I've been trying to understand why
FullSimplify is giving a condition that is implied by the assumptions (otherwise the set is empty). However, I couldn't understand why:
Clear["Global`*"] l[v_] := v; q[\[Beta]_, v_] := (\[Beta] - n*c) /(1 + (l[v] + n^2)*c); Assuming[a > 0 && \[Beta] > 0 && c > 0 && v > 0 && n > 0 && c < (\[Beta]*n - 1)/(l[v] + n^2*(a + 1)), FullSimplify@Reduce[D[q[\[Beta], v], v] < 0]]
c n < \[Beta]
The inequality is reversed if I reverse the inequality in the derivative, when I'd expect (reply to comment below explains why):
Any ideas about what could possibly be the problem?