reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;

theorem
  for p,q being FinSequence, i being Nat st
  1 <= i & i <= len p holds (p ^ q).i = p.i
proof
  let p,q be FinSequence, i be Nat;
  assume
A1: 1 <= i & i <= len p;
  i in NAT & Seg len p = dom p by Def3,ORDINAL1:def 12;
  then i in dom p by A1;
  hence thesis by Def7;
end;
