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Proof step 74 from proof inv-rmdir (previous step)

# links(entries0[str], dirs0) = m2 + 1, (ino = m ⊃ mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str) ;mkdir(# entries1, md0, # links(ino, dirs0), # subdirs(ino, dirs0), entries1) ) = mkdir(m12, md4, m13, m14, entries2), dirs0[ino] = mkdir(# entries1, md0, # links(ino, dirs0), # subdirs(ino, dirs0), entries1), files[ino] = mkfile(m6, md, m8, content), dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), ino = m, afs-cons(dirs0, files), str ∈ entries0, m ∈ dirs0, ROOT_INO ∈ dirs0, entries0[str] ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = m, entries0[str] = ROOT_INO, ino = entries0[str], m14 = # subdirs(ino, dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
# subdirs(m, dirs0) = m14 + 1, # entries0 = m3 + 1, # links(entries0[str], dirs0) = m2 + 1, dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), files[m] = mkfile(m6, md, m8, content), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m14 + 1, entries0), afs-cons(dirs0, files), entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, str ∈ entries0, # links(m, dirs0) ≤ 1, name ∈ entries0 → entries0[name] ∈ dirs0 ∨ entries0[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m, entries0 = ∅, m14 = #(subdirs(m, dirs0) -- str), m ≠ ROOT_INO ∧ links(m, dirs0) = ∅

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # ∅ = 0; (s)%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n0, n1, entries) → subdirs (p_ino, dirs[p_ino, mkdir(m0, md, n0, n2, entries -- str)]) = (str ∈ entries ∧ entries[str] ∈ dirs ⊃ subdirs(p_ino, dirs) -- str ;subdirs(p_ino, dirs) ); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)