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Proof step 43 from proof at-mod (previous step)

sdt[str] = dnode(md0, sdt0), q0 ∈ sdt[str0], str ∈ sdt, str0 ∈ sdt, ∀ md2, sdt2, md3, sdt3, q, md4, sdt4. dnode(md2, sdt2) = dnode(md3, sdt3) ∧ q ∈ dnode(md4, sdt4) → dnode(md4, sdt4)[q] = (q = ε ⊃ dnode(md4, sdt4);dnode(md3, sdt4)[q]) ⊦ sdt[str0][q0] = (str0 ' + q0 = str ' ⊃ sdt[str0][q0][restn(# q0, ε), dnode(md1, sdt1)];dnode(md, sdt[str, dnode(md0, sdt1)])[str0 ' + q0]), 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, dnode(md0, sdt1)], md] flags: <all paths>

Additional information

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