theorem
  m<=n & n<=len p implies
  (1, m)-cut p ^ (m+1, n)-cut p ^ (n+1, len p)-cut p = p
proof
  assume that
A1: m<=n and
A2: n<=len p;
  set cp3 = (n+1, len p)-cut p;
  set cp2 = (m+1, n)-cut p;
  set cp1 = (1, m)-cut p;
A3: 0+1=1;
  hence cp1^cp2^cp3 = (1, n)-cut p ^cp3 by A1,A2,Th8
    .= (1, len p)-cut p by A2,A3,Th8
    .= p by Th7;
end;
