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Proof step 140 from proof inv-rmdir (previous step)

# 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 141:
dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries0), dirs[entries0[str]] = mkdir(m1, md0, # links(entries0[str], dirs), m4, ∅), 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

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)