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

theorem Th46:
  i1+1<=i2 implies i1-'1<i2 & i1-'2<i2 & i1<=i2
proof
  assume
A1: i1+1<=i2;
  then
A2: i1<i2 by NAT_1:13;
  i1-'1<=i1 by Th35;
  hence
A3: i1-'1<i2 by A2,XXREAL_0:2;
A4: i1-'1-'1=i1-'2 by Th45;
  reconsider i1 as Nat by TARSKI:1;
  i1-'1-'1<=i1-'1 by Th35;
  hence thesis by A1,A3,A4,XXREAL_0:2,NAT_1:13;
end;
