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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
p ≠ ε ⊦ str ∈ sdt → dnode(md, sdt)[str ' + p, tree0] = dnode(md, sdt[str, sdt[str][p, tree0]])
Proof step 15:
p0 ∈ sdt[str], str ∈ sdt, ∀ tree, q, tree0. p0 ∈ tree → tree[p0 + q, tree0] = tree[p0, tree[p0][q, tree0]] ⊦ dnode(md, sdt)[(str ' + p0) + q, tree0] = dnode(md, sdt)[str ' + p0, sdt[str][p0][q, tree0]], p0 ≠ ε ∧ str ∈ sdt
Proof step 24:
p0 ∈ sdt[str], str ∈ sdt, ∀ tree, q, tree0. p0 ∈ tree → tree[p0 + q, tree0] = tree[p0, tree[p0][q, tree0]] ⊦ dnode(md, sdt)[(str ' + p0) + q, tree0] = dnode(md, sdt[str, sdt[str][p0, sdt[str][p0][q, tree0]]]), p0 = ε

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

Additional information

Used terms: sdt[str][p0][q, tree0], p0, str, sdt, md