reserve X,Y for set;
reserve G for Group;
reserve n for Nat;

theorem Th9:
  SymGroup({}) = Trivial-multMagma
  proof
    set G = SymGroup({});
A1: the carrier of G = permutations {} by Def2;
    now
      let x,y be Element of {{}};
      reconsider f = x, g = y as Element of G by Th4,Def2;
      thus (the multF of G).(x,y) = f * g
      .= {} by A1,Th4,TARSKI:def 1
      .= op2.(x,y) by FUNCOP_1:77;
    end;
    hence thesis by A1,Th4,BINOP_1:2;
  end;
