Fact map_mx_key : unit.Definition map_mx m n (A : 'M_(m, n)) := \matrix[map_mx_key]_(i, j) f (A i j).

Lemma map_block_mx : (block_mx Aul Aur Adl Adr)^f = block_mx Aul^f Aur^f Adl^f Adr^f.