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Proof step 56 from proof refine-readmeta (previous step)

dirs[m] = mkdir(# entries, md1, # links(m, dirs), m2, entries), root.dir?, root[path].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 ∈ dirs, psynced → asynced ⊦ md1 = root[path].meta ∧ m2 = # root[path].subdirs ∧ # entries = # root[path].entries

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
dirs[m] = mkdir(# entries, md1, # links(m, dirs), m2, entries), root[path] = dnode(md, sdt), root[path].dir?, 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 ∈ dirs, psynced → asynced ⊦ md1 = md ∧ m2 = # root[path].subdirs ∧ # entries = # sdt

Rule argument

spec: directory-tree name: dnode-elim seq: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt) subst: [tree, md, sdt] → [root[path], md, sdt]

Additional information

Used simplifier rules: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt); (elim) Used terms: root[path], md, sdt