Definition ulsubmx := lsubmx (usubmx A).Definition ursubmx := rsubmx (usubmx A).Definition dlsubmx := lsubmx (dsubmx A).Definition drsubmx := rsubmx (dsubmx A).

Lemma block_mxA m1 m2 m3 n1 n2 n3 (A11 : 'M_(m1, n1)) (A12 : 'M_(m1, n2)) (A13 : 'M_(m1, n3)) (A21 : 'M_(m2, n1)) (A22 : 'M_(m2, n2)) (A23 : 'M_(m2, n3)) (A31 : 'M_(m3, n1)) (A32 : 'M_(m3, n2)) (A33 : 'M_(m3, n3)) : let cast := (esym (addnA m1 m2 m3), esym (addnA n1 n2 n3)) in let row1 := row_mx A12 A13 in let col1 := col_mx A21 A31 in let row3 := row_mx A31 A32 in let col3 := col_mx A13 A23 in block_mx A11 row1 col1 (block_mx A22 A23 A32 A33) = castmx cast (block_mx (block_mx A11 A12 A21 A22) col3 row3 A33).