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

theorem
  i1<i2 or i1+1<=i2 implies i1<=i2-'1
proof
  assume
A1: i1<i2 or i1+1<=i2;
  per cases by A1;
  suppose
A2: i1<i2;
    then i1+1<=i2 by NAT_1:13;
    then
A3: i1+1-1<=i2-1 by XREAL_1:9;
    0+1<=i2 by A2,NAT_1:13;
    hence thesis by A3,XREAL_1:233;
  end;
  suppose
A4: i1+1<=i2;
    then
A5: i1+1-1<=i2-1 by XREAL_1:9;
    0+1<=i2 by A4,NAT_1:13;
    hence thesis by A5,XREAL_1:233;
  end;
end;
