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Proof step 15 from proof gcd-mult (previous step)

n = n4 + m ∧ m ≤ n, n0 * n = n3 + n0 * m, m < n, ∀ n1, m1, n2. n1 * m1 + n1 * n2 < n0 * m + n0 * n → true → gcd(n1 * m1, n1 * n2) = n1 * gcd(m1, n2) ⊦ n0 = 0, gcd(n0 * m, n3) = n0 * gcd(m, n4)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
∀ n1, m1, n2. n1 * m1 + n1 * n2 < n0 * m + n0 * (n4 + m) → true → gcd(n1 * m1, n1 * n2) = n1 * gcd(m1, n2) ⊦ n4 = 0, gcd(n0 * m, n0 * n4) = n0 * gcd(m, n4), n0 = 0

Rule argument

Additional information

Used simplifier rules: l-01: ⊦ m < m + n ↔ n ≠ 0; from specification nat-basic2%lels-03: ⊦ m < n → m ≤ n; from specification nat%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%dist: ⊦ m0 * (m + n) = m0 * m + m0 * n; from specification nat-mult