 reserve x for Real,
    p,k,l,m,n,s,h,i,j,k1,t,t1 for Nat,
    X for Subset of REAL;
reserve x for object, X,Y,Z for set;
 reserve M,N for Cardinal;
reserve X for non empty set,
  s for sequence of X;

theorem
  m <= i & i <= m+k implies i = m+0 or ... or i = m+k
proof assume that
A1: m <= i and
A2: i <= m+k;
  take j = i;
  thus thesis by A1,A2;
end;
