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Proof step 88 from proof refine-readdir (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root.dir?, root[path].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced ⊦ dom entries = dom root[path].entries

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 89:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root[path] = dnode(md0, sdt), root[path].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced ⊦ dom entries = dom 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], md0, sdt]

Additional information

Used simplifier rules: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt); (elim) Used terms: root[path], md0, sdt