| m < n0 → n0 = 0 ∨ (∃ m0. m + m0 = n0 ∧ m0 ≠ 0), ∀ m. m < n0 → n0 = 0 ∨ (∃ m0. m + m0 = n0 ∧ m0 ≠ 0) ⊦ n0 = 0, n0 < m, ∃ m0. m + m0 = n0 + 1 ∧ m0 ≠ 0 |
m < n0 → m + m0 = n0 ∧ m0 ≠ 0, ∀ m1. m1 < n0 → (∃ m0. m1 + m0 = n0 ∧ m0 ≠ 0) ⊦ n0 = 0, n0 < m, ∃ m0. m + m0 = n0 + 1 ∧ m0 ≠ 0