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Proof step 3 from proof two-identity (previous step)

⊦ (i1 ^2 + i2 ^2) * (j1 ^2 + j2 ^2) = ((i1 * j1)^2 + 2 * (i1 * j1) * i2 * j2 + (i2 * j2)^2) + (i1 * j2 - i2 * j1)^2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ (i - j)^2 = (i ^2 - 2 * i * j) + j ^2
Proof step 5:
⊦ (i1 ^2 + i2 ^2) * (j1 ^2 + j2 ^2) = ((i1 * j1)^2 + 2 * (i1 * j1) * i2 * j2 + (i2 * j2)^2) + ((i1 * j2)^2 - 2 * (i1 * j2) * i2 * j1) + (i2 * j1)^2

Rule argument

spec: int-square inst: name: two-minus seq: ⊦ (i - j)^2 = (i ^2 - 2 * i * j) + j ^2 subst: [j, i] → [i2 * j1, i1 * j2] flags: rewrite, current

Additional information

Used terms: i2 * j1, i1 * j2