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Proof step 3 from proof again-put (previous step)

p ∈ tree ⊦ tree[p, tree[p]] = tree, p = ε

User applied rule structural induction

And obtained the following new goals

Proof step 4:
str + p0 ∈ tree, ∀ tree. p0 ∈ tree → tree[p0, tree[p0]] = tree ∨ p0 = ε ⊦ str + p0 = ε, tree[str + p0, tree[str + p0]] = tree

Rule argument

indvar: p

Additional information

Used simplifier rules: path freely generated by ε, +;;