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Proof step 4 from proof from-succ (previous step)

n < # x ⊦ x[n] ' + (x from n + 1) = x from n, x = []

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ n. n < # x0 → x0[n] ' + (x0 from n + 1) = x0 from n ∨ x0 = [], n < #(a + x0) ⊦ (a + x0)[n] ' + (a + x0 from n + 1) = a + x0 from n, a + x0 = []

Rule argument

indvar: x

Additional information

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