reserve D for non empty set,
  D1,D2,x,y for set,
  n,k for Nat,
  p,x1 ,r for Real,
  f for Function;
reserve F for Functional_Sequence of D1,D2;
reserve G,H,H1,H2,J for Functional_Sequence of D,REAL;
reserve x for Element of D,
  X,Y for set,
  S1,S2 for Real_Sequence,
  f for PartFunc of D,REAL;

theorem Th32:
  X common_on_dom H implies for x st x in X holds (r(#)H)#x = r(#) (H#x)
proof
  assume
A1: X common_on_dom H;
  let x;
  assume x in X;
  then {x} common_on_dom H by A1,Th25;
  hence thesis by Th29;
end;
