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Proof step 11 from proof est-4-big (previous step)

0 ≤ j0, 2 * j0 < j, (2 * i0 * j + 2 * j0) / 3 < j, j ≤ i0 * j + j0, 2 < i0 * j + j0, 2 * i0 * j + 2 * j0 < j * j, j0 < j, j0 < i0 * j, 0 < i0 * j + j0, 0 ≤ i0, 0 < j, 0 < i0 ⊦ (2 * i0 * j + 2 * j0) / j = 2 * i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-add1-pospos seq: ⊦ i % j = 0 ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) / j = i / j + i0 / j subst: [j, i0, i] → [j, 2 * j0, 2 * i0 * j] flags: rewrite

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0; from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div%div-zero-05: ⊦ i < j ∧ 0 < j ∧ 0 ≤ i → i / j = 0; from specification int-div%ax-04: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult%mod-mult-04: j ≠ 0 ⊦ (i * j) % j = 0; from specification int-div%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, 2 * j0, 2 * i0 * j