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Proof step 21 from proof inv-write_inode (previous step)

(ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)) = mkdir(m9, md4, m10, m11, entries1), dirs[m] = mkdir(m5, md1, # links(m, dirs), m7, entries), files[m] = mkfile(m3, md0, m4, content), files[ino] = mkfile(m0, md2, m1, content0), dirs[ino] = mkdir(m2, md3, m6, m8, entries0), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino ∈ dirs → m6 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m2 = # entries0 ∧ m8 = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries0 = ∅ ⊦ (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries1 = ∅) ∧ (ino ∈ dirs → m10 = # links(ino, dirs) ∧ m10 ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries1 → entries1[name] ∈ dirs ∨ entries1[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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