spurious results as inequality solution

[rws]

From, ​http://ask.sagemath.org/question/26941/solving-system-of-inequalities-in-one-variable/:

x = var('x')
a = var('a')
solve([a*x>0,a>0],[x])
[[0 < x, a > 0], [x < 0, -a > 0, a > 0]]

The second solution contradicts one given precondition.

Also, from ​http://ask.sagemath.org/question/26410/test-if-an-inequality-is-feasible-under-assumptions/

sage: (l1,l2) = var("l1 l2")
sage: assume (l1>=0)
sage: assume (l2>=0)
sage: solve (l1*l2<0, [l1,l2])
[[0 < l2, l1 < 0], [l2 < 0, 0 < l1]]