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Proof step 187 from proof refine-truncate (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: directory-tree name: fnode-elim seq: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid) subst: [tree, fid] → [root[path], fid]

Additional information

Used simplifier rules: fid-ino: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ files → (tree[p] = fnode(fid) ↔ fid = ⌜m⌝ );% ⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files; (s)%¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid); (elim) Used terms: root[path], fid