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Proof step 183 from proof refine-unlink (previous step)

dirs[entries[str]].size = 0, dirs[entries[str]].entries = ∅ ↔ root[q + str '].entries = ∅, dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), fs = abs-files(files), root.dir?, root[q].dir?, root[q + str '].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), str ∈ entries, ino1 ∈ dirs, entries[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_unlink#(q + str ', user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EISDIR = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 184:
entries0 = ∅ ↔ root[q + str '].entries = ∅, dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), dirs[entries[str]] = mkdir(m, md0, m0, m2, entries0), fs = abs-files(files), m = 0, root[q + str '].dir?, 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), entries[str] ∈ dirs, ino1 ∈ dirs, str ∈ entries, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_unlink#(q + str ', user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EISDIR = err0)

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[entries[str]], m, md0, m0, m2, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[entries[str]], m, md0, m0, m2, entries0