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

theorem
  i1+2<=i2 or i1+1+1<=i2 implies i1+1<i2 & i1+1-'1<i2 & i1+1-'2<i2 & i1+1<=i2 &
  i1-'1+1<i2 & i1-'1+1-'1<i2 & i1<i2 & i1-'1<i2 & i1-'2<i2 & i1<=i2
proof
  assume i1+2<=i2 or i1+1+1<=i2;
  then i1+1+1<=i2;
  hence
A1: i1+1<i2 & i1+1-'1<i2 & i1+1-'2<i2 & i1+1<=i2 by Th46,NAT_1:13;
  i1-'1<=i1 by Th35;
  then i1-'1+1<=i1+1 by XREAL_1:6;
  then
A2: i1-'1+1<i2 by A1,XXREAL_0:2;
  reconsider i1 as Nat by TARSKI:1;
  i1-'1+1-'1<=i1-'1+1 by Th35;
  hence thesis by A1,Th46,A2,XXREAL_0:2,NAT_1:13;
end;
