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Proof step 381 from proof afs-cons-rename-dir-dentry (previous step)

(ino = entries0[str0] ⊃ (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md ;(ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries0);mkdir(m5, md4, m7, m8, entries)) ) = mkdir(m9, md5, m10, m11, entries1), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), files[ino] = mkfile(m0, md0, m2, content), dirs0[ino] = mkdir(m5, md4, m7, m8, entries), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries0[str0] ∈ dirs0, str0 ∈ entries0, m ∈ dirs0, ino ∈ dirs0 → m7 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m5 = # entries ∧ m8 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m2 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str0] = ROOT_INO, entries0[str0] = m, ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links (ino, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md ]) = ∅ → entries1 = ∅) ∧ ( ino ∈ dirs0 → m10 = # links (ino, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md ]) ∧ # links (ino, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md ]) ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs (ino, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md ])) ∧ ( ino ∈ files → ¬ ino ∈ dirs0 ∧ m2 = # links (ino, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md ])) ∧ (ino ∈ dirs0 ∧ name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 382:
(ino = entries0[str0] ⊃ mkdir(m3, md, # links(entries0[str0], dirs0), m6, ∅) ;(ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries0);mkdir(m5, md4, m7, m8, entries)) ) = mkdir(m9, md5, m10, m11, entries1), dirs0[ino] = mkdir(m5, md4, m7, m8, entries), files[ino] = mkfile(m0, md0, m2, content), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), afs-cons(dirs0, files), m ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, ROOT_INO ∈ dirs0, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files → ¬ ino ∈ dirs0 ∧ m2 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ dirs0 → m7 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m5 = # entries ∧ m8 = # subdirs(ino, dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str0] = m, entries0[str0] = ROOT_INO, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅) ∧ ( ino ∈ dirs0 → m10 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs (ino, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0], mkdir(m3, md, # links(entries0[str0], dirs0), m6, ∅)])) ∧ (ino ∈ dirs0 ∧ name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[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)%⊦ 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)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)