theorem
  for p being n-element FinSequence, q being FinSequence
    holds (p^q).1 = p.1 & ... & (p^q).n = p.n
proof let p be n-element FinSequence, q be FinSequence;
   let k be Nat;
A1: len p = n by Th151;
   assume 1 <= k & k <= n;
   then k in dom p by A1,Th25;
   hence (p^q).k = p.k by FINSEQ_1:def 7;
end;
