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Proof step 78 from proof Lagrange-SumOf4Squares-primes (previous step)

⊦ (j0 * i11)^2 + (j0 * i10)^2 + (j0 * i8)^2 + (j0 * i9)^2 = j0 ^2 * i11 ^2 + j0 ^2 * (i10 ^2 + i8 ^2 + i9 ^2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 79:
⊦ (i * j)^2 = i ^2 * j ^2
Proof step 80:
⊦ j0 ^2 * i11 ^2 + (j0 * i10)^2 + (j0 * i8)^2 + (j0 * i9)^2 = j0 ^2 * i11 ^2 + j0 ^2 * (i10 ^2 + i8 ^2 + i9 ^2)

Rule argument

spec: int-square inst: name: two-mult seq: ⊦ (i * j)^2 = i ^2 * j ^2 subst: [j, i] → [i11, j0] flags: rewrite

Additional information

Used terms: i11, j0