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

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

User applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: i * j < i * j0

Additional information

Used simplifier rules: ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);%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