End Partitions.
Arguments trivIsetP {T P}.
Arguments big_trivIset_cond [T R idx op] P [K E].
Arguments set_partition_big_cond [T R idx op] P [D K E].
Arguments big_trivIset [T R idx op] P [E].
Arguments set_partition_big [T R idx op] P [D E].
Prenex Implicits cover trivIset partition pblock.

Lemma partition_partition (T : finType) (D : {set T}) P Q :
partition P D -> partition Q P ->
partition (cover @: Q) D /\ {in Q &, injective cover}.