reserve x,y for object,X,Y for set,
  D for non empty set,
  i,j,k,l,m,n,m9,n9 for Nat,
  i0,j0,n0,m0 for non zero Nat,
  K for Field,
  a,b for Element of K,
  p for FinSequence of K,
  M for Matrix of n,K;

theorem Th10:
  card 2Set Seg n = n choose 2
proof
  {Y where Y is Subset of Seg n: card Y = 2} = 2Set Seg n by SGRAPH1:def 2;
  hence card 2Set Seg n = card (Seg n) choose 2 by Th9
    .= n choose 2 by FINSEQ_1:57;
end;
