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Proof step 4 from proof pls-pos (previous step)

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

User applied rule apply lemma

And obtained the following new goals

Proof step 5:
⊦ i ≤ j ∧ j < j0 → i < j0

Rule argument

spec: int-abs name: forward-lels seq: ⊦ i ≤ j ∧ j < j0 → i < j0 subst: [i, j, j0] → [i0 * j0, 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 ↔ false); (as) Used terms: i0 * j0, i * j, i * j0