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Proof step 3 from proof pls-neg (previous step)

j0 < 0, i0 < 0, j0 < j, j < 0, i < 0, j0 + 1 < 0, i0 * j0 ≤ i * j, i0 ≤ i ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 4:
j0 + 1 < 0, i < 0, j < 0, j0 < j, i0 < 0, j0 < 0, i * j < i * j0, i0 ≤ i, i0 * j0 ≤ i * j ⊦

Rule argument

fma: i * j < i * j0

Additional information

Used simplifier rules: ls-neg: ⊦ i < 0 → (i * j < i * j0 ↔ j0 < j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as) Used formulas: i * j < i * j0