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

i < 0, i / j * j < i, 0 < j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 19:
0 < j, i / j * j < i, i < 0, ~ i < ~(j * i / j) ⊦

Rule argument

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

Additional information

Used simplifier rules: ⊦ ~ j < ~ i ↔ i < j; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < j → (j ≤ i ↔ false); (as) Used formulas: ~ i < ~(j * i / j)