theorem Th39: :: SIMPLEX1:39

for V being RealLinearSpace
for Sf being c=-linear finite finite-membered Subset-Family of V st Sf is with_non-empty_elements & (card Sf) + 1 = card (union Sf) & union Sf is affinely-independent holds
card { S1 where S1 is Simplex of card Sf, BCS (Complex_of {(union Sf)}) : (center_of_mass V) .: Sf c= S1 } = 2