theorem Th10: :: PRVECT_1:10

for n being Nat
for D being non empty set
for H, G being BinOp of D
for d being Element of D
for t1, t2 being Element of n -tuples_on D st H is_distributive_wrt G holds
H [;] (d,(G .: (t1,t2))) = G .: ((H [;] (d,t1)),(H [;] (d,t2)))