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Proof step 18 from proof divi-same (previous step)

m * n1 = dist(n0, m0), m0 < n0 ⊦ m * n2 + m0 = 0, m = 0, n2 = 0, n0 = 0, m | dist(m * n2 + m0, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ n < m → dist(m, n) = m - n
Proof step 20:
m0 < n0, m * n1 = n0 - m0, m0 < n0 ⊦ m * n2 + m0 = 0, m = 0, n2 = 0, n0 = 0, m | dist(m * n2 + m0, n0)

Rule argument

spec: nat-prime inst: name: dist-snd seq: ⊦ n < m → dist(m, n) = m - n subst: [n, m] → [m0, n0] flags: rewrite, current

Additional information

Used terms: m0, n0