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Proof step 137 from proof inv-rmdir (previous step)

# links(entries[str], dirs) = dirs[entries[str]].nlink, # links(m, dirs) = dirs[m].nlink, dirs[entries[str]].entries = ∅, entries[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md2, dirs[m].nlink, dirs[m].nsubdirs, entries), dirs[entries[str]] = mkdir(dirs[entries[str]].size, md1, dirs[entries[str]].nlink, dirs[entries[str]].nsubdirs, ∅), entries[str] ≠ ROOT_INO, afs-cons(dirs, files), str ∈ dirs[m].entries, m ∈ dirs, str ∈ entries, entries[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 138:
# links(m, dirs) = m1, # links(entries[str], dirs) = dirs[entries[str]].nlink, dirs[entries[str]].entries = ∅, dirs[entries[str]] = mkdir(dirs[entries[str]].size, md1, dirs[entries[str]].nlink, dirs[entries[str]].nsubdirs, ∅), dirs[m] = mkdir(m0, md2, m1, m2, entries), entries[str] = entries0[str], dirs[m] = mkdir(m0, md, m1, m2, entries0), afs-cons(dirs, files), entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, str ∈ entries0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, entries[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[m], m0, md, m1, 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[m], m0, md, m1, m2, entries0