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Proof step 12 from proof two-identity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ (i * j)^2 = i ^2 * j ^2
Proof step 14:
⊦ (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

Rule argument

spec: <toplevel> name: two-mult seq: ⊦ (i * j)^2 = i ^2 * j ^2 subst: [j, i] → [j2, i1] flags: <all paths>

Additional information

Used terms: j2, i1