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Proof step 30 from proof two-even (previous step)

2 * i = (j * 2 + j2)^2 + j2 ^2 ⊦ i = j ^2 + ((2 * j2 + j * 2) / 2)^2, (2 * j2 + j * 2) % 2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-rmerge seq: ⊦ i * j + i * j0 = i * (j + j0) subst: [j0, j, i] → [j, j2, 2] flags: rewrite

Additional information

Used simplifier rules: div-mult-num: j ≠ 0, j0 % j = 0 ⊦ (i * (* j0)) / (* j) = i * j0 / j; from specification int-div%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%mod-two-02: ⊦ (i * 2) % 2 = 0; from specification int-div%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, j2, 2