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Proof step 67 from proof two-even (previous step)

2 * i = 2 * j2 ^2 + 2 ^2 * i1 ^2 + 4 * i1 + 1 + 2 * (2 * i1 + 1) * j2 ⊦ 4 * i1 ^2 = 2 ^2 * i1 ^2, i = ((2 * i1 + 1) / 2)^2 + ((2 * j2 + 2 * i1 + 1) / 2)^2, i1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: Square-def seq: ⊦ i ^2 = i * i subst: [i] → [2] flags: rewrite, current

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult Used terms: 2