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Proof step 116 from proof inv-rmdir (previous step)

# links(m, dirs) = m3, dirs[entries[str]] = mkdir(m0, md, # links(entries[str], dirs), m2, ∅), dirs[m] = mkdir(m1, md2, m3, 0, entries), entries[str] = entries0[str], dirs[m] = mkdir(m1, md0, m3, m4, entries0), m4 = 0, afs-cons(dirs, files), entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, str ∈ entries0, 1 ≤ m1, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ entries[str] = ROOT_INO, m1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 117:
dirs[m] = mkdir(m1, md0, # links(m, dirs), 0, entries0), dirs[entries0[str]] = mkdir(m0, md, # links(entries0[str], dirs), m2, ∅), afs-cons(dirs, files), m ∈ dirs, str ∈ entries0, entries0[str] ∈ dirs, 1 ≤ m1, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, m1 = 0

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