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Proof step 2 from proof div-ls-pos-mon (previous step)

i < i0 / j, i0 ≤ i1, i1 / j ≤ i, 0 ≤ i1, 0 ≤ i0, 0 < j, i1 / j < i0 / j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ i < i0 ∧ 0 ≤ i0 ∧ 0 < j → ¬ i / j < i0 / j

Rule argument

spec: inst: name: div-est-nls seq: ⊦ ¬ i < i0 ∧ 0 ≤ i0 ∧ 0 < j → ¬ i / j < i0 / j subst: [i0, j, i] → [i0, j, i1] flags: rewrite, current

Additional information

Used simplifier rules: lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i0, j, i1