Definition 5.7. Let $n>0$, $k\in \{1,\dots ,n\}$. Define:

• ${\pi }_k(x_1,\dots ,x_n)=(x_1,\dots ,x_{k-1},x_{k+1},\dots ,x_n)$.

• For $X$ a set of $n$-tuples,

  $${\pi }_k(X)=\{(x_1,\dots ,x_{k-1},x_{k+1},\dots ,x_n):(x_1,\dots ,x_n)\in X\}.$$