Does a correctly synchronized program still allow data race?(Part I)

Question

There are two conclusions from JLS:

• C1: If a program is free of data races, then all executions of the program will appear to be sequentially consistent:

Answer 1

http://rsim.cs.illinois.edu/Pubs/popl05.pdf

The proof seems to go this way:

Suppose an execution of a correctly synchronized program contains data race, we can find a sequential execution that contains data race, violating the definition of "correctly synchronized program" [C1]

Therefore the execution must not contain data race. [C3] From there, the execution can be proven to be sequentially consistent. [C2]

So C3 is true, and it is used to prove C2.