reserve a,b,i,j,k,l,m,n for Nat;

theorem AMP:
  for a,b be Complex holds
    a(#)<*b*> = <*a*b*>
  proof
    let a,b be Complex;
    A1: dom <*(a*b)*> = Seg 1 & dom <*b*> = Seg 1 by FINSEQ_1:def 8;
    for x be object st x in Seg 1 holds <*a*b*>.x = a*<*b*>.x
    proof
       let x be object;
       assume  x in Seg 1;
       then x = 1 by FINSEQ_1:2,TARSKI:def 1;
       hence thesis;
    end;
    hence thesis by A1,VALUED_1:def 5;
  end;
