reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;
reserve D for set;

theorem Th44:
  for x1, x2, x3, x4, x5, x6 being set st
     p = <%x1%>^<%x2%>^<%x3%>^<%x4%>^<%x5%>^<%x6%>
  holds len p = 6 & p.0 = x1 & p.1 = x2 & p.2 = x3 & p.3 = x4 & p.4 = x5 &
  p.5 = x6
proof
  let x1, x2, x3, x4, x5, x6 be set;
  assume
A1: p = <%x1%>^<%x2%>^<%x3%>^<%x4%>^<%x5%>^<%x6%>;
  set p15 = <%x1%>^<%x2%>^<%x3%>^<%x4%>^<%x5%>;
A2: len p15 = 5 by Th43;
A3: p15.0 = x1 & p15.1 = x2 by Th43;
A4: p15.2 = x3 & p15.3 = x4 by Th43;
A5: p15.4 = x5 by Th43;
  thus len p = len p15 + len <%x6%> by A1,Def3
    .= 5 + 1 by A2,Th30
    .= 6;
   0 in 5 & ... & 4 in 5 by CARD_1:53,ENUMSET1:def 3;
  hence p.0 = x1 & p.1 = x2 & p.2 = x3 & p.3 = x4 & p.4 = x5
  by A1,A3,A4,A5,Def3,A2;
  thus p.5 = p.len p15 by Th43
    .= x6 by A1,Th33;
end;
