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Proof step 2 from proof nds-eq-empty (previous step)

gndx.nds = [] ⊦ gndx = []

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: gndx

Additional information

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