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Proof step 6 from proof put-app-left (previous step)

n ≤ # x0, ∀ n, y, a. n < # x0 → (x0 + y)[n, a] = x0[n, a] + y ⊦ a0 ' + (x0 + y)[n -1, a] = (a0 ' + x0)[n, a] + y, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
n ≤ # x0, ∀ n, y, a. n < # x0 → (x0 + y)[n, a] = x0[n, a] + y ⊦ a0 ' + (x0 + y)[n - 1, a] = (a0 ' + x0)[n, a] + y, n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ n -1 = n - 1; (s)