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Proof step 4 from proof at-last (previous step)

# x = m + 1 ⊦ x[m] = x.last, x = []

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ m. # x0 = m + 1 → x0[m] = x0.last ∨ x0 = [], #(a + x0) = m + 1 ⊦ (a + x0)[m] = (a + x0).last, a + x0 = []

Rule argument

indvar: x

Additional information

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