In Sage 5.3, I get the following:

sage: p = MixedIntegerLinearProgram()
sage: x = p.new_variable(integer=True)
sage: c = x[0]-x[1]
sage: p.add_constraint(10 <= c)
sage: p.show()
Maximization:
 
Constraints:
Variables:
  x_0 is an integer variable (min=0.0, max=+oo)
  x_1 is an integer variable (min=0.0, max=+oo)

Thus, the constraint was not added to p. If I however do

sage: p.add_constraint(c >= 10)
sage: p.show()
Maximization:
 
Constraints:
  R0: - x_0 + x_1 <= -10.0
Variables:
  x_0 is an integer variable (min=0.0, max=+oo)
  x_1 is an integer variable (min=0.0, max=+oo)

then things are fine.

According to the doc, this seems to be a bug. Unfortunately, this behavior 
produces wrong results. It took me some time to isolate the problem! Bugs 
which just produce error messages are much friendlier ...

-- Peter Mueller

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