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Proof step 4 from proof append-from-le (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ x0, a, y. n0 ≤ # x0 + 1 ∧ (∀ n, y. n ≤ # x0 → x0 + y from n = (x0 from n) + y) → (a ' + x0) + y from n0 = (a ' + x0 from n0) + y, n0 +1 ≤ # x0 + 1, ∀ n, y. n ≤ # x0 → x0 + y from n = (x0 from n) + y ⊦ (a ' + x0) + y from n0 +1 = (a ' + x0 from n0 +1) + y

Rule argument

indvar: n

Additional information

Used simplifier rules: from-zero-l: ⊦ x from 0 = x;%nat freely generated by 0, +1;;%a: ⊦ (x + y) + z = x + y + z; from specification list%app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list