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Proof step 2 from proof bl (previous step)

⊦ (a ' + x).butlast + (a ' + x).last ' = a ' + x

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a. (a ' + x0).butlast + (a ' + x0).last ' = a ' + x0 ⊦ (a ' + (a0 + x0)).butlast + (a ' + (a0 + x0)).last ' = a ' + (a0 + x0)

Rule argument

term: x

Additional information

Used simplifier rules: butlast-one: ⊦ a '.butlast = [];%last-one: ⊦ a '.last = a;%list freely generated by [], +;;% ⊦ x + [] = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ [] + x = x; (s)% ⊦ a ' = b ' ↔ a = b; (s)