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Proof step 12 from proof is-aligned-still-space (previous step)

n * n1 < ((m0 * n + m) * n1) % (n * n1) + n1, m < n ⊦ ((m0 * n + m) * n1) % (n * n1) = 0, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 14:
m < n, n * n1 < (n1 * m0 * n + n1 * m) % (n * n1) + n1 ⊦ (n1 * m0 * n + n1 * m) % (n * n1) = 0, n1 = 0

Rule argument

spec: nat-mult name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [m0, n, m] → [n1, m, m0 * n] flags: <all paths>

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: n1, m, m0 * n