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Proof step 6 from proof div-le-modnotzero (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 7:
i0 ≤ i1, j0 < j, 1 < j, 0 < j, 0 ≤ i1, 0 ≤ i1 * j + j0, 0 < j0 ⊦ i0 * j < i1 * j + j0, j0 = 0
Proof step 10:
i0 * j < i1 * j + j0, j0 < j, 1 < j, 0 < j, 0 ≤ i1, 0 ≤ i1 * j + j0, 0 < j0 ⊦ i0 ≤ i1, j0 = 0

Rule argument

pos: right 1

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