reserve x,y, X,Y,Z for set,
        D for non empty set,
        n,k for Nat,
        i,i1,i2 for Integer;
reserve K for SimplicialComplexStr;

theorem Th23:
  -1 <= degree K
 proof
  per cases;
  suppose K is void;
   hence thesis by Def12;
  end;
  suppose A1: K is non void finite-degree;
   then reconsider d=degree K as Integer;
   0=-1+1 & d+1>=0 by A1;
   hence thesis by XREAL_1:6;
  end;
  suppose K is non void non finite-degree;
   hence thesis by Def12;
  end;
 end;
