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Proof step 7 from proof from-from (previous step)

n + m ≤ 1 + # x0, ∀ n, m. n + m ≤ # x0 → x0 from m from n = x0 from m + n ⊦ a ' + x0 from m from n = a ' + x0 from m + n

User applied rule structural induction

And obtained the following new goals

Proof step 8:
n + m0 +1 ≤ 1 + # x0, ∀ n, m. n + m ≤ # x0 → x0 from m from n = x0 from m + n, ∀ n, x0, a. n + m0 ≤ 1 + # x0 ∧ (∀ n, m. n + m ≤ # x0 → x0 from m from n = x0 from m + n) → a ' + x0 from m0 from n = a ' + x0 from m0 + n ⊦ a ' + x0 from m0 +1 from n = a ' + x0 from m0 +1 + n

Rule argument

indvar: m

Additional information

Used simplifier rules: from-zero-l: ⊦ x from 0 = x;%nat freely generated by 0, +1;;% ⊦ 0 + m = m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic