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Proof step 38 from proof lagrange-lemma (previous step)

j0 ^2 ≤ ((j - 1) / 2)^2, 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 ⊦ j = 2

User applied rule cut formula

And obtained the following new goals

Proof step 39:
j1 ^2 ≤ ((j - 1) / 2)^2, j0 ^2 ≤ ((j - 1) / 2)^2, 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 ⊦ j = 2
Proof step 65:
j0 ^2 ≤ ((j - 1) / 2)^2, 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 ⊦ j1 ^2 ≤ ((j - 1) / 2)^2, j = 2

Rule argument

fma: j1 ^2 ≤ ((j - 1) / 2)^2

Additional information

Used formulas: j1 ^2 ≤ ((j - 1) / 2)^2