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Proof step 59 from proof lagrange-lemma (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: ls-same-01 seq: ⊦ 0 < i → (i < i * j ↔ 1 < j) subst: [j, i] → [2, j - 1] flags: rewrite

Additional information

Used simplifier rules: prime-odd-01: ⊦ prime(j) ∧ j ≠ 2 → (j - 1) % 2 = 0; from specification int-gcd%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 2, j - 1