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Proof step 264 from proof afs-cons-rename-dir-negdentry (previous step)

# links(entries2[str], dirs) = m6, dirs[entries2[str]] = mkdir(m4, md3, m6, m7, entries0), dirs[m0] = mkdir(m2, md4, # links(m0, dirs), m5, entries1), dirs[m] = mkdir(m1, md, # links(m, dirs), m3, entries2), dirs[entries2[str]] = mkdir(m4, md2, m6, m7, entries), afs-cons(dirs, files), m0 ∈ dirs, m ∈ dirs, entries2[str] ∈ dirs, str ∈ entries2, m0 = m → md1 = md0, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 265:
dirs[m] = mkdir(m1, md, # links(m, dirs), m3, entries2), dirs[m0] = mkdir(m2, md4, # links(m0, dirs), m5, entries1), dirs[entries2[str]] = mkdir(m4, md2, # links(entries2[str], dirs), m7, entries), afs-cons(dirs, files), str ∈ entries2, entries2[str] ∈ dirs, m ∈ dirs, m0 ∈ dirs, ¬ str0 ∈ entries1, m0 = m → md1 = md0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

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)