We follow the paper by James Hyde and Justin Moore "Subgroups of $PL_0 I$ which do not embed into Thompson's group $F$". We introduce the notation of an $F$-obstruction and as an intermediate step to showing that Subgroups containing $F$-obstructions don't embed into $F$ we give a result that shows $F$ embeds into each subgroup containing an $F$-obstruction.