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Proof step 4 from proof two-minus (previous step)

⊦ j ^2 + i ^2 = (i - j) * (i - j) + 2 * i * j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ j ^2 + i ^2 = i * i + j * j

Rule argument

Additional information

Used simplifier rules: ⊦ i + (j - i) = j; (s)% ⊦ i - (j - j0) = i + j0 - j; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + i = 2 * i; (s)% ⊦ i + (j - i0) = i + j - i0; (s)% ⊦ i - i1 - j = i - i1 + j; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ (i - j) * j0 = i * j0 - j * j0; (s)