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

dnode(md0, sdt0)[p] = dnode(md, sdt), p ∈ dnode(md0, sdt0) ⊦ q ∈ dnode(md0, sdt0)[p, dnode(md, sdt[str, tree0])] ↔ (p + str ' ⊑ q ⊃ restn(# p, q.tail) ∈ tree0;q ∈ dnode(md0, sdt0))

User applied rule structural induction

And obtained the following new goals

Proof step 6:
dnode(md0, sdt0)[ε] = dnode(md, sdt), ε ∈ dnode(md0, sdt0) ⊦ q ∈ dnode(md0, sdt0)[ε, dnode(md, sdt[str, tree0])] ↔ (ε + str ' ⊑ q ⊃ restn(# ε, q.tail) ∈ tree0;q ∈ dnode(md0, sdt0))
Proof step 15:
dnode(md0, sdt0)[str0 + p0] = dnode(md, sdt), str0 + p0 ∈ dnode(md0, sdt0), ∀ md0, sdt0, md, sdt, q, str, tree0. dnode(md0, sdt0)[p0] = dnode(md, sdt) ∧ p0 ∈ dnode(md0, sdt0) → (q ∈ dnode(md0, sdt0)[p0, dnode(md, sdt[str, tree0])] ↔ (p0 + str ' ⊑ q ⊃ restn(# p0, q.tail) ∈ tree0;q ∈ dnode(md0, sdt0))) ⊦ q ∈ dnode(md0, sdt0)[str0 + p0, dnode(md, sdt[str, tree0])] ↔ ((str0 + p0) + str ' ⊑ q ⊃ restn(#(str0 + p0), q.tail) ∈ tree0;q ∈ dnode(md0, sdt0))

Rule argument

indvar: p

Additional information

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