[Non-Sequitur]

The Constitution does not mention succession. However, we can infer that the states did not have a right to leave the Union.

Not necessarily. I believe that a state could leave the union in the same manner in which almost all of them joined - with the approval of a majority vote in Congress. It was the unilateral manner of their actions which violated the Constitution. IMHO, of course.

[republicanwizard]

You are correct. Congress did not give its consent; therefore, the Union could not be dissolved.

Suffice it to say that the Constitution is clear enough that states cannot willy-nilly leave the Union.