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Proof step 26 from proof abs-nlinks-h (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ str ' ∈ tree ↔ (∃ md, sdt. tree = dnode(md, sdt) ∧ str ∈ sdt)
Proof step 28:
tree[p0 + str '] = fnode(⌜ino1⌝ ), dirs[m0] = mkdir(m, md, m1, m2, entries), links(ino1, dirs) = ∅, ((abs|(tree, ino0, p0, m0) * abs(tree[p0], m0)))(dirs), ispath(p0, ino0, m0, dirs, files), p0 ∈ tree, ino1 ∈ files, ino0 ∈ dirs, m0 ∈ dirs, str ∈ entries, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∃ md, sdt. tree[p0] = dnode(md, sdt) ∧ str ∈ sdt, entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦

Rule argument

spec: directory-tree name: dnode-onein seq: ⊦ str ' ∈ tree ↔ (∃ md, sdt. tree = dnode(md, sdt) ∧ str ∈ sdt) subst: [tree, str] → [tree[p0], str] flags: <all paths>

Additional information

Used terms: tree[p0], str