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Proof step 17 from proof same-put (previous step)

p0 ∈ sdt[str], str ∈ sdt, str ∈ sdt[str, sdt[str][p0, tree0]], ∀ tree, tree0, tree1. p0 ∈ tree → tree[p0, tree0][p0, tree1] = tree[p0, tree1] ⊦ dnode(md, sdt[str, sdt[str][p0, tree0]][str, sdt[str, sdt[str][p0, tree0]][str][p0, tree1]]) = dnode(md, sdt[str, sdt[str][p0, tree1]]), p0 = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
str ∈ sdt, p0 ∈ sdt[str], ∀ tree, tree0, tree1. p0 ∈ tree → tree[p0, tree0][p0, tree1] = tree[p0, tree1] ⊦ dnode(md, sdt[str, sdt[str][p0, tree0][p0, tree1]]) = dnode(md, sdt[str, sdt[str][p0, tree1]]), p0 = ε

Rule argument

Additional information

Used simplifier rules: ⊦ str ∈ sdt[str, tree]; (s)% ⊦ sdt[str, tree0][str, tree] = sdt[str, tree]; (s)% ⊦ sdt[str, tree][str] = tree; (s)