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Proof step 1 from proof keys-app (conclusion)

⊦ (ndx0 + ndx1).keys = ndx0.keys + ndx1.keys

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ ndx1. (ndx + ndx1).keys = ndx.keys + ndx1.keys ⊦ ((nd + ndx) + ndx1).keys = (nd + ndx).keys + ndx1.keys

Rule argument

term: ndx0

Additional information

Used simplifier rules: keys-base-01: ⊦ [].keys = [];%node-list freely generated by [], +;;% ⊦ [] + ndx = ndx; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ [] + kx = kx; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]