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Proof step 19 from proof div-nearer-zero (previous step)

0 < j, i / j * j < i, i < 0, ~ i < ~(j * i / j) ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 20:
~(j * i / j) = j * ~ i / j, ~ i < ~(j * i / j), i < 0, i / j * j < i, 0 < j ⊦

Rule argument

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

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ ~ 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 = ~ j ↔ i = j; (s) Used formulas: ~(j * i / j) = j * ~ i / j