
theorem Th2:
for n,b being Nat holds value(<%n%>,b)=n
proof
  let n,b be Nat;
  A1: Sum <%n%> = n by AFINSQ_2:53;
  now
    let i be Nat;
    assume i in dom <%n%>;
    then i in 1 by AFINSQ_1:def 4;
    then i in {0} by CARD_1:49;
    then A2: i = 0 by TARSKI:def 1;
    thus <%n%>.i = (<%n%>.i) * 1 .= (<%n%>.i)*(b|^i) by A2,NEWTON:4;
  end;
  hence thesis by A1,NUMERAL1:def 1;
end;
