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Proof step 91 from proof crash-neutral-rmdir (previous step)

# links(m, dirs) = m1, entries[str] = entries0[str], dirs[m] = mkdir(m0, md0, m1, 0, entries), dirs[entries[str]] = mkdir(m3, md1, # links(entries[str], dirs), m2, ∅), dirs[m] = mkdir(m0, md, m1, m4, entries0), m4 = 0, afs-cons(dirs, files), str ∈ entries0, entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, 1 ≤ m0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, entries[str] = ROOT_INO, m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 92:
dirs[entries0[str]] = mkdir(m3, md1, # links(entries0[str], dirs), m2, ∅), dirs[m] = mkdir(m0, md, # links(m, dirs), 0, entries0), entries0[str] ≠ ROOT_INO, m0 ≠ 0, afs-cons(dirs, files), m ∈ dirs, entries0[str] ∈ dirs, str ∈ entries0, 1 ≤ m0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat