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Proof step 67 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 ≤ i, 0 < i, 0 ≤ i ⊦ j0 ^2 ≤ ((j - 1) / 2)^2, j = 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-square inst: name: le seq: ⊦ i ^2 ≤ j ^2 ↔ abs(i) ≤ abs(j) subst: [j, i] → [(j - 1) / 2, j0] flags: rewrite

Additional information

Used simplifier rules: absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%abs: j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j); from specification int-div%abs-09: ⊦ 0 < i → abs(i - 1) = abs(i) - 1; from specification int-abs%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: (j - 1) / 2, j0