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Proof step 14 from proof in-mod (previous step)

sdt0[str][p0] = dnode(md0, sdt), str ∈ sdt0, p0 ∈ sdt0[str], ∀ md, sdt0, md0, sdt, q, md1. dnode(md, sdt0)[p0] = dnode(md0, sdt) ∧ p0 ∈ dnode(md, sdt0) → (q ∈ dnode(md, sdt0)[p0, dnode(md1, sdt)] ↔ q ∈ dnode(md, sdt0)) ∨ p0 = ε ⊦ str0 ' ∈ dnode(md, sdt0)[str ' + p0, dnode(md1, sdt)] ∧ q0 ∈ dnode(md, sdt0)[str ' + p0, dnode(md1, sdt)][str0 '] ↔ str0 ∈ sdt0 ∧ q0 ∈ sdt0[str0]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: put-rec seq: p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]]) subst: [tree0, p, str, sdt, md] → [dnode(md1, sdt), p0, str, sdt0, md] flags: <all paths>

Additional information

Used terms: dnode(md1, sdt), p0, str, sdt0, md