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Proof step 25 from proof equality-02 (previous step)

i * j0 = i0 * j, 0 < j, 0 < j0, 0 < i, i0 ≤ 0, i0 < j, i0 < j0, i0 < i ⊦ i = 0, rational(i, j) = rational(i0, j0)

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i0 * j < 0

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i * 0 = 0;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; Used formulas: i0 * j < 0