Floor plus One

Theorem
Let $$x \in \R$$.

Then:
 * $$\left \lfloor {x + 1} \right \rfloor = \left \lfloor {x} \right \rfloor + 1$$

where $$\left \lfloor {x} \right \rfloor$$ is the floor function of $$x$$.

Proof
$$ $$ $$ $$ $$

In general:
 * $$\forall n \in \Z: \left \lfloor {x} \right \rfloor + n = \left \lfloor {x + n} \right \rfloor$$