reserve N,M,K for ExtNat;
reserve X for ext-natural-membered set;

theorem
  <% 0, 1 %> = id 2
proof
  A1: dom <% 0, 1 %> = dom id 2 by Th7, CARD_1:50;
  now
    let x be object;
    assume x in dom <% 0, 1 %>;
    then A2: x in 2 & x in {0,1} by A1, Th7;
    then per cases by TARSKI:def 2;
    suppose x = 0;
      hence <% 0, 1 %>.x = (id 2).x by A2, FUNCT_1:18;
    end;
    suppose x = 1;
      hence <% 0, 1 %>.x = (id 2).x by A2, FUNCT_1:18;
    end;
  end;
  hence thesis by A1, FUNCT_1:2;
end;
