reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;

theorem Th20:
  s >= t & r = s-t implies s choose t = s choose r
proof
  assume
A1: s>=t;
  t-s>=0-s by XREAL_1:9;
  then
A2: --s>=-(t-s) by XREAL_1:24;
  assume
A3: r = s-t;
  then t = s-r;
  then s choose r = (s!)/((r!) * (t!)) by A2,Def3;
  hence thesis by A1,A3,Def3;
end;
