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Proof step 10 from proof mod-ex-div (previous step)

i % j < 0 ⊦ j < 0 ∧ i < 0, j = 0, ∃ j0. i = j * j0 + i % j + j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: mod-less-01: ⊦ 0 < j → i % j < j; from specification int-div%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%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%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%mod-zero-06: ⊦ 0 ≤ i ∧ j ≠ 0 → ¬ i % j < 0; from specification int-div%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs