reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem Th7:
  Seg k = {} iff not k in Seg k
   proof
    thus Seg k = {} implies not k in Seg k;
    assume not k in Seg k;
    then k = 0 by FINSEQ_1:3;
    hence Seg k = {};
   end;
