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Proof step 8 from proof divi-same (previous step)

m * n1 = dist(n0, m0), m * n2 = dist(n, m0) ⊦ m | dist(n, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ m ≤ n → dist(m, n) = n - m
Proof step 10:
¬ n ≤ m0, m * n1 = dist(n0, m0), m * n2 = dist(n, m0) ⊦ m | dist(n, n0)
Proof step 22:
n ≤ m0, m * n1 = dist(n0, m0), m * n2 = m0 - n ⊦ m | dist(n, n0)

Rule argument

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

Additional information

Used terms: m0, n