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Proof step 20 from proof cong-equiv (previous step)

n1 + m1 * m = m0 * m, n2 < m ⊦ m * (m0 - m1) = n1, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n
Proof step 22:
n1 + m1 * m = m0 * m, n2 < m ⊦ m * (m0 - m1) = n1, n1 = 0, m1 ≤ m0
Proof step 25:
n1 + m1 * m = m0 * m, n2 < m, m1 ≤ m0 ⊦ m0 * m - m1 * m = n1, n1 = 0

Rule argument

spec: nat-mult name: dist-sub seq: ⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n subst: [n, m0, m] → [m, m1, m0] flags: <all paths>

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: m, m1, m0