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Proof step 9 from proof prod-div-less (previous step)

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

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1