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Proof step 24 from proof div-nearer-zero (previous step)

~ i < ~(j * i / j), j + 1 < i / j, 0 < i / j, i < i / j, i + 1 < i / j, i < 0, j * i / j < i, j * i / j < ~1, j < 0, j < i / j ⊦ j = 0

User applied rule cut formula

And obtained the following new goals

Proof step 25:
~(j * i / j) = ~ j * ~ i / ~ j, ~ i < ~(j * i / j), j + 1 < i / j, 0 < i / j, i < i / j, i + 1 < i / j, i < 0, j * i / j < i, j * i / j < ~1, j < 0, j < i / j ⊦ j = 0

Rule argument

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

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);%Div-right: ⊦ j ≠ 0 → i / ~ j = ~(i / j);%neg-10: ⊦ ~ i = 0 ↔ i = 0; from specification int-abs%neg-02: ⊦ ~ ~ i = i; 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-12: ⊦ ~ i = ~ j ↔ i = j; from specification int-abs Used formulas: ~(j * i / j) = ~ j * ~ i / ~ j