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Proof step 688 from proof refine-rmdir (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root[q].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(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ pre-rmdir(q + str ', ENOENT, user, root, abs-files(files), abs-of(of)), str ∈ entries

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: posix-pre name: pre-rmdir-enoent seq: ⊦ pre-rmdir(p, ENOENT, user, root, fs, ofh) ↔ ¬ p ∈ root subst: [ofh, fs, root, user, p] → [abs-of(of), abs-files(files), root, user, q + str '] flags: <all paths>

Additional information

Used simplifier rules: path-in-last: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries);%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s) Used terms: abs-of(of), abs-files(files), root, user, q + str '