theorem
  for F being Function of [:D,D9:],E for p being FinSequence of D st p =
  <*d1*> holds F[:](p,d9) = <*F.(d1,d9)*>
proof
  let F be Function of [:D,D9:],E;
  let p be FinSequence of D such that
A1: p = <*d1*>;
A2: p.1 = d1 by A1;
  reconsider r = F[:](p,d9) as FinSequence of E by Th81;
  len p = 1 by A1,FINSEQ_1:39;
  then
A3: len r = 1 by Th82;
  then 1 in Seg len r;
  then 1 in dom r by FINSEQ_1:def 3;
  then r.1 = F.(d1,d9) by A2,FUNCOP_1:27;
  hence thesis by A3,FINSEQ_1:40;
end;
