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Proof step 12 from proof afs-cons-links-rmorphans (previous step)

dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries), links(m, dirs) = ∅, afs-cons(dirs, files), valid-ino(m, dirs, files), str ∈ entries, m ∈ dirs ⊦ # orphans(dirs, files) = 0, m = ROOT_INO, orphans(dirs, files) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs, files), str ∈ entries, m ∈ dirs ⊦ # orphans(dirs, files) = 0, m = ROOT_INO, orphans(dirs, files) = ∅

Rule argument

Additional information

Used simplifier rules: afs-cons-links-empty: ⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0));%afs-cons-notfile: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files;%valid-ino: ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files;%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n;%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)