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Proof step 14 from proof two-identity (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
⊦ i1 ^2 * j1 ^2 + i2 ^2 * j1 ^2 + i2 ^2 * 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 + i0 ↔ j = i0; (s)