reserve a,b,c,d,e,x,r for Real,
  A for non empty closed_interval Subset of REAL,
  f,g for PartFunc of REAL,REAL;

theorem Th2: ::: XXREAL_1
  a <= b implies ].x-a,x+a.[ c= ].x-b,x+b.[
proof
  assume a <= b;
  then x-b <= x - a & x+a <= x+b by XREAL_1:7,10;
  hence thesis by XXREAL_1:46;
end;
