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Proof step 72 from proof lagrange-lemma (previous step)

(j1 ^2 + j0 ^2) + 1 ≤ 0, i < j, i ≤ 0, 0 < j, 0 ≤ j0, j1 ≤ (j - 1) / 2, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j1 ⊦ j = 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
j1 ^2 + j0 ^2 < 0, 0 ≤ j1, 0 ≤ j, prime(j), j0 ≤ (j - 1) / 2, j1 ≤ (j - 1) / 2, 0 ≤ j0, 0 < j, i ≤ 0, i < j ⊦ j = 2

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%mone-05: ⊦ i ≤ ~1 ↔ i < 0; from specification int-abs%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs