reserve a,b,c,k,m,n for Nat;
reserve i,j,x,y for Integer;
reserve p,q for Prime;
reserve r,s for Real;

theorem
  primeindex p = primeindex q implies p = q
  proof
    primenumber primeindex p = p & primenumber primeindex q = q by Def4;
    hence thesis;
  end;
