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Proof step 1 from proof ple-pos (conclusion)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: 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] flags: current, []

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;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: i, j, i0, j0