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Let $X$ be a homologically bounded to the right complex and $Q$ a bounded to the right complex of Gorenstein flat $R$-modules such that $Q$ and $X$ are isomorphic in $\\mathcal{D}(R)$. We establish a natural isomorphism ${\\bf L}\\Lambda^{\\fa}(X)\\simeq \\Lambda^{\\fa}(Q)$ in $\\mathcal{D}(R)$ which immediately asserts that $\\sup {\\bf L}\\Lambda^{\\fa}(X)\\leq \\Gfd_RX$. 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