reserve i,j,k,n for Nat,
  X,Y,a,b,c,x for set,
  r,s for Real;

theorem
  1 < i implies 0 < i-'1
proof
  assume 1 < i;
  then 1-1=0 & 1-'1<i-'1 by NAT_D:56;
  hence thesis by XREAL_0:def 2;
end;
