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Proof step 2 from proof get-last-01 (previous step)

⊦ (a ' + x)[# x] = (a ' + x).last

Heuristic structural induction applied rule structural induction

And obtained the following new goals

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

Rule argument

term: x

Additional information

Used simplifier rules: one-03: ⊦ a '[0] = a;%list freely generated by [], +;;%app: ⊦ x + [] = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%size-01: ⊦ # [] = 0; from specification list-data%l: ⊦ a '.last = a; from specification list-last