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Proof step 19 from proof inv-write_inode (previous step)

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 ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs → m6 = # links(ino, dirs) ∧ m6 ≤ 1 ∧ m2 = # entries0 ∧ m8 = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries0 = ∅ ⊦ (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).entries = ∅) ∧ ( ino ∈ dirs → (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).nlink = # links(ino, dirs) ∧ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).nlink ≤ 1 ∧ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).size = # (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).entries ∧ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).nsubdirs = # subdirs(ino, dirs)) ∧ ( ino ∈ dirs ∧ name ∈ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).entries → (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).entries[name] ∈ dirs ∨ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);dirs[ino]).entries[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
dirs[ino] = mkdir(m2, md3, m6, m8, entries0), files[ino] = mkfile(m0, md2, m1, content0), files[m] = mkfile(m3, md0, m4, content), dirs[m] = mkdir(m5, md1, # links(m, dirs), m7, entries), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries0 = ∅, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino ∈ dirs → m6 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m2 = # entries0 ∧ m8 = # subdirs(ino, dirs) ⊦ ( ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).entries = ∅) ∧ ( ino ∈ dirs → (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).nlink = # links(ino, dirs) ∧ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).nlink ≤ 1 ∧ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).size = # (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).entries ∧ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).nsubdirs = # subdirs(ino, dirs)) ∧ ( ino ∈ dirs ∧ name ∈ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).entries → (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).entries[name] ∈ dirs ∨ (ino = m ⊃ mkdir(m5, md, # links(m, dirs), m7, entries);mkdir(m2, md3, m6, m8, entries0)).entries[name] ∈ files)

Proof step 19 from proof inv-write_inode (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information