Simply put, $~$p \\prec q$~$ means that $~$q$~$ is the smallest element of $~$P$~$ which is strictly greater than $~$p$~$\. $~$p \\prec q$~$ is pronounced "$~$p$~$ is covered by $~$q$~$", or "$~$p$~$ covers $~$q$~$"\. $~$q$~$ is said to be a cover of $~$p$~$\.

Should the p's and q's in one of these be switched?