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Proof step 1 from proof div-sum-ls (conclusion)

⊦ 0 ≤ i ∧ 0 ≤ i1 ∧ 0 < i + i1 ∧ 0 < j1 ∧ 0 < j2 ∧ 0 < j ∧ j1 < j ∧ j2 < j → (i * j1 + i1 * j2) / j < i + i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ 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%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs