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Proof step 1 from proof dist-mult (conclusion)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ m ≤ n → dist(m, n) = n - m
Proof step 3:
¬ n ≤ n0 ⊦ dist(m * n, m * n0) = m * dist(n, n0)
Proof step 7:
n ≤ n0 ⊦ dist(m * n, m * n0) = m * (n0 - n)

Rule argument

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

Additional information

Used terms: n0, n