reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem
  i1<=i2 implies n-'i2<=n-'i1
proof
  assume
A1: i1<=i2;
  per cases;
  suppose
A2: i2<=n;
    then
A3: n-'i1=n-i1 by A1,XREAL_1:233,XXREAL_0:2;
    n-'i2=n-i2 by A2,XREAL_1:233;
    hence thesis by A1,A3,XREAL_1:10;
  end;
  suppose i2>n;
    then n-i2<0 by XREAL_1:49;
    hence thesis by XREAL_0:def 2;
  end;
end;
