reserve x,y for set,
  i for Nat;
reserve V for non empty CLSStruct,
  u,v,v1,v2,v3 for VECTOR of V,
  A for Subset of V,
  l, l1, l2 for C_Linear_Combination of A,
  x,y,y1,y2 for set,
  a,b for Complex,
  F for FinSequence of the carrier of V,
  f for Function of the carrier of V, COMPLEX;

theorem
  f (#) <*>(the carrier of V) = <*>(the carrier of V)
proof
  len(f (#) <*>(the carrier of V)) = len(<*>(the carrier of V)) by Def5
    .= 0;
  hence thesis;
end;
