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Proof step 5 from proof abs-fold-del-p (previous step)

# entries = m + 1, tree[p] = dnode(md, sdt), ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(m, md, m0, m1, entries -- str) * abs(sdt -- str, entries -- str) * D))(dirs), p ∈ tree, str ∈ entries ⊦ entries = ∅, ((abs(tree -- (p + str '), ROOT_INO) * D))(dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
q ≠ ε ⊦ p ∈ tree → tree -- (p + q) = tree[p, tree[p] -- q]
Proof step 7:
# entries = m + 1, tree[p] = dnode(md, sdt), ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(m, md, m0, m1, entries -- str) * abs(sdt -- str, entries -- str) * D))(dirs), str ∈ entries, p ∈ tree ⊦ str ' = ε, entries = ∅, ((abs(tree[p, tree[p] -- str '], ROOT_INO) * D))(dirs)

Rule argument

spec: directory-tree name: split-del seq: q ≠ ε ⊦ p ∈ tree → tree -- (p + q) = tree[p, tree[p] -- q] subst: [q, p, tree] → [str ', p, tree] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ' ≠ ε; (s) Used terms: str ', p, tree