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Proof step 68 from proof at-mod (previous step)

sdt[str][p0] = dnode(md0, sdt0), str0 ∈ sdt, str ∈ sdt, p0 ∈ sdt[str], q0 ∈ sdt[str0], ∀ md, sdt, md0, sdt0, q, md1, sdt1. dnode(md, sdt)[p0] = dnode(md0, sdt0) ∧ p0 ∈ dnode(md, sdt) ∧ q ∈ dnode(md, sdt)[p0, dnode(md1, sdt1)] → dnode(md, sdt)[p0, dnode(md1, sdt1)][q] = (q ⊑ p0 ⊃ dnode(md, sdt)[q][restn(# q, p0), dnode(md1, sdt1)];dnode(md, sdt)[p0, dnode(md0, sdt1)][q]) ⊦ sdt[str0][q0] = dnode(md, sdt[str, sdt[str][p0, dnode(md0, sdt1)]])[str0 ' + q0], p0 = ε, str0 = str

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-dnode seq: ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p] = sdt[str][p] subst: [p, str, sdt, md] → [q0, str0, sdt[str, sdt[str][p0, dnode(md0, sdt1)]], md] flags: <all paths>

Additional information

Used simplifier rules: ⊦ str ≠ str0 → sdt[str0, tree][str] = sdt[str]; (s)% ⊦ str ≠ str0 → (str ∈ sdt[str0, tree] ↔ str ∈ sdt); (s) Used terms: q0, str0, sdt[str, sdt[str][p0, dnode(md0, sdt1)]], md