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Proof step 32 from proof lagrange-lemma (previous step)

0 < j, 0 ≤ j0, j1 ≤ (j - 1) / 2, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j1, ∃ i0. j * i0 = (j1 ^2 + j0 ^2) + 1 ⊦ 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 33:
j * i = (j1 ^2 + j0 ^2) + 1, 0 ≤ j1, 0 ≤ j, prime(j), j0 ≤ (j - 1) / 2, j1 ≤ (j - 1) / 2, 0 ≤ j0, 0 < j ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

Proof step 32 from proof lagrange-lemma (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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