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Proof step 25 from proof diff-primes-dups (previous step)

j0 ^2 |%| j < 0, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j0 ⊦ j = 2, dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j) + countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)), dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j)), dups(countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: mod-pos seq: ⊦ 0 < j → ¬ i |%| j < 0 subst: [j, i] → [j, j0 ^2] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd Used terms: j, j0 ^2