theorem
  for F being Function of [:D,D9:],E for p being FinSequence of D for q
being FinSequence of D9 st p = <*d1,d2*> & q = <*d19,d29*> holds F.:(p,q) = <*F
  .(d1,d19),F.(d2,d29)*>
proof
  let F be Function of [:D,D9:],E;
  let p be FinSequence of D;
  let q be FinSequence of D9 such that
A1: p = <*d1,d2*> & q = <*d19,d29*>;
A2: p.2 = d2 & q.2 = d29 by A1;
  reconsider r = F.:(p,q) as FinSequence of E by Th68;
  len p = 2 & len q = 2 by A1,FINSEQ_1:44;
  then
A3: len r = 2 by Th70;
  then 2 in Seg len r;
  then 2 in dom r by FINSEQ_1:def 3;
  then
A4: r.2 = F.(d2,d29) by A2,FUNCOP_1:22;
  1 in Seg len r by A3;
  then
A5: 1 in dom r by FINSEQ_1:def 3;
  p.1 = d1 & q.1 = d19 by A1;
  then r.1 = F.(d1,d19) by A5,FUNCOP_1:22;
  hence thesis by A3,A4,FINSEQ_1:44;
end;
