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Proof step 2 from proof less-mult-div (previous step)

0 < i, 0 < i1, 0 < j, i1 < j ⊦ i * i1 / j < i

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: div-lezero: ⊦ 0 < j → (i / j ≤ 0 ↔ i < j);%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < 1 ↔ i ≤ 0; (s)% ⊦ 0 < i → (i * j < i ↔ j < 1); (s)