reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
reserve A,B for set;
reserve x,y,i,j,k for object;

theorem
  for f, g being Function, A being set st A /\ dom f c= A /\ dom g holds
  (f+*g|A)|A = g|A
proof
  let f, g be Function, A be set;
  assume
A1: A /\ dom f c= A /\ dom g;
A2: dom (f|A) = A /\ dom f & dom (g|A) = A /\ dom g by RELAT_1:61;
  thus (f+*g|A)|A = (f|A)+*(g|A)|A by Th71
    .= (f|A)+*g|A
    .= g|A by A1,A2,Th19;
end;
