
theorem Th1:
for b being Nat
for E being XFinSequence of NAT st E={} holds value(E,b)=0
proof
  let b be Nat;
  let E be XFinSequence of NAT;
  assume A1: E={};
  then A2: for i being Nat st i in dom E holds E.i = (E.i)*(b|^i);
  Sum E=0 by A1;
  hence value(E,b)=0 by A2,NUMERAL1:def 1;
end;
