Leigh.Samphier/Sandbox/Bound for Cardinality of Matroid Circuit

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Theorem

Let $M = \struct {S, \mathscr I}$ be a matroid.

Let $C \subseteq S$ be a circuit of $M$.

Let $\rho: \powerset S \to \Z$ denote the rank function of $M$.


Then:

$\card C \le \map \rho S + 1$

Proof

$\blacksquare$