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

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

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;