
theorem Th21:
for n being Nat, X being n-at_most_dimensional set,
    x being Element of X
 st x in X holds card x <= n+1
 proof let n be Nat, X be n-at_most_dimensional set, x be Element of X;
  assume x in X;
   then
A1:  card x c= n+1 by Def4;
   reconsider x as finite set;
   Segm card x c= Segm(n+1) by A1;
  hence thesis by NAT_1:39;
 end;
