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Proof step 12 from proof div-nearer-zero (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: Div-right: ⊦ j ≠ 0 → i / ~ j = ~(i / j);% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ 0 < ~ i ↔ i < 0; (s)% ⊦ ~ i * j = ~(i * j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ ~ ~ i = i; (s) Used terms: i, ~ j