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Proof step 53 from proof lagrange-lemma (previous step)

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) * (j - 1) / 2 + 1 ≤ (j - 1) * (j - 1), j = 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ i + 1 ≤ j ↔ i < j
Proof step 55:
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) * (j - 1) / 2 < (j - 1) * (j - 1), j = 2

Rule argument

spec: int-abs inst: name: succ-01 seq: ⊦ i + 1 ≤ j ↔ i < j subst: [j, i] → [(j - 1) * (j - 1), (j - 1) * (j - 1) / 2] flags: rewrite

Additional information

Used terms: (j - 1) * (j - 1), (j - 1) * (j - 1) / 2