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Proof step 2 from proof mod-mult-neg-01 (previous step)

0 < j, i0 < j, i ≤ 0, 0 ≤ i0 ⊦ (j * i - i0) % j = ~ i0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: j * i - i0 = j * i + ~ i0

Additional information

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