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Proof step 17 from proof mod-mult-law (previous step)

i = i |%| j + j * j0, i0 = i0 |%| j + j * j1, 0 < j ⊦ (i * i0) |%| j = (i * (i0 - j * j1) - (j * j0) * (i0 - j * j1)) |%| j, j = 0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i * (i0 - j * j1) - (j * j0) * (i0 - j * j1) = i * (i0 - j * j1) + (~ j0 * (i0 - j * j1)) * j

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%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 Used formulas: i * (i0 - j * j1) - (j * j0) * (i0 - j * j1) = i * (i0 - j * j1) + (~ j0 * (i0 - j * j1)) * j