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Proof step 83 from proof inv-link (previous step)

# links(m, dirs) = m3, dirs[m] = mkdir(m0, md2, m3, m4, entries), files[entries0[str]] = mkfile(m1, md, # links(entries0[str], dirs), content0), dirs[ino] = mkdir(m2, md3, # links(ino, dirs), m6, entries0), entries0[str] = dirs[ino0].entries[str], dirs[m] = mkdir(m0, md0, m3, m4, entries1), afs-cons(dirs, files), ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries0[str] ∈ files, ino0 ∈ dirs, str ∈ dirs[ino0].entries, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, str0 ∈ entries, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
entries0[str] = dirs[ino0].entries[str], dirs[ino] = mkdir(m2, md3, # links(ino, dirs), m6, entries0), files[entries0[str]] = mkfile(m1, md, # links(entries0[str], dirs), content0), dirs[m] = mkdir(m0, md0, # links(m, dirs), m4, entries1), afs-cons(dirs, files), str ∈ dirs[ino0].entries, ino0 ∈ dirs, entries0[str] ∈ files, m ∈ dirs, str ∈ entries0, ino ∈ dirs, ¬ str0 ∈ entries1, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = 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)