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Proof step 51 from proof afs-cons-mkdir-ino (previous step)

dirs[ino0] = mkdir(# entries1, md2, # links(ino0, dirs), # subdirs(ino0, dirs), entries1), 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, # links(ino0, dirs) ≤ 1, name ∈ entries1 → entries1[name] ∈ dirs ∨ entries1[name] ∈ files, ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries1 = ∅, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ # subdirs(ino0, dirs) = # subdirs(ino0, dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino), str0 ∈ entries1 ∧ entries1[str0] ∈ dirs ↔ str0 ∈ (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0].entries ∧ ( (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0].entries[str0] = ino ∨ (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0].entries[str0] ∈ dirs), ino = 0, ino0 = m, str ∈ entries, ino ∈ files, ino ∈ dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 52:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), files[ino0] = mkfile(m1, md1, m3, content), dirs[ino0] = mkdir(# entries1, md2, # links(ino0, dirs), # subdirs(ino0, dirs), entries1), (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino0] = mkdir(m4, md, m5, m6, entries0), afs-cons(dirs, files), ino0 ∈ dirs, m ∈ dirs, ROOT_INO ∈ dirs, # links(ino0, dirs) ≤ 1, ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries1 = ∅, name ∈ entries1 → entries1[name] ∈ dirs ∨ entries1[name] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ # subdirs(ino0, dirs) = # subdirs(ino0, dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino), str0 ∈ entries1 ∧ entries1[str0] ∈ dirs ↔ str0 ∈ entries0 ∧ (entries0[str0] = ino ∨ entries0[str0] ∈ dirs), ino = 0, ino0 = m, ino ∈ dirs, ino ∈ files, str ∈ entries

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [( dirs [m, mkdir (m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino]) ] ++ ino )[ino0 ], m4, md3, m5, m6, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: ( dirs [m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino]) ] ++ ino )[ino0 ], m4, md3, m5, m6, entries0