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

theorem
  i1<=i2 or i1<=i2-'1 implies
  i1<i2+1 & i1<=i2+1 & i1<i2+1+1 & i1<=i2+1+1 & i1<i2+2 & i1<=i2+2
proof
  assume
A1: i1<=i2 or i1<=i2-'1;
A2: now
    assume i1<=i2;
    then
A3: i1<i2+1 by NAT_1:13;
    i2+1+1=i2+(1+1);
    hence thesis by A3,NAT_1:13;
  end;
  now
    assume
A4: i1<=i2-'1;
    i2-'1<=i2 by Th35;
    hence thesis by A2,A4,XXREAL_0:2;
  end;
  hence thesis by A1,A2;
end;
