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;
