I know that the role of dependent claims has been thoroughly explained in another post in this forum. However, I wanted to clarify something, to see if I am getting this right:
A dependent claim must always narrow down the scope of the associated independent claim. Hence, if someone infringes on a dependent claim, he will surely be infringing on the respective independent claim (it's like saying, if B is a subset of A, and x belongs to B, then it also belongs to A). Therefore, when a court is deciding whether someone is infringing on a patent, wouldn't it be redundant to check the dependent claims? Shouldn't one just examine the broader, independent claims? (I am relatively new to patent law, so I have actually no clue how patent courts decide...).
If dependent claims are mathematically redundant for a court ruling about infringement on a granted patent (I don't know if this is true), then do the dependent claims play a role only during the application process?