  Let $\underline{x} = x_1,\ldots,x_k$ denote an ordered sequence of elements
of a commutative ring $R$. Let $M$ be an $R$-module. We recall the two notions
that $\underline{x}$ is $M$-proregular given by Greenlees and May (see
\cite{[5]}) and Lipman (see \cite{[1]}) and show that both notions are
equivalent. As a main result we prove a cohomological characterization for
$\underline{x}$ to be $M$-proregular in terms of \v{C}ech homology. This
implies also that $\underline{x}$ is $M$-weakly proregular if it is
$M$-proregular. A local-global principle for proregularity and weakly
proregularity is proved. This is used for a result about prisms as introduced
by Bhatt and Scholze (see \cite{[3]}).
