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Proof step 2 from proof mod-sub-02 (previous step)

0 < i0, 2 < (i0 + 1) * j, j + 1 < (i0 + 1) * j, 1 < i, 0 < i, 0 < j, 0 ≤ i0, j < i, i0 * j ≤ i, i < (i0 + 1) * j, 0 ≤ i ⊦ i = i % j + i0 * j

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i0 = i / j

Additional information

Used simplifier rules: divmod-rew: j ≠ 0 ⊦ i / j * j + i % j = i;%zero-left: ⊦ 0 * i = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: i0 = i / j