I need to prove the following:
Let $H$ be a finite set of at least three half-planes. We call a half-plane $h ∈ H$ redundant if it does not contribute an edge to$∩H$. Prove that for any redundant half-plane $h ∈ H$ there are two half-planes $h ′ , h′′ ∈ H$ such that $ h ′ ∩ h ′′ ⊂ h.$
What I can tell for sure, Is that $∩H$ Must be above the line that defines the half plane $h$. If that Is the case then the big intersection $∩H$ Is contained in $h$, But I don't know how to go further with this.
Any help will be appericiated, Thanks!
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