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Proof step 37 from proof inv-evict (previous step)

# links(m1, dirs) = 0, files[ino] = mkfile(m, md, m0, content), files[m1] = mkfile(m2, md0, 0, content0), afs-cons(dirs, files), m1 ∈ files, ROOT_INO ∈ dirs, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅ ⊦ m1 ∈ dirs, (ino ≠ m1 ∧ ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ≠ m1 ∧ dirs[ino].entries[name] ∈ files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 38:
# links(m1, dirs) = 0, files[m1] = mkfile(m2, md0, 0, content0), files[ino] = mkfile(m, md, m0, content), dirs[ino] = mkdir(m3, md1, m4, m5, entries), afs-cons(dirs, files), ROOT_INO ∈ dirs, m1 ∈ files, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs → m4 = # links(ino, dirs) ∧ m4 ≤ 1 ∧ m3 = # entries ∧ m5 = # subdirs(ino, dirs), ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files ⊦ m1 ∈ dirs, (ino ≠ m1 ∧ ino ∈ files → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ≠ m1 ∧ entries[name] ∈ files)

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[ino], m3, md1, m4, m5, entries]

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[ino], m3, md1, m4, m5, entries