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Proof step 3 from proof le-fin-add (previous step)

n + i→n(i) < m, n→i(m) ≤ n→i(n) + i, 0 ≤ i ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 4:
n + i→n(i) < m0 +1, 0 ≤ i, n→i(m0 +1) ≤ n→i(n) + i, ∀ n, i. ¬(n + i→n(i) < m0 ∧ n→i(m0) ≤ n→i(n) + i ∧ 0 ≤ i) ⊦

Rule argument

indvar: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ ¬ n < 0; (s)