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Proof step 4 from proof coef-05 (previous step)

n ≠ 0 → (n * (m + m0) ≤ n * m1 ↔ m + m0 ≤ m1) ⊦ m * n + m0 * n ≤ m1 * n ↔ m + m0 ≤ m1 ∨ n = 0

User applied rule case distinction

And obtained the following new goals

Proof step 5:
n * (m + m0) ≤ n * m1 ↔ m + m0 ≤ m1 ⊦ m * n + m0 * n ≤ m1 * n ↔ m + m0 ≤ m1 ∨ n = 0

Rule argument

pos: left 1

Additional information

Used simplifier rules: mult-base: ⊦ m * 0 = 0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;