theorem Th75:
  F is associative & F is having_a_unity & e = the_unity_wrt F &
    F is having_an_inverseOp & G is_distributive_wrt F implies
      G[;](e,f) = C-->e
proof
  reconsider g = C-->e as Function of C,D;
  assume
A1: F is associative & F is having_a_unity & e = the_unity_wrt F & F is
  having_an_inverseOp & G is_distributive_wrt F;
  now
    let c;
    thus (G[;](e,f)).c = G.(e,f.c) by FUNCOP_1:53
      .= e by A1,Th66
      .= g.c;
  end;
  hence thesis by FUNCT_2:63;
end;
