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Proof step 1 from proof nds-length (conclusion)

⊦ # gndx.nds = # gndx

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: gndx

Additional information

Used simplifier rules: nds-base: ⊦ [].nds = [];%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]% ⊦ #(nd ' + ndx) = (# ndx)+1; (s)% ⊦ m +1 = m + 1; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ #(gnd ' + gndx) = (# gndx)+1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # [] = 0; (s)% ⊦ # [] = 0; (s)