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Proof step 23 from proof at-put (previous step)

sdt0[str0][p0] = dnode(md, sdt), q = ε, q ∈ dnode(md0, sdt0)[str0 ' + p0, dnode(md, sdt[str, tree0])], p0 ∈ sdt0[str0], str0 ∈ 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(# p0 + 1, q.tail)] ;(q ⊑ str0 ' + p0 ⊃ dnode(md0, sdt0)[q][restn(# q, str0 ' + p0) + str ', tree0];dnode(md0, sdt0)[q]) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: nil-at: ⊦ tree[ε] = tree;%put-rec: p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]]);%split-put: ⊦ p ∈ tree → tree[p + q, tree0] = tree[p, tree[p][q, tree0]];%nil-in: ⊦ ε ∈ tree;%put-here: ⊦ dnode(md, sdt)[str ', tree0] = dnode(md, sdt[str, tree0]);% ⊦ p + str ' ≠ ε; (s)% ⊦ restn(0, p) = p; (s)% ⊦ # ε = 0; (s)% ⊦ ε ⊑ p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ str ' + p ≠ ε; (s)% ⊦ p ⊑ ε ↔ p = ε; (s)