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

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

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-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 ↔ false); (as) Used terms: i0 * j0, i * j, i * j0