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 Th6:
  i1 + k = i2 implies i1 <= i2
proof
  reconsider i0 = k as Integer;
  assume i1 + k = i2;
  then 0 + (i1 + k) <= k + i2 by XREAL_1:6;
  then i1 + i0 - i0 <= i2 + i0 - i0 by XREAL_1:9;
  hence thesis;
end;
