for D being non empty set
for d1, d2 being Element of D
for M1, M2, N1, N2 being Matrix of D st len M1 = len N1 & width M1 = width N1 & len M2 = len N2 & width M2 = width N2 & block_diagonal (<*M1,M2*>,d1) = block_diagonal (<*N1,N2*>,d2) holds
( M1 = N1 & M2 = N2 )