What is the purpose of blades on a compressor?
The statement about the rotor blades ("the rotors increase the speed of the air and descrease the pressure") is not correct, because Bernoulli's Equation does not apply in this situation. Hence, the statement "as the flow of a fluid increases, the pressure decreases, and vice versa" isn't appropriate for the rotating compresser blades.

Bernouilli's equation (below) assumes no energy is being added or removed from the fluid. This is true when the fluid is flowing through the stationary stator vanes, but not the rotating blades.

The rotating blades increase the velocity, but do not decrease the static pressure, becuase they are adding mechanical work (energy) to the fluid. This energy (or power) comes from the turbine. 

When no energy is being added to the fluid:

$$
total\space pressure = static\space pressure + 1/2 \rho v^2
$$

where
$\rho$ is the density and $v$ is the velocity.

This is the mathematical equivalent of your statement "as the flow of the fluid increase, the static pressure decreases".

But, the rotating blades add total energy. So this equation does not apply, so as the velocity increases, static pressure does not go down. But, total energy has increased, by the mechanical work done by the blades. So the value on the left of the equation goes up as the fluid flows through the rotating blades. Next, the fluid flows through the stationary stator vanes. Because they are static, they add no energy, so Bernoulli's equation now does apply. Hence, as the velocity is decreased, the static pressure goes up (i.e. there is no change in total pressure).

If you just have the rotor blades, and no stator vanes, the compressor would just make the fluid move (i.e an increase in the total pressure) but with no increase in static pressure. The stator vanes slow the fluid down, and convert the velocity into an increase in static pressure.

You need to understand the difference between total and static pressures.