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Proof step 22 from proof diff-primes (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 24:
0 < j, j | abs(n→i(m) ^2 - n→i(n) ^2), 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 ⊦ countFun(0, (j - 1) / 2, λ i. i ^2 |%| j) = [], j = 2, m = n, ~1 = (j - 1) / 2

Rule argument

spec: inst: name: congmod-def seq: ⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0) subst: [j, i0, i] → [j, n→i(n) ^2, n→i(m) ^2] flags: rewrite, current

Additional information

Used terms: j, n→i(n) ^2, n→i(m) ^2