reserve A,B,O for Ordinal,
        o for object,
        x,y,z for Surreal,
        n,m for Nat;
reserve d,d1,d2 for Dyadic;
reserve i,j for Integer,
        n,m,p for Nat;

theorem Th22:
  rng uInt c= Day NAT
proof
  let y be object;
  assume y in rng uInt;
  then consider x be object such that
A1: x in dom uInt & uInt.x = y by FUNCT_1:def 3;
  reconsider x as Integer by A1;
  consider k be Nat such that
A2: x = k or x = - k by A1,INT_1:def 1;
  k c= NAT;
  then
A3: Day k c= Day NAT by SURREAL0:35;
  y in Day k by A1,A2,Th1;
  hence thesis by A3;
end;
