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Proof step 3 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: <toplevel> name: exeven seq: i % 2 = 0 ⊦ ∃ j. i = 2 * j subst: [i] → [i]

Additional information

Used simplifier rules: mod-two-02: ⊦ (i * 2) % 2 = 0;%mod-mult-02: 0 ≠ j, i0 ≠ 0 ⊦ (i0 * i) % (i0 * j) = i % j * i0;%div-mult-num: j ≠ 0, j0 % j = 0 ⊦ (i * (* j0)) / (* j) = i * j0 / j;%nummult-eq-01: j ≠ 0, j0 % j = 0 ⊦ i * (* j) = i0 * (* j0) ↔ i = i0 * j0 / j;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 1 * i = i; (s) Used terms: i