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Proof step 8 from proof div-le-modnotzero (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 < j0, 0 < j, 1 < j, j0 < j, i1 * j + j0 ≤ i0 * j, 0 ≤ i1, 0 ≤ i1 * j + j0, i0 ≤ i1, 0 ≤ i0 ⊦ j0 = 0

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)