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Proof step 139 from proof inv-rmdir (previous step)

# links(entries0[str], dirs) = dirs[entries0[str]].nlink, dirs[entries0[str]].entries = ∅, dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries0), dirs[entries0[str]] = mkdir(dirs[entries0[str]].size, md1, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, ∅), entries0[str] ≠ ROOT_INO, afs-cons(dirs, files), m ∈ dirs, str ∈ entries0, entries0[str] ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 140:
# links(entries0[str], dirs) = m3, dirs[entries0[str]] = mkdir(m1, md1, m3, m4, ∅), dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries0), dirs[entries0[str]] = mkdir(m1, md0, m3, m4, entries), entries = ∅, afs-cons(dirs, files), entries0[str] ∈ dirs, str ∈ entries0, m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, entries0[str] = ROOT_INO

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[entries0[str]], m1, md0, m3, m4, entries]

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[entries0[str]], m1, md0, m3, m4, entries