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Proof step 2 from proof mod-twoeven (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: exeven seq: i % 2 = 0 ⊦ ∃ j. i = 2 * j subst: [i] → [i] flags: current, []

Additional information

Used simplifier rules: mod-two-02: ⊦ (i * 2) % 2 = 0;%mod-mult-03: 0 ≠ j ⊦ (2 * i) % (2 * j) = i % j * 2;%div-mult-num-01: j % j0 = 0, j ≠ 0, j0 ≠ 0 ⊦ (i * (* j0)) / (* j) = i / j / j0;%one: ⊦ i / 1 = i;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult Used terms: i