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Proof step 5 from proof append-to-le (previous step)

n ≤ 1 + # x0, ∀ n, y. n ≤ # x0 → x0 + y to n = x0 to n ⊦ (a ' + x0) + y to n = a ' + x0 to n

User applied rule structural induction

And obtained the following new goals

Proof step 6:
n0 +1 ≤ 1 + # x0, ∀ n, y. n ≤ # x0 → x0 + y to n = x0 to n, ∀ x0, a, y. n0 ≤ 1 + # x0 ∧ (∀ n, y. n ≤ # x0 → x0 + y to n = x0 to n) → (a ' + x0) + y to n0 = a ' + x0 to n0 ⊦ (a ' + x0) + y to n0 +1 = a ' + x0 to n0 +1

Rule argument

indvar: n

Additional information

Used simplifier rules: to-zero-l: ⊦ x to 0 = [];%nat freely generated by 0, +1;;