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Proof step 21 from proof mod-mult-law (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 22:
i * (i0 - j * j1) = i * i0 + (~ j1 * i) * j, 0 < j, i = i |%| j + j * j0, i0 = i0 |%| j + j * j1, 0 < j ⊦ (i * i0) |%| j = (i * (i0 - j * j1)) |%| j, j = 0
Proof step 25:
0 < j, i = i |%| j + j * j0, i0 = i0 |%| j + j * j1, 0 < j ⊦ i * (i0 - j * j1) = i * i0 + (~ j1 * i) * j, (i * i0) |%| j = (i * (i0 - j * j1)) |%| j, j = 0

Rule argument

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

Additional information

Used formulas: i * (i0 - j * j1) = i * i0 + (~ j1 * i) * j