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Proof step 1 from proof mod-lezero (conclusion)

⊦ 0 < j → ¬ j + i % j ≤ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i % j < 0, 0 < j, j + i % j ≤ 0, i % j + 1 < j ⊦

Rule argument

Additional information

Used simplifier rules: mod-less-01: ⊦ 0 < j → i % j < j;%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ 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