reserve i,j,k,n for Nat;
reserve x,x1,x2,x3,y1,y2,y3 for set;

theorem Th20:
  for n,i be Nat st i+1 < n holds [i,i+1] in the InternalRel of Necklace n
proof
  let n,j be Nat such that
A1: j+1 < n;
  reconsider j as Element of NAT by ORDINAL1:def 12;
A2: [j,j+1] in {[i,i+1] where i is Element of NAT:i+1 < n} by A1;
  the InternalRel of Necklace n = {[i,i+1] where i is Element of NAT:i+1 <
  n} \/ {[i+1,i] where i is Element of NAT:i+1 < n} by Th17;
  hence thesis by A2,XBOOLE_0:def 3;
end;
