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Proof step 2 from proof put-app-left (previous step)

n < # x ⊦ (x + y)[n, a] = x[n, a] + y

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;% ⊦ [] + x = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # [] = 0; (s)% ⊦ ¬ n < 0; (s)