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Proof step 245 from proof refine-readmeta (previous step)

files[m] = mkfile(m0, md1, # links(m, dirs), content), root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m ∈ files, ROOT_INO ∈ dirs, psynced → asynced ⊦ root[path].dir?, m ∈ dirs, root[path].fid ∈ abs-files(files)

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)%⊦ afs-cons(dirs, files) ∧ ¬ ino ∈ dirs ∧ ¬ ino ∈ files → links(ino, dirs) = ∅; (s)% ⊦ # ∅ = 0; (s)%¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid); (elim) Used terms: root[path], fid