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

∀ gndx1. (gndx + gndx1).nds = gndx.nds + gndx1.nds ⊦ ((gnd + gndx) + gndx1).nds = (gnd + gndx).nds + gndx1.nds

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ gndx1. (gndx + gndx1).nds = gndx.nds + gndx1.nds ⊦ (gndx + gndx1).nds = gndx.nds + gndx1.nds

Rule argument

Additional information

Used simplifier rules: nds-rec: ⊦ (gnd ' + gndx).nds = gnd.nd + gndx.nds;% ⊦ nd ' + ndx = nd ' + ndx0 ↔ ndx = ndx0; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ nd + ndx = nd ' + ndx; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gnd + gndx = gnd ' + gndx; (s)