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Proof step 181 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries[str], dirs0) = m12 + 1, (ino = entries[str] ⊃ mkdir(m13, md, m12, m15, ∅) ;(ino = m ⊃ mkdir(m8, md1, # links(m, dirs0), m11, entries[str, entries2[str0]]) ;(ino = m0 ⊃ mkdir(m1, md2, # links(m0, dirs0), m2, entries2 -- str0) ;mkdir(# entries4, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries4) ) ) ) = mkdir(m20, md10, m21, m22, entries5), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m11, entries), dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), files[ino] = mkfile(m14, md8, m16, content), dirs0[ino] = mkdir(# entries4, md9, # links(ino, dirs0), # subdirs(ino, dirs0), entries4), entries2[str0] = ino, afs-cons(dirs0, files), m ∈ dirs0, ROOT_INO ∈ dirs0, entries[str] ∈ dirs0, m0 ∈ dirs0, str0 ∈ entries2, entries2[str0] ∈ dirs0, str ∈ entries, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries4 = ∅, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ # (entries2[str0] = ino ⊃ (links(entries2[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str) ;(entries[str] = ino ⊃ links(entries[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ) = 1, #((links(entries2[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str)) = 0, (entries2[str0] = ino ⊃ (links(entries2[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str) ;(entries[str] = ino ⊃ links(entries[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ) = ∅, entries[str] = ROOT_INO, entries[str] = m, entries[str] = m0, m0 = m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 182:
# links(entries[str], dirs0) = m12 + 1, (entries2[str0] = entries[str] ⊃ mkdir(m13, md, m12, m15, ∅) ;(entries2[str0] = m ⊃ mkdir(m8, md1, # links(entries2[str0], dirs0), m11, entries[str, entries2[str0]]) ;(entries2[str0] = m0 ⊃ mkdir(m1, md2, # links(entries2[str0], dirs0), m2, entries2 -- str0) ;mkdir(# entries4, md9, # links(entries2[str0], dirs0), # subdirs(entries2[str0], dirs0), entries4) ) ) ) = mkdir(m20, md10, m21, m22, entries5), files[entries2[str0]] = mkfile(m14, md8, m16, content), dirs0[entries2[str0]] = mkdir(# entries4, md9, # links(entries2[str0], dirs0), # subdirs(entries2[str0], dirs0), entries4), dirs0[entries[str]] = mkdir(m13, md6, m12 + 1, m15, ∅), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m11, entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), afs-cons(dirs0, files), str ∈ entries, entries2[str0] ∈ dirs0, str0 ∈ entries2, m0 ∈ dirs0, entries[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, # links(entries2[str0], dirs0) ≤ 1, name ∈ entries4 → entries4[name] ∈ dirs0 ∨ entries4[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ #((links(entries2[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str)) = 0, #((links(entries2[str0], dirs0) -- mklink(m0, str0)) ++ mklink(m, str)) = 1, entries[str] = m0, entries[str] = m, entries[str] = ROOT_INO, m0 = m

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)%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)% ⊦ ∅ ≠ ls ++ alink; (s)