reserve x,X for set,
        r,r1,r2,s for Real,
        i,j,k,m,n for Nat;
reserve p,q for Point of TOP-REAL n;
reserve f,f1,f2 for homogeneous additive Function of TOP-REAL n,TOP-REAL n;

theorem Th29:
  AutMt (f1*f2) = (AutMt f2) * (AutMt f1)
proof
  set A1=AutMt f1,A2=AutMt f2;
  A1:width A1=n & width A2 =n & len A2=n by MATRIX_0:24;
  n =0 implies n=0;
  then Mx2Tran(A2*A1)=(Mx2Tran A1) * (Mx2Tran A2) by A1,MATRTOP1:32
  .= f1 *(Mx2Tran A2) by Def6
  .= f1 *f2 by Def6;
  hence thesis by Def6;
end;
