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Proof step 13 from proof same-put (previous step)

str ∈ sdt, p0 ∈ sdt[str], ∀ tree, tree0, tree1. p0 ∈ tree → tree[p0, tree0][p0, tree1] = tree[p0, tree1] ⊦ dnode(md, sdt[str, sdt[str][p0, tree0]])[str ' + p0, tree1] = dnode(md, sdt[str, sdt[str][p0, tree1]])

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [tree1, p0, str, sdt[str, sdt[str][p0, tree0]], md] flags: <all paths>

Additional information

Used simplifier rules: nil-put: ⊦ tree[ε, tree0] = tree0;%put-here: ⊦ dnode(md, sdt)[str ', tree0] = dnode(md, sdt[str, tree0]);% ⊦ str ∈ sdt[str, tree]; (s)% ⊦ p + ε = p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ sdt[str, tree0][str, tree] = sdt[str, tree]; (s) Used terms: tree1, p0, str, sdt[str, sdt[str][p0, tree0]], md