theorem :: CONVEX1:14

for V being non empty Abelian add-associative vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
for M1, M2, M3 being Subset of V
for r1, r2, r3 being Real st M1 is convex & M2 is convex & M3 is convex holds
((r1 * M1) + (r2 * M2)) + (r3 * M3) is convex