Simplify may or may not simplify depending on the symbols you use for its assumptions are good. For example, here is a case where
Simplify is uncooperative
Simplify[b + c, b + c == a] (* b + c *)
Here is a case where
Simplify is happy with using the assumptions because it likes
Simplify[x + y, x + y == z] (* z *)
Simplify is guilty of symbol favoritism. How do I formulate the assumptions in
Simplify so that it will consistently simplify?