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Proof step 1 from proof put-at (conclusion)

m < # x ⊦ m ≠ n → x[m, a][n] = x[n]

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ m, n, a. m < # x0 → m ≠ n → x0[m, a][n] = x0[n], m < #(a0 + x0) ⊦ m ≠ n → (a0 + x0)[m, a][n] = (a0 + x0)[n]

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data%zero-01: ⊦ ¬ m < 0; from specification nat-basic1