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Proof step 5 from proof coef-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 7:
n * m + n * m0 ≤ n * m1 ↔ m + m0 ≤ m1 ⊦ m * n + m0 * n ≤ m1 * n ↔ m + m0 ≤ m1 ∨ n = 0

Rule argument

spec: <toplevel> name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [n, m, m0] → [m0, m, n] flags: <all paths>

Additional information

Used terms: m0, m, n