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Proof step 113 from proof inv-rmdir (previous step)

# links(entries[str], dirs) = dirs[entries[str]].nlink, # links(m, dirs) = dirs[m].nlink, dirs[entries[str]].entries = ∅, dirs[m].nsubdirs = 0, entries[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md2, dirs[m].nlink, 0, entries), dirs[entries[str]] = mkdir(dirs[entries[str]].size, md1, dirs[entries[str]].nlink, dirs[entries[str]].nsubdirs, ∅), afs-cons(dirs, files), str ∈ dirs[m].entries, m ∈ dirs, str ∈ entries, entries[str] ∈ dirs, 1 ≤ dirs[m].size, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ dirs[m].size = 0, entries[str] = ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 114:
# links(m, dirs) = dirs[m].nlink, # links(entries[str], dirs) = m1, dirs[m].nsubdirs = 0, dirs[entries[str]] = mkdir(m0, md1, m1, m2, ∅), dirs[m] = mkdir(dirs[m].size, md2, dirs[m].nlink, 0, entries), entries[str] = dirs[m].entries[str], dirs[entries[str]] = mkdir(m0, md, m1, m2, entries0), entries0 = ∅, afs-cons(dirs, files), entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, str ∈ dirs[m].entries, 1 ≤ dirs[m].size, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ dirs[m].size = 0, entries[str] = ROOT_INO

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[entries[str]], m0, md, m1, m2, 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[entries[str]], m0, md, m1, m2, entries0