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Proof step 10 from proof in-put (previous step)

⊦ q ∈ dnode(md, sdt[str, tree0]) ↔ (str ' ⊑ q ⊃ q.tail ∈ tree0;q ∈ dnode(md, sdt))

User applied rule constructor cut

And obtained the following new goals

Proof step 11:
⊦ ε ∈ tree
Proof step 12:
q = str0 + q0 ⊦ q ∈ dnode(md, sdt[str, tree0]) ↔ (str ' ⊑ q ⊃ q.tail ∈ tree0;q ∈ dnode(md, sdt))

Rule argument

var: q

Additional information

Used simplifier rules: nil-in: ⊦ ε ∈ tree;%path freely generated by ε, +;;% ⊦ p ⊑ ε ↔ p = ε; (s)% ⊦ str ' ≠ ε; (s)