reserve T for non empty Abelian
  add-associative right_zeroed right_complementable RLSStruct,
  X,Y,Z,B,C,B1,B2 for Subset of T,
  x,y,p for Point of T;
reserve t,s,r1 for Real;
reserve n for Element of NAT;
reserve X,Y,B1,B2 for Subset of TOP-REAL n;
reserve x,y for Point of TOP-REAL n;
reserve n for Element of NAT;
reserve X,B for Subset of TOP-REAL n;

theorem
  X is convex & B is convex implies X (O) B is convex & X (o) B is convex
proof
  assume that
A1: X is convex and
A2: B is convex;
  X (-) B is convex by A1,A2,Th76;
  hence X (O) B is convex by A2,Th76;
  X (+) B is convex by A1,A2,Th76;
  hence thesis by A2,Th76;
end;
