reserve k,m,n for Element of NAT,
  a,X,Y for set,
  D,D1,D2 for non empty set;
reserve p,q for FinSequence of NAT;
reserve x,y,z,t for Variable;
reserve F,F1,G,G1,H,H1 for ZF-formula;

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;
