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 Th69:
  for x1, x2, x3, x4, x5, x6, x7 being set, p being FinSequence
  st p = <*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>^<*x6*>^<*x7*>
  holds len p = 7 & p.1 = x1 & p.2 = x2 & p.3 = x3 & p.4 = x4 & p.5 = x5 &
  p.6 = x6 & p.7 = x7
proof
  let x1, x2, x3, x4, x5, x6, x7 be set, p be FinSequence;
  assume
A1: p = <*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>^<*x6*>^<*x7*>;
  set p16 = <*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>^<*x6*>;
A2: len p16 = 6 by Th68;
A3: p16.1 = x1 & p16.2 = x2 by Th68;
A4: p16.3 = x3 & p16.4 = x4 by Th68;
A5: p16.5 = x5 & p16.6 = x6 by Th68;
  thus len p = len p16 + len <*x7*> by A1,Th22
    .= 6 + 1 by A2,Th40
    .= 7;
A6: dom p16 = Seg 6 by A2,Def3;
   1 in Seg 6 & ...& 6 in Seg 6;
  hence p.1 = x1 & p.2 = x2 & p.3 = x3 & p.4 = x4 & p.5 = x5 & p.6 = x6
  by A1,A3,A4,A5,Def7,A6;
  thus p.7 = p.(len p16 + 1) by A2
    .= x7 by A1,Th42;
end;
