦ content0[m1][n1] = (m1 * VFS_PAGE_SIZE < (n < m2 * VFS_PAGE_SIZE + n0 ⊃ n;m2 * VFS_PAGE_SIZE + n0) ∧ m1 ∈ content0 ⊃ content0[m1];zeropage)[n1], root[path].dir?, ino2 ∈ dirs, m2 * VFS_PAGE_SIZE + n0 ≤ n ∧ n0 ≠ 0 ∧ m2 ∈ content0

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ n < VFS_PAGE_SIZE → (zeropage)[n] = zero; (s)