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Proof step 17 from proof le-abs-numerator (previous step)

i < 0, 0 < i / j + i, 0 ≤ i ∧ 0 < j → i / j * j ≤ i ⊦ j < 0, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
0 < j, 0 < i / j + i, i < 0 ⊦

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1