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Proof step 10 from proof div-add-succ (previous step)

j0 < j, 0 < j, 0 ≤ j, 0 ≤ i0, 0 ≤ i0 * j + j0, 0 < i0 * j + j0, 0 < j0, 1 < j ⊦ j0 = 0, (i0 * j + j0 - 1) / j = i0

User applied rule cut formula

And obtained the following new goals

Proof step 11:
i0 * j + j0 - 1 = (j0 - 1) + i0 * j, j0 < j, 0 < j, 0 ≤ j, 0 ≤ i0, 0 ≤ i0 * j + j0, 0 < i0 * j + j0, 0 < j0, 1 < j ⊦ j0 = 0, (i0 * j + j0 - 1) / j = i0

Rule argument

fma: i0 * j + j0 - 1 = (j0 - 1) + i0 * j

Additional information

Used simplifier rules: sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2 Used formulas: i0 * j + j0 - 1 = (j0 - 1) + i0 * j