In the general theory of relativity, the speed of light is c locally. In the special theory of relativity, a postulate is made that the speed of light is the same (called c) in all inertial frames. 

Consider the following statement:

"The speed of light is c in all inertial frames but it can vary (even locally) in accelerating frames."

My question is:

Does this statement violate the principle of equivalence or the special theory of relativity or any fundamental law of physics?