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Proof step 69 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 ⊦ 0 < i, j = 2, 0 < i ∧ i < j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
j * i = (j1 ^2 + j0 ^2) + 1, i < j, i ≤ 0, 0 < j, 0 ≤ j0, j1 ≤ (j - 1) / 2, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j1 ⊦ j = 2

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs