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Proof step 6 from proof mult-gt-both (previous step)

i < i1, j < j1, i1 * j1 ≤ i * j, 0 ≤ i, 0 ≤ j, 0 ≤ i1, 0 ≤ j1, 0 < i1, 0 < j1, i1 * j ≤ i * j, i * j1 ≤ i * j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: numle-10 seq: ⊦ 0 < i → ((* i) * j ≤ (* i) * j0 ↔ j ≤ j0) subst: [j0, j, i] → [j, j1, i] flags: rewrite, current

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-le: ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0);%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: j, j1, i