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Proof step 4 from proof dist-mult (previous step)

n0 < n ⊦ dist(m * n, m * n0) = m * dist(n, n0), n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ n < m → dist(m, n) = m - n
Proof step 6:
n0 < n, n0 < n ⊦ dist(m * n, m * n0) = m * (n - n0), n = 0

Rule argument

spec: nat-prime inst: name: dist-snd seq: ⊦ n < m → dist(m, n) = m - n subst: [n, m] → [n0, n] flags: rewrite, current

Additional information

Used terms: n0, n