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Proof step 12 from proof lagrange-lemma (previous step)

prime(j) ∧ j ≠ 2, prime(j), false ∨ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
prime(j) ⊦ j = 2, filter(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j), countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)) = [], ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

Proof step 12 from proof lagrange-lemma (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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