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Proof step 35 from proof div-two-intro (previous step)

j0 * 2 < 0, j0 < 0, 0 ≤ i0 ⊦ ~((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-twoodd seq: 0 ≤ i, 0 < j ⊦ (2 * i + 1) / (2 * j) = i / j subst: [j, i] → [~ j0, i0] flags: rewrite, current

Additional information

Used simplifier rules: neg: j ≠ 0 ⊦ i / ~ j = ~(i / j);%neg: j ≠ 0 ⊦ i / ~ j = ~(i / j);%neg-02: ⊦ ~ ~ i = i; from specification int-abs%minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); from specification int-mult%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: ~ j0, i0