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;

theorem Th51:
  not H is_immediate_constituent_of x 'in' y
proof
  assume H is_immediate_constituent_of x 'in' y;
  then
A1: x 'in' y = 'not' H or ( ex H1 st x 'in' y = H '&' H1 or x 'in' y = H1
  '&' H ) or ex z st x 'in' y = All(z,H);
  (x 'in' y).1 = 1 by Th15;
  hence contradiction by A1,Th16,Th17,FINSEQ_1:41;
end;
