theorem
  m<=len p implies (1, m)-cut p ^ (m+1, len p)-cut p = p
proof
  set cp1 = (1, m)-cut p;
  set cpm = (m+1, len p)-cut p;
A1: 0+1=1;
  assume m<=len p;
  hence cp1 ^ cpm = (1, len p)-cut p by A1,Th8
    .= p by Th7;
end;
