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Proof step 11 from proof div-le-modnotzero (previous step)

0 < j0, 0 < j, 1 < j, j0 < j, i0 * j < i1 * j + j0, 0 ≤ i1, 0 ≤ i1 * j + j0 ⊦ j0 = 0, i0 ≤ i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
i0 * j < i1 * j + j0, j0 < j, 1 < j, 0 < j, 0 < j0, i1 < i0, 0 < i0, 0 ≤ i1 * j + j0, 0 ≤ i1 ⊦ j0 = 0

Rule argument

Additional information

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