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

0 ≤ i0, i0 < i1, 0 < j, 0 ≤ i ⊦ (i0 + i1 * i % j) / j < i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 ≤ i, 0 < j, 0 < i1, i0 < (i0 + i1 * i % j) / j, 0 ≤ i0, i1 ≤ (i0 + i1 * i % j) / j, i0 < i1, 0 < (i0 + i1 * i % j) / j ⊦

Rule argument

Additional information

Used simplifier rules: forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs