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Proof step 33 from proof in-mod (previous step)

sdt0[str][p0] = dnode(md0, sdt), str ∈ sdt0, p0 ∈ sdt0[str], ∀ md2, sdt1, md3, sdt2, q, md4. dnode(md2, sdt1)[p0] = dnode(md3, sdt2) ∧ p0 ∈ dnode(md2, sdt1) → (q ∈ dnode(md2, sdt1)[p0, dnode(md4, sdt2)] ↔ q ∈ dnode(md2, sdt1)) ⊦ str0 ∈ sdt0[str, sdt0[str][p0, dnode(md1, sdt)]] ∧ q0 ∈ dnode(md, sdt0[str, sdt0[str][p0, dnode(md1, sdt)]])[str0 '] ↔ str0 ∈ sdt0 ∧ q0 ∈ sdt0[str0], p0 = ε

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: one-at seq: str ∈ sdt ⊦ dnode(md, sdt)[str '] = sdt[str] subst: [str, sdt, md] → [str0, sdt0[str, sdt0[str][p0, dnode(md1, sdt)]], md] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ∈ sdt[str0, tree] ↔ str = str0 ∨ str ∈ sdt; (ws) Used terms: str0, sdt0[str, sdt0[str][p0, dnode(md1, sdt)]], md