
theorem Th56:
  for L be ExtREAL_sequence holds for n be Nat holds L.n <= sup rng L
proof
  let L be ExtREAL_sequence;
  let n be Nat;
  reconsider n as Element of NAT by ORDINAL1:def 12;
  dom L = NAT by FUNCT_2:def 1;
  then
A1: L.n in rng L by FUNCT_1:def 3;
  sup rng L is UpperBound of rng L by XXREAL_2:def 3;
  hence thesis by A1,XXREAL_2:def 1;
end;
