Section Transversals.
Variables (X : {set T}) (P : {set {set T}}) (D : {set T}).
Hypothesis trPX : is_transversal X P D.
Let tiP : trivIset P. Proof. by case/andP: trPX => /and3P[]. Qed.
Let sXP : {subset X <= cover P}.

Lemma card_transversal : #|X| = #|P|.