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Proof step 21 from proof abs-nlinks-h (previous step)

tree[p0 + str '] = fnode(⌜ino1⌝ ), links(ino1, dirs) = ∅, abs(tree, ino0)(dirs), ispath(p0, ino0, m0, dirs, files), str ∈ dirs[m0].entries, m0 ∈ dirs, ino0 ∈ dirs, str ' ∈ tree[p0], p0 ∈ tree, ino1 ∈ files, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, dirs[m0].entries[str] ∈ dirs ∨ dirs[m0].entries[str] ∈ files ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
tree[p0 + str '] = fnode(⌜ino1⌝ ), dirs[m0] = mkdir(m, md, m1, m2, entries), links(ino1, dirs) = ∅, abs(tree, ino0)(dirs), ispath(p0, ino0, m0, dirs, files), ino1 ∈ files, p0 ∈ tree, str ' ∈ tree[p0], ino0 ∈ dirs, m0 ∈ dirs, str ∈ entries, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, entries[str] ∈ dirs ∨ entries[str] ∈ 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[m0], m, md, m1, 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[m0], m, md, m1, m2, entries