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Proof step 1 from proof len (conclusion)

⊦ # ins≤(a, x) = # x + 1

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ a. # ins≤(a, x0) = # x0 + 1 ⊦ # ins≤(a, a0 + x0) = #(a0 + x0) + 1

Rule argument

term: x

Additional information

Used simplifier rules: ins-e: ⊦ ins≤(a, []) = a ';%list freely generated by [], +;;%len-02: ⊦ # a ' = 0 +1; from specification list%size-01: ⊦ # [] = 0; from specification list-data%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2