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Proof step 1 from proof mod-mult-neg-01 (conclusion)

⊦ 0 < j ∧ i ≤ 0 ∧ 0 ≤ i0 ∧ i0 < j → (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: neg-15: ⊦ i + ~ j = i - j; 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%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult%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