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Proof step 19 from proof afs-cons-mkdir-ino (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), files[ino0] = mkfile(m1, md1, m3, content), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dirs[ino0].entries = ∅, ino0 ∈ dirs → dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs), ino0 ∈ files → ¬ ino0 ∈ dirs ∧ m3 = # links(ino0, dirs), ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → dirs[ino0].entries[name] ∈ dirs ∨ dirs[ino0].entries[name] ∈ files, ino0 ∈ files ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, ino ∈ files, ino ∈ dirs, str ∈ entries, ( (ino0 = ino ∨ ino0 ∈ dirs) ∧ ino0 ≠ ROOT_INO ∧ links(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)]) = ∅ → (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries = ∅) ∧ ( ino0 = ino ∨ ino0 ∈ dirs → ¬ ino0 ∈ files ∧ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).nlink = # links(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)]) ∧ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).nlink ≤ 1 ∧ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).size = # (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries ∧ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).nsubdirs = # subdirs(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)])) ∧ ( ino0 ∈ files → ¬ ino0 ∈ dirs ∧ m3 = # links(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)])) ∧ ( (ino0 = ino ∨ ino0 ∈ dirs) ∧ name ∈ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries → (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries [name ] = ino ∨ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries [name ] ∈ dirs ∨ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries [name ] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
files[ino0] = mkfile(m1, md1, m3, content), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → dirs[ino0].entries[name] ∈ dirs ∨ dirs[ino0].entries[name] ∈ files, ino0 ∈ files → ¬ ino0 ∈ dirs ∧ m3 = # links(ino0, dirs), ino0 ∈ dirs → dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs), ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dirs[ino0].entries = ∅, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, str ∈ entries, ino ∈ dirs, ino ∈ files, ( (ino0 = ino ∨ ino0 ∈ dirs) ∧ ino0 ≠ ROOT_INO ∧ links(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)]) = ∅ → (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries = ∅) ∧ ( ino0 = ino ∨ ino0 ∈ dirs → ¬ ino0 ∈ files ∧ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).nlink = # links(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)]) ∧ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).nlink ≤ 1 ∧ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).size = # (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries ∧ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).nsubdirs = # subdirs(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)])) ∧ ( ino0 ∈ files → ¬ ino0 ∈ dirs ∧ m3 = # links(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)])) ∧ ( (ino0 = ino ∨ ino0 ∈ dirs) ∧ name ∈ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries → (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries [name ] = ino ∨ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries [name ] ∈ dirs ∨ (ino0 = ino ⊃ mkdir(0, md, 1, 0, ∅);(dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0]).entries [name ] ∈ files)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)