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Proof step 43 from proof lagrange-lemma (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ i ^2 = i * i
Proof step 45:
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 ≤ 2 * (j - 1) / 2 * (j - 1) / 2 + 1, j ≤ i, j * i ≤ 2 * (j - 1) / 2 * (j - 1) / 2 + 1 ⊦ j = 2

Rule argument

spec: int-square inst: name: Square-def seq: ⊦ i ^2 = i * i subst: [i] → [(j - 1) / 2] flags: rewrite

Additional information

Used terms: (j - 1) / 2