theorem Th43: :: SIMPLEX1:43

for V being RealLinearSpace
for K being non void total affinely-independent simplex-join-closed SimplicialComplex of V
for Sk being finite simplex-like Subset-Family of K st Sk is c=-linear & Sk is with_non-empty_elements & (card Sk) + 1 = card (union Sk) holds
card { S1 where S1 is Simplex of card Sk, BCS K : ( (center_of_mass V) .: Sk c= S1 & conv (@ S1) c= conv (@ (union Sk)) ) } = 2