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 Th12:
  ex b st a,b ==> b,c
proof
  consider b being Element of ADG such that
A1: b + b = a + c by Def1;
  take b;
  thus thesis by A1,Th5;
end;
