Congruence of Sum with Constant

Theorem
Let $$a, b, z \in \R$$.

Let $$a$$ be congruent to $b$ modulo $z$, i.e. $$a \equiv b \left({\bmod\, z}\right)$$.

Then:
 * $$\forall c \in \R: a + c \equiv b + c \left({\bmod\, z}\right)$$.

Proof
Follows directly from the definition of Modulo Addition:

$$ $$ $$