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Proof step 17 from proof div-nearer-zero (previous step)

i / j + 1 < j, i + 1 < j, i < 0, i / j * j < i, i / j * j < ~1, 0 < j, i / j < 0, i / j < j, i < j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 18:
~ i < ~(j * i / j), i / j + 1 < j, i + 1 < j, i < 0, i / j * j < i, i / j * j < ~1, 0 < j, i / j < 0, i / j < j, i < j ⊦

Rule argument

fma: ~ i < ~(j * i / j)

Additional information

Used simplifier rules: neg-01: ⊦ ~ j < ~ i ↔ i < j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used formulas: ~ i < ~(j * i / j)