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...ce the original proof by Sperner, which uses concepts called '''shadows''' and '''shades''' of set systems. :Let <math>|X|=n\,</math> and <math>\mathcal{F}\subseteq {X\choose k}</math>, <math>k<n\,</math>. ...

...do, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...<math>|\mathcal{F}|>r-1</math>, we can choose <math>r</math> of these sets and form a sunflower. ...