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 Th67:
  for x1, x2, x3, x4, x5 being set, p being FinSequence
  st p = <*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>
  holds len p = 5 & p.1 = x1 & p.2 = x2 & p.3 = x3 & p.4 = x4 & p.5 = x5
proof
  let x1, x2, x3, x4, x5 be set, p be FinSequence;
  assume
A1: p = <*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>;
  set p14 = <*x1*>^<*x2*>^<*x3*>^<*x4*>;
A2: len p14 = 4 by Th66;
A3: p14.1 = x1 & p14.2 = x2 by Th66;
A4: p14.3 = x3 & p14.4 = x4 by Th66;
  thus len p = len p14 + len <*x5*> by A1,Th22
    .= 4 + 1 by A2,Th40
    .= 5;
A5:  dom p14 = Seg 4 by A2,Def3;
   1 in Seg 4 & ...& 4 in Seg 4;
  hence p.1 = x1 & p.2 = x2 & p.3 = x3 & p.4 = x4 by A1,A3,A4,Def7,A5;
  thus p.5 = p.(len p14 + 1) by A2
    .= x5 by A1,Th42;
end;
