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Proof step 57 from proof diff-primes-neg (previous step)

0 ≤ j, m < i→n(1 + (j - 1) / 2), n < i→n(1 + (j - 1) / 2), prime(j), n→i(m) ≤ (j - 1) / 2, n→i(n) ≤ (j - 1) / 2, j | n→i(n) * n→i(n) - n→i(m) * n→i(m), 0 < j ⊦ countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j) = [], j = 2, m = n, ~1 = (j - 1) / 2, n→i(n) * n→i(n) = (n→i(n) - n→i(m)) * (n→i(n) + n→i(m)) + n→i(m) * n→i(m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 58:
⊦ (i - j) * j0 = i * j0 - j * j0
Proof step 59:
0 ≤ j, m < i→n(1 + (j - 1) / 2), n < i→n(1 + (j - 1) / 2), prime(j), n→i(m) ≤ (j - 1) / 2, n→i(n) ≤ (j - 1) / 2, j | n→i(n) * n→i(n) - n→i(m) * n→i(m), 0 < j ⊦ countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j) = [], j = 2, m = n, ~1 = (j - 1) / 2, n→i(n) * n→i(n) = (n→i(n) * (n→i(n) + n→i(m)) - n→i(m) * (n→i(n) + n→i(m))) + n→i(m) * n→i(m)

Rule argument

spec: int-mult inst: name: dist-sub-split seq: ⊦ (i - j) * j0 = i * j0 - j * j0 subst: [j0, j, i] → [n→i(n) + n→i(m), n→i(m), n→i(n)] flags: rewrite

Additional information

Used terms: n→i(n) + n→i(m), n→i(m), n→i(n)