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Proof step 2 from proof ple-pos (previous step)

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

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: pls-pos seq: 0 < i, 0 < j, i ≤ i0, j < j0 ⊦ i * j < i0 * j0 subst: [i, j, i0, j0] → [i, j, i0, j0]

Additional information

Used simplifier rules: ls-pos-01: ⊦ 0 < j → (i * j < i0 * j ↔ i < i0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i ≤ j → (j < i ↔ false); (as) Used terms: i, j, i0, j0