reserve u,v,x,y,z,X,Y for set;
reserve r,s for Real;

theorem
  x in X implies <%x%> in product <%X%>
  proof
    set f = <%X%>;
    set g = <%x%>;
    assume
A1: x in X;
A2: len f = 1 by AFINSQ_1:34;
A3: len g = dom g;
    now
      let a be object;
      assume a in dom f;
      then a = 0 by A2,CARD_1:49,TARSKI:def 1;
      hence g.a in f.a by A1;
    end;
    hence thesis by A2,A3,CARD_3:9,AFINSQ_1:34;
  end;
