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Proof step 5 from proof in-mod (previous step)

dnode(md, sdt0)[p] = dnode(md0, sdt), p ∈ dnode(md, sdt0) ⊦ q ∈ dnode(md, sdt0)[p, dnode(md1, sdt)] ↔ q ∈ dnode(md, sdt0), p = ε

User applied rule structural induction

And obtained the following new goals

Proof step 6:
dnode(md, sdt0)[str + p0] = dnode(md0, sdt), str + p0 ∈ dnode(md, sdt0), ∀ 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 ⊦ str + p0 = ε, q ∈ dnode(md, sdt0)[str + p0, dnode(md1, sdt)] ↔ q ∈ dnode(md, sdt0)

Rule argument

indvar: p

Additional information

Used simplifier rules: path freely generated by ε, +;;