Let $G=(V,E)$ be a graph and $F \subseteq E$ an edge set. Proof that $G(F)$ is a spanning forest iff $E \backslash F$ is an inclusion-wise maximal edge set which doesn't include an inclusion-wise minimal cut of $G$.
I need to prove this equivalence for my exercise but I'm lacking the approach for a solution. On top of that, I find it hard to even understand what this statement means in a concrete visualisation.