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Proof step 62 from proof lagrange-lemma (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 63:
j1 ^2 ≤ ((j - 1) / 2)^2, j0 ^2 ≤ ((j - 1) / 2)^2, 0 ≤ j1, 0 ≤ j, prime(j), j0 ≤ (j - 1) / 2, j1 ≤ (j - 1) / 2, 0 ≤ j0, 0 < j, j ≤ i, 0 < i, 0 ≤ i ⊦ j1 ^2 + j0 ^2 ≤ ((j - 1) / 2)^2 + ((j - 1) / 2)^2, (j1 ^2 + j0 ^2) + 1 ≤ ((j - 1) / 2)^2 + ((j - 1) / 2)^2 + 1, j = 2

Rule argument

fma: j1 ^2 + j0 ^2 ≤ ((j - 1) / 2)^2 + ((j - 1) / 2)^2

Additional information

Used simplifier rules: add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%le-add: ⊦ i + j ≤ i0 + j ↔ i ≤ i0; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used formulas: j1 ^2 + j0 ^2 ≤ ((j - 1) / 2)^2 + ((j - 1) / 2)^2