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Proof step 1 from proof coef-16 (conclusion)

⊦ m * n + m0 * n < n ↔ ¬ ¬(m + m0 = 0 ∧ n ≠ 0)

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: ls-08: ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%ls-01: ⊦ m0 * m < m ↔ m0 = 0 ∧ m ≠ 0;%ls-08: ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n;%ls-01: ⊦ m0 * m < m ↔ m0 = 0 ∧ m ≠ 0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2