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Proof step 7 from proof tree-induction (previous step)

(∀ str. str ∈ sdt0 → Ptree(sdt0[str])) → Ptree(dnode(md0, sdt0)), ∀ md, sdt. (∀ str. str ∈ sdt → Ptree(sdt[str])) → Ptree(dnode(md, sdt)), ∀ fid. Ptree(fnode(fid)), ∀ tree0, Ptree. #n tree0 < #n dnode(md0, sdt0) → (∀ md, sdt. (∀ str. str ∈ sdt → Ptree(sdt[str])) → Ptree(dnode(md, sdt))) ∧ (∀ fid. Ptree(fnode(fid))) → Ptree(tree0) ⊦ Ptree(dnode(md0, sdt0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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