reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;
reserve i,i0,i1,i2,i3,i4,i5,i8,i9,j for Integer;

theorem Th7:
  i0 < i1 implies i0 + 1 <= i1
proof
  assume i0 < i1;
  then i0 + (- i0) < i1 + (- i0) by XREAL_1:6;
  then 1 <= i1 + (- i0) by Lm4;
  then 1 + i0 <= i1 + (- i0) + i0 by XREAL_1:6;
  hence thesis;
end;
