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Proof step 3 from proof mult-03 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 4:
i * j - i0 = (i - 1) * j + (j - i0), 0 < j, 0 < j0, 0 < i, i0 < j, 0 < i0, 1 < j, 0 ≤ j ⊦ (i * j - i0) / (j0 * j) = (i - 1) / j0

Rule argument

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

Additional information

Used simplifier rules: ⊦ i + (j - i0) = i + j - i0; (s)% ⊦ i * j + i = i * (j + 1); (s)% ⊦ i + (j - i) = j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i - j = i0 ↔ i = i0 + j; (s)% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); (s) Used formulas: i * j - i0 = (i - 1) * j + (j - i0)