reserve x,X for set;
reserve x0,r1,r2,g,g1,g2,p,s for Real;
reserve r for Real;
reserve n,m for Nat;
reserve a,b,d for Real_Sequence;
reserve f for PartFunc of REAL,REAL;

theorem
  g in ].x0 - r,x0 + r.[ implies g - x0 in ].-r,r.[
proof
  set r1 = g-x0;
  assume g in ].x0 - r,x0 + r.[;
  then
 |.g-x0.| < r by Th1;
  then |.r1 - 0.| < r;
  then r1 in ].0 - r, 0 + r.[ by RCOMP_1:1;
  hence thesis;
end;
