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Proof step 40 from proof four-square-mod-zero (previous step)

1 < j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3), 0 ≤ i0 * i0 + i2 * i2 + i * i + i3 * i3, 0 < j0, prime(j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3)), 1 < i0 * i0 + i2 * i2 + i * i + i3 * i3, 0 < i0 * i0 + i2 * i2 + i * i + i3 * i3 ⊦ j0 = 1, j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3) = 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: prime-mult-not seq: ⊦ 1 < i ∧ 1 < j → ¬ prime(i * j) subst: [j, i] → [i0 * i0 + i2 * i2 + i * i + i3 * i3, j0] flags: rewrite

Additional information

Used simplifier rules: lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: i0 * i0 + i2 * i2 + i * i + i3 * i3, j0