reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem
  k <= i & i < j implies i -' k < j -' k
proof
  assume that
A1: k <= i and
A2: i < j;
  i -' k + k = i by A1,XREAL_1:235;
  then i -' k + k < j -' k + k by A1,A2,XREAL_1:235,XXREAL_0:2;
  hence thesis by XREAL_1:6;
end;
