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Proof step 4 from proof afs-cons-links-empty (previous step)

files[ino] = mkfile(m, md, m0, content), afs-cons(dirs, files) ⊦ links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → m0 = 0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
files[ino] = mkfile(m, md, m0, content), dirs[ino] = mkdir(m1, md0, m2, m3, entries), afs-cons(dirs, files) ⊦ links(ino, dirs) = ∅ ↔ (ino ∈ dirs → m2 = 0) ∧ (ino ∈ files → m0 = 0)

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, entries] → [dirs[ino], m1, md0, m2, 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], m1, md0, m2, entries