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;
