reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem Th37:
  {a} |^ {b} = {a |^ b}
proof
A1: {b}" * {a} * {b} = {b"} * {a} * {b} by GROUP_2:3
    .= {b" * a} * {b} by GROUP_2:18
    .= {a |^ b} by GROUP_2:18;
  {a} |^ {b} c= {b}" * {a} * {b} & {a} |^ {b} <> {} by Th32,Th33;
  hence thesis by A1,ZFMISC_1:33;
end;
