theorem Th2: :: MEASURE4:2

for X being set
for S being non empty Subset-Family of X
for F, G being sequence of S st G . 0 = F . 0 & ( for n being Nat holds G . (n + 1) = (F . (n + 1)) \/ (G . n) ) holds
for H being sequence of S st H . 0 = F . 0 & ( for n being Nat holds H . (n + 1) = (F . (n + 1)) \ (G . n) ) holds
union (rng F) = union (rng H)