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Proof step 17 from proof modmod-pos (previous step)

j1 < j, 0 < j, j2 < j0, 0 < j0, 0 ≤ j1, 0 ≤ j2, 0 ≤ i1, j * j0 ≤ j2 * j + j1 ⊦ (j2 * j + j1) % (j * j0) = j1 + j2 * j

User applied rule cut formula

And obtained the following new goals

Proof step 18:
j * j0 = j2 * j + j1, 0 < j0, j2 < j0, 0 < j, j1 < j, j * j0 ≤ j2 * j + j1, 0 ≤ i1, 0 ≤ j2, 0 ≤ j1 ⊦ (j2 * j + j1) % (j * j0) = j1 + j2 * j
Proof step 21:
0 < j0, j2 < j0, 0 < j, j1 < j, j * j0 ≤ j2 * j + j1, 0 ≤ i1, 0 ≤ j2, 0 ≤ j1 ⊦ (j2 * j + j1) % (j * j0) = j1 + j2 * j, j * j0 = j2 * j + j1

Rule argument

fma: j * j0 = j2 * j + j1

Additional information

Used formulas: j * j0 = j2 * j + j1