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Proof step 7 from proof mult-gt-both (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: numle-10 seq: ⊦ 0 < i → ((* i) * j ≤ (* i) * j0 ↔ j ≤ j0) subst: [j0, j, i] → [j, j1, i] flags: <all paths>

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-le: ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0);% ⊦ i ≤ j → (j < i ↔ false); (as)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s) Used terms: j, j1, i