theorem
  len H = 3 implies H is atomic
proof
  assume
A1: len H = 3;
  assume not H is atomic;
  then consider H1 such that
A2: len H1 + 1 <= len H by Th12;
  3 <= len H1 by Th13;
  then 3 + 1 <= len H1 + 1 by XREAL_1:7;
  hence contradiction by A1,A2,XXREAL_0:2;
end;
