theorem Th73:
  p is x-context_including implies p just_once_values x-context_in p
  proof set k = p, z = x;
    assume
A0: k is z-context_including;
    Coim(k, z-context_in k) = {z-context_pos_in k}
    proof
      thus Coim(k, z-context_in k) c= {z-context_pos_in k}
      proof
        let a; reconsider x = a as set by TARSKI:1;
        assume a in Coim(k, z-context_in k);
        then x in dom k & k.x in {z-context_in k} by FUNCT_1:def 7;
        then x is Nat & k.x = z-context_in k by TARSKI:def 1;
        then x = z-context_pos_in k by A0,CPI;
        hence a in {z-context_pos_in k} by TARSKI:def 1;
      end;
      let a be Nat;
      assume a in {z-context_pos_in k};
      then a = z-context_pos_in k by TARSKI:def 1;
      then k.a = z-context_in k by A0,Th71;
      then a in dom k & k.a in {z-context_in k} by TARSKI:def 1,FUNCT_1:def 2;
      hence thesis by FUNCT_1:def 7;
    end;
    hence card Coim(k, z-context_in k) = 1 by CARD_1:30;
  end;
