A Course in Universal Algebra (Millennium edition), page 74

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The line before Theorem 10.12 says that

"In general $F_K(\overline{X})$ is not isomorphic to a member of K (for example, let K={L} where L is a two-element lattice, then $F_K(\bar{x}, \bar{y}) \notin I(K))$." (The definition of $F_K(\overline{X})$ is shown in page 73.)

Why this is the case? Any example?

Thank you.

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This book is freely available as a pdf format : http://www.math.uwaterloo.ca/~snburris/htdocs/UALG/univ-algebra.pdf

Due to the lengthy definitions, I provide the link instead of giving full definitions involving the above question. Thanks.