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Proof step 2 from proof keys-app (previous step)

∀ ndx1. (ndx + ndx1).keys = ndx.keys + ndx1.keys ⊦ ((nd + ndx) + ndx1).keys = (nd + ndx).keys + ndx1.keys

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ ndx1. (ndx + ndx1).keys = ndx.keys + ndx1.keys ⊦ (ndx + ndx1).keys = ndx.keys + ndx1.keys

Rule argument

Additional information

Used simplifier rules: keys-rec-01: ⊦ (nd ' + ndx).keys = nd.key + ndx.keys;% ⊦ key ' + kx = key ' + kx0 ↔ kx = kx0; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ key + kx = key ' + kx; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ nd + ndx = nd ' + ndx; (s)