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Proof step 1 from proof nds-app (conclusion)

⊦ (gndx0 + gndx1).nds = gndx0.nds + gndx1.nds

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ gndx1. (gndx + gndx1).nds = gndx.nds + gndx1.nds ⊦ ((gnd + gndx) + gndx1).nds = (gnd + gndx).nds + gndx1.nds

Rule argument

term: gndx0

Additional information

Used simplifier rules: nds-base: ⊦ [].nds = [];%group-node-list freely generated by [], +;;% ⊦ [] + gndx = gndx; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ [] + ndx = ndx; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]