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Proof step 18 from proof div-nearer-zero (previous step)

~ 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 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 19:
~(j * i / j) = j * ~ i / j, ~ 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: ~(j * i / j) = j * ~ i / j

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);%zero-left: ⊦ 0 * i = 0; 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-05: ⊦ ~ i < 0 ↔ 0 < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%neg-12: ⊦ ~ i = ~ j ↔ i = j; from specification int-abs Used formulas: ~(j * i / j) = j * ~ i / j