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Proof step 27 from proof divi-same (previous step)

m * n1 = dist(n0, m * n2 + n), m * n2 + n < n0 ⊦ n0 = 0, m | dist(n, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ n < m → dist(m, n) = m - n
Proof step 29:
m * n2 + n < n0, m * n1 = n0 - m * n2 + n, m * n2 + n < n0 ⊦ n0 = 0, m | dist(n, n0)

Rule argument

spec: nat-prime inst: name: dist-snd seq: ⊦ n < m → dist(m, n) = m - n subst: [n, m] → [m * n2 + n, n0] flags: rewrite, current

Additional information

Used terms: m * n2 + n, n0