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Proof step 6 from proof at-put (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 7:
dnode(md0, sdt0)[ε] = dnode(md, sdt), q ∈ dnode(md0, sdt0)[ε, dnode(md, sdt[str, tree0])], ε ∈ dnode(md0, sdt0) ⊦ dnode(md0, sdt0)[ε, dnode(md, sdt[str, tree0])][q] = (ε + str ' ⊑ q ⊃ tree0[restn(# ε, q.tail)];(q ⊑ ε ⊃ dnode(md0, sdt0)[q][restn(# q, ε) + str ', tree0];dnode(md0, sdt0)[q]))
Proof step 19:
dnode(md0, sdt0)[str0 + p0] = dnode(md, sdt), q ∈ dnode(md0, sdt0)[str0 + p0, dnode(md, sdt[str, tree0])], 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])] → dnode(md0, sdt0)[p0, dnode(md, sdt[str, tree0])][q] = (p0 + str ' ⊑ q ⊃ tree0[restn(# p0, q.tail)];(q ⊑ p0 ⊃ dnode(md0, sdt0)[q][restn(# q, p0) + str ', tree0];dnode(md0, sdt0)[q])) ⊦ dnode(md0, sdt0)[str0 + p0, dnode(md, sdt[str, tree0])][q] = ((str0 + p0) + str ' ⊑ q ⊃ tree0[restn(#(str0 + p0), q.tail)] ;(q ⊑ str0 + p0 ⊃ dnode(md0, sdt0)[q][restn(# q, str0 + p0) + str ', tree0];dnode(md0, sdt0)[q]) )

Rule argument

indvar: p

Additional information

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