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Proof step 2 from proof key-cons-app (previous step)

⊦ key-cons(ndx0 + ndx1) ↔ key-cons(ndx0) ∧ key-cons(ndx1)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ ndx1. key-cons(ndx + ndx1) ↔ key-cons(ndx) ∧ key-cons(ndx1) ⊦ key-cons((nd + ndx) + ndx1) ↔ key-cons(nd + ndx) ∧ key-cons(ndx1)

Rule argument

term: ndx0

Additional information

Used simplifier rules: key-cons-base: ⊦ key-cons([]);%node-list freely generated by [], +;;% ⊦ [] + ndx = ndx; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]