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Proof step 4 from proof mod-mult-add (previous step)

0 < i0 ∧ 0 < j, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 < i1 ∧ 0 < j → (i + i1 * j) |%| j = i |%| j ⊦ (i + i0 * j) |%| j = i |%| j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 < j, 0 < i0, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 < i1 ∧ 0 < j → (i + i1 * j) |%| j = i |%| j ⊦ (i + i0 * j) |%| j = i |%| j

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs