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Proof step 4 from proof mod-abs-neg-div (previous step)

j ≠ 0, ∃ j0. i = j0 * j, i < 0, j < 0 ⊦ i |%| ~ j = i |%| j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
j < 0, j < j0, 0 < j0 ⊦ j = 0, (j0 * j) |%| ~ j = 0

Rule argument

Additional information

Used simplifier rules: mod-mult: ⊦ j ≠ 0 → (i * j) |%| j = 0;%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%zero-ls-01: ⊦ i < 0 → (i * j < 0 ↔ 0 < j); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult