for i, j being Nat
for D being non empty set
for d being Element of D
for F1, F2 being FinSequence_of_Matrix of D st [i,j] in Indices (block_diagonal (F2,d)) holds
(block_diagonal (F2,d)) * (i,j) = (block_diagonal ((F1 ^ F2),d)) * ((i + (Sum (Len F1))),(j + (Sum (Width F1))))