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Proof step 2 from proof put-length (previous step)

n < # x ⊦ # x[n, a] = # x, x = []

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ n, a. n < # x0 → # x0[n, a] = # x0 ∨ x0 = [], n < #(a0 + x0) ⊦ # (a0 + x0)[n, a] = #(a0 + x0), a0 + x0 = []

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;