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Proof step 5 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)^2 - 2 * (i1 * j2) * i2 * j1) + (i2 * j1)^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ (i1 ^2 + i2 ^2) * (j1 ^2 + j2 ^2) = (i1 * j2)^2 + (i1 * j1)^2 + (i2 * j2)^2 + (i2 * j1)^2

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + (j - i) = j; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult