Leigh.Samphier/Sandbox/Matroid Unique Circuit Property/Proof 2
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Theorem
Let $M = \struct {S, \mathscr I}$ be a matroid.
Let $X \subseteq S$ be an independent subset of $M$.
Let $x \in S$ such that:
- $X \cup \set x$ is a dependent subset of $M$.
Then there exists a unique circuit $C$ such that:
- $x \in C \subseteq X \cup \set x$
Proof
$\blacksquare$