How was the appointment of two Consuls during the Roman Republic an example of a democratic principle?

One Consul represented patricians and one represented plebeians, so that all citizens had representation.
Each Consul had control over the same number of military legions, which prevented either one from a forceful takeover.
Consuls had to agree on all decisions, which prevented any one person from gaining too much power.
Consuls had to make decisions based on majority rule in the Senate.