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

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