reserve i,j,m,n,k for Nat,
  x,y for set,
  K for Field,
  a for Element of K;
reserve V for non trivial VectSp of K,
  V1,V2 for VectSp of K,
  f for linear-transformation of V1,V1,
  v,w for Vector of V,
  v1 for Vector of V1,
  L for Scalar of K;
reserve S for 1-sorted,
  F for Function of S,S;

theorem Th18:
  F |^ 0 = id S
proof
  set G=GFuncs the carrier of S;
  reconsider F9=F as Element of G by MONOID_0:73;
  0|->F9=<*>the carrier of G;
  then Product(0|->F9) = 1_G by GROUP_4:8
    .= the_unity_wrt the multF of G by GROUP_1:22
    .= id S by MONOID_0:75;
  hence thesis by Def4;
end;
