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Proof step 7 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), str ∈ entries, p ∈ tree ⊦ str ' = ε, entries = ∅, ((abs(tree[p, tree[p] -- str '], ROOT_INO) * D))(dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# 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 ⊦ entries = ∅, ((abs(tree[p, dnode(md, sdt -- str)], ROOT_INO) * D))(dirs)

Rule argument

Additional information

Used simplifier rules: ⊦ dnode(md, sdt) -- str ' = dnode(md, sdt -- str); (s)% ⊦ str ' ≠ ε; (s)