Modulo Operation/Examples/0.11 mod 0.1/Proof 2

Proof
From Modulo Operation: $1 \cdotp 1 \bmod 1$:
 * $1 \cdotp 1 \bmod 1 = 0 \cdotp 1$

From Product Distributes over Modulo Operation:
 * $z \left({x \bmod y}\right) = \left({z x}\right) \bmod \left({z y}\right)$

and so: