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Proof step 5 from proof le-one (previous step)

1 < j, i * j < j, i * j ≤ 1 ⊦ i ≤ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i ≤ j ↔ ¬ j < i

Rule argument

spec: int-abs name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [0, i] flags: <all paths>

Additional information

Used simplifier rules: ls-same-05: ⊦ 1 < i → (j * i < i ↔ j < 1);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i < 1 ↔ i ≤ 0; (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: 0, i