The "assembly" produced or includable in C is not standardized, and is thus not a "subset" of C in any way.
(whereas C is a standardized subset of C++ (except for divergence), and C++ is a standardized subset of Arduino (if you consider Arduino a separate lanaguage.))
Not all C compilers generate asm on the way to machine code, BTW. I've used at least one where they'd skip that step unless it was "necessitate" by, say, using inline asm in the C code. Which resulted in some very mysterious bugs when the assembler didn't support the same data types as the compiler 