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 Th66:
  for x1, x2, x3, x4 being set, p being FinSequence
  st p = <*x1*>^<*x2*>^<*x3*>^<*x4*>
  holds len p = 4 & p.1 = x1 & p.2 = x2 & p.3 = x3 & p.4 = x4
proof
  let x1, x2, x3, x4 be set, p be FinSequence;
  assume
A1: p = <*x1*>^<*x2*>^<*x3*>^<*x4*>;
  set p13 = <*x1*>^<*x2*>^<*x3*>;
A2: p13 = <*x1, x2, x3*>;
  then
A3: len p13 = 3 by Th45;
A4: p13.1 = x1 & p13.2 = x2 by A2;
A5: p13.3 = x3 by A2;
  thus len p = len p13 + len <*x4*> by A1,Th22
    .= 3 + 1 by A3,Th40
    .= 4;
A6: dom p13 = Seg 3 by A3,Def3;
   1 in Seg 3 & ...& 3 in Seg 3;
  hence p.1 = x1 & p.2 = x2 & p.3 = x3 by A1,A4,A5,Def7,A6;
  thus p.4 = p.(len p13 + 1) by A3
    .= x4 by A1,Th42;
end;
