Ma's multiplicity conjecture for perfect ideals

Let $(R,\mathfrak{m})$ be a complete local ring and let $J$ be a perfect ideal of $R$.

Ma's multiplicity conjecture.

$$e(R/J)\geq e(R).$$

This is presented as a weaker form of a conjecture that would imply Lech's conjecture; the source notes that Ma did not state it himself. No resolution is given here.