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Proof step 34 from proof lagrange-lemma (previous step)

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, 1 + j1 ^2 + j0 ^2 = i * j ∧ 0 < i ∧ i < j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
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, 0 < i ∧ i < j

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2