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Proof step 28 from proof div-two-intro (previous step)

0 ≤ i0 ⊦ j0 = 0, (i0 * 2 + 1) / (j0 * 2) = i0 / j0

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] → [j0 * 2, 1, i0 * 2] flags: rewrite, current

Additional information

Used simplifier rules: mod-mult-03: 0 ≠ j ⊦ (2 * i) % (2 * j) = i % j * 2;%div-two-01: j ≠ 0 ⊦ (2 * i) / (2 * j) = i / j;%div-eq-zero: ⊦ 0 < i ∧ 0 < j → (i / j = 0 ↔ i < j);%nummult-ls-02: ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); from specification int-mult%eq: ⊦ i = i + j ↔ j = 0; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j0 * 2, 1, i0 * 2