I found the following result in an unpublished lectures notes
Let $\mathbb X\subset P^N$ be a non degenerate subvariety of codimension $l>k$. Then the general $(k+1)$-secant $\mathbb P^k$ is not $(k+2)$-secant.
The result was called $the$ $classical$ $trisecant$ $lemma$.
Question 1: I am interested on any references where this result is formulated.
Question 2: Does the result hold over $\mathbb R$?