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Proof step 53 from proof inv-rmdir (previous step)

(entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m5, md1, m2 + 1, m7, entries), (ino = entries0[str] ⊃ mkdir(m5, md1, m2, m7, entries) ;(ino = m ⊃ mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str);mkdir(m9, md0, m10, m11, entries1)) ) = mkdir(m12, md4, m13, m14, entries2), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs0[entries0[str]] = mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅), files[ino] = mkfile(m6, md, m8, content), dirs0[ino] = mkdir(m9, md0, m10, m11, entries1), afs-cons(dirs0, files), entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, str ∈ entries0, ino ∈ dirs0 → m10 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m8 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m, ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, entries)]) = ∅ → entries2 = ∅) ∧ ( ino ∈ dirs0 → m13 = # links(ino, dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, entries)]) ∧ # links(ino, dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, entries)]) ≤ 1 ∧ m12 = # entries2 ∧ m14 = # subdirs(ino, dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, entries)])) ∧ ( ino ∈ files → ¬ ino ∈ dirs0 ∧ m8 = # links(ino, dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, entries)])) ∧ (ino ∈ dirs0 ∧ name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
# links(entries0[str], dirs0) = m2 + 1, (ino = entries0[str] ⊃ mkdir(m5, md1, m2, m7, ∅) ;(ino = m ⊃ mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str);mkdir(m9, md0, m10, m11, entries1)) ) = mkdir(m12, md4, m13, m14, entries2), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), files[ino] = mkfile(m6, md, m8, content), dirs0[ino] = mkdir(m9, md0, m10, m11, entries1), afs-cons(dirs0, files), entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, str ∈ entries0, ino ∈ dirs0 → m10 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m8 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) = ∅ → entries2 = ∅) ∧ ( ino ∈ dirs0 → m13 = # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ∧ # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ≤ 1 ∧ m12 = # entries2 ∧ m14 = # subdirs(ino, dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, ∅)])) ∧ (ino ∈ dirs0 ∧ name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files)

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs); (s)%⊦ ino0 ∈ dirs → links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries -- str)]) = (str ∈ entries ∧ entries[str] = ino ⊃ links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str) ;links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) ); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) ∧ ino ≠ ino1 → links(ino0, dirs[ino1, ad][ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs[ino1, ad]); (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)