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;

theorem Th41:
  X (O) B c= X & X c= X (o) B
proof
  thus X (O) B c= X
  proof
    let x be object;
    assume x in X (O) B;
    then consider y1,y2 being Point of T such that
A1: x=y1+y2 and
A2: y1 in X (-) B and
A3: y2 in B;
    consider y being Point of T such that
A4: y1=y and
A5: B+y c= X by A2;
    x in B+y by A1,A3,A4;
    hence thesis by A5;
  end;
  thus thesis by Th20;
end;
