theorem
  F is commutative associative & (B <> {} or F is having_a_unity) & f|B
  = f9|B implies F $$(B,f) = F $$(B,f9)
proof
  assume
A1: F is commutative associative &( B <> {} or F is having_a_unity);
  set s = id B;
A2: dom s = B & rng s = B;
  assume f|B = f9|B;
  then f|B = f9*s by RELAT_1:65;
  hence thesis by A1,A2,Th5;
end;
