Let sXP : {subset X <= cover P}.

(* Specifications: *)
Lemma repr_mem_pblock x0 B : B \in P -> transversal_repr x0 X B \in B.
Lemma pblock_inj : {in X &, injective (pblock P)}.
Lemma card_transversal : #|X| = #|P|.
End Transversals.