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Proof step 7 from proof lagrange-lemma (previous step)

prime(j), dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j)) ∨ dups(countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)) ∨ filter(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j), countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)) ≠ [] ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ prime(j) ∧ j ≠ 2 → ¬ dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j))
Proof step 9:
prime(j) ∧ j ≠ 2, prime(j), false ∨ dups(countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)) ∨ filter(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j), countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)) ≠ [] ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

Rule argument

spec: inst: name: diff-primes seq: ⊦ prime(j) ∧ j ≠ 2 → ¬ dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j)) subst: [j] → [j] flags: rewrite, current

Additional information

Used terms: j