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Proof step 1 from proof le-sum (conclusion)

⊦ n ≤ n0 ∧ n1 ≤ m → n + n1 ≤ n0 + m

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ n, n0, n1. n ≤ n0 ∧ n1 ≤ m0 → n + n1 ≤ n0 + m0 ⊦ n ≤ n0 ∧ n1 ≤ m0 +1 → n + n1 ≤ n0 + m0 +1

Rule argument

indvar: m

Additional information

Used simplifier rules: lez-01: ⊦ m ≤ 0 ↔ m = 0;%lels-01: ⊦ ¬ m ≤ n ↔ n < m;%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false);%nat freely generated by 0, +1;;%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1