reserve ADG for Uniquely_Two_Divisible_Group;
reserve a,b,c,d,a9,b9,c9,p,q for Element of ADG;
reserve x,y for set;

theorem Th10:
  ex d st a,b ==> c,d
proof
  set d9 = (-a) + (b + c);
  take d9;
  a + d9 = (a + (-a)) + (b + c) by RLVECT_1:def 3
    .= 0.ADG + (b + c) by RLVECT_1:5
    .= b + c by RLVECT_1:4;
  hence thesis by Th5;
end;
