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;
reserve sq,sq9 for FinSequence;
reserve L,L9 for FinSequence;

theorem Th60:
  H is_immediate_constituent_of F implies len H < len F
proof
A1: now
    assume F = 'not' H;
    then len F = len <*2*> + len H by FINSEQ_1:22
      .= len H + 1 by FINSEQ_1:40;
    hence thesis by NAT_1:13;
  end;
A2: now
    given H1 such that
A3: F = H '&' H1 or F = H1 '&' H;
A4: len(<*3*>^H1^H) = len(<*3*>^(H1^H)) by FINSEQ_1:32
      .= len <*3*> + len(H1^H) by FINSEQ_1:22
      .= 1 + len(H1^H) by FINSEQ_1:40
      .= 1 + (len H + len H1) by FINSEQ_1:22
      .= 1 + len H + len H1;
    len(<*3*>^H^H1) = len(<*3*>^H) + len H1 by FINSEQ_1:22
      .= len <*3*> + len H + len H1 by FINSEQ_1:22
      .= 1 + len H + len H1 by FINSEQ_1:40;
    then 1 + len H <= len F by A3,A4,NAT_1:11;
    hence thesis by NAT_1:13;
  end;
A5: now
    given x such that
A6: F = All(x,H);
    len F = len(<*4*>^<*x*>) + len H by A6,FINSEQ_1:22
      .= len <*4*> + len <*x*> + len H by FINSEQ_1:22
      .= 1 + len <*x*> + len H by FINSEQ_1:40
      .= 1 + 1 + len H by FINSEQ_1:40
      .= (1 + len H) + 1;
    then 1 + len H <= len F by NAT_1:11;
    hence thesis by NAT_1:13;
  end;
  assume H is_immediate_constituent_of F;
  hence thesis by A1,A2,A5;
end;
