Sagemath says that my assumption about $A$ and $B$ are inconsistent in the following code
var ('p θ A B ds')
#assume(1<θ)
assume(0<p<=1)
assume(A<0)
assume(B<0)
bool((p - 1)^2*p*θ^2*A - ((p - 1)*θ + 1)^2*(p - 1)*B<0)
but $(p - 1)^2>0$, $p>0$ $θ^2>0$ so $A<0$ make the first term negative. For the second, for the same type of reasons, we arrive to the fact that both hypothesis are necessary to arrive to a negative formula. So I do not understand the SageMath claim.
