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Proof step 29 from proof at-put (previous step)

sdt0[str0][p0] = dnode(md, sdt), 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])] = dnode(md0, sdt0[str0, sdt0[str0][p0, dnode(md, sdt[str, tree0])]])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]])
Proof step 31:
⊦ tree[ε] = tree
Proof step 32:
⊦ dnode(md, sdt)[str ', tree0] = dnode(md, sdt[str, tree0])
Proof step 33:
⊦ tree[ε, tree0] = tree0

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(md, sdt[str, tree0]), p0, str0, sdt0, md0] flags: <all paths>

Additional information

Used simplifier rules: nil-at: ⊦ tree[ε] = tree;%put-here: ⊦ dnode(md, sdt)[str ', tree0] = dnode(md, sdt[str, tree0]);%nil-put: ⊦ tree[ε, tree0] = tree0;% ⊦ p + ε = p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path] Used terms: dnode(md, sdt[str, tree0]), p0, str0, sdt0, md0