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Proof step 82 from proof inv-link (previous step)

# links(m, dirs) = dirs[m].nlink, entries0[str] = dirs[ino0].entries[str], dirs[ino] = mkdir(m2, md3, # links(ino, dirs), m6, entries0), files[entries0[str]] = mkfile(m1, md, # links(entries0[str], dirs), content0), dirs[m] = mkdir(dirs[m].size, md2, dirs[m].nlink, dirs[m].nsubdirs, entries), afs-cons(dirs, files), str ∈ dirs[ino0].entries, ino0 ∈ dirs, entries0[str] ∈ files, m ∈ dirs, str ∈ entries0, ino ∈ dirs, ¬ str0 ∈ entries, ¬ str0 ∈ dirs[m].entries, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 83:
# links(m, dirs) = m3, dirs[m] = mkdir(m0, md2, m3, m4, entries), files[entries0[str]] = mkfile(m1, md, # links(entries0[str], dirs), content0), dirs[ino] = mkdir(m2, md3, # links(ino, dirs), m6, entries0), entries0[str] = dirs[ino0].entries[str], dirs[m] = mkdir(m0, md0, m3, m4, entries1), afs-cons(dirs, files), ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries0[str] ∈ files, ino0 ∈ dirs, str ∈ dirs[ino0].entries, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, str0 ∈ entries, str0 ∈ entries1

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], m0, md0, m3, m4, entries1]

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], m0, md0, m3, m4, entries1