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Proof step 11 from proof div-nearer-zero (previous step)

i / j < 0, j < 0, 0 ≤ i, i < j * i / j ⊦ j = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: ls-same-pos-02 seq: ⊦ 0 ≤ i ∧ 0 < j → ¬ i < i / j * j subst: [i, j] → [i, ~ j] flags: current, []

Additional information

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