reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;
reserve z for Complex;

theorem Th56:
  k in GreaterOrEqualsNumbers(n) iff n <= k
  proof
    thus k in GreaterOrEqualsNumbers(n) implies n <= k
    proof
      assume k in GreaterOrEqualsNumbers(n);
      then not k in Segm n by XBOOLE_0:def 5;
      hence thesis by NAT_1:44;
    end;
A1: k in NAT by ORDINAL1:def 12;
    assume n <= k;
    then not k in Segm n by NAT_1:44;
    hence thesis by A1,XBOOLE_0:def 5;
  end;
