Normal form for a theta counterexample #
This connects the general rank-theoretic reduction to the strand geometry.
theorem
Bananas.theta_negative_rankDelta_normal_form
(B : Banana 2)
(u v : (Utilities.Certificate.SubdivisionGraph.Spec.graph B).V)
(huv : u ≠ v)
(D : CFDiv (Utilities.Certificate.SubdivisionGraph.Spec.graph B))
(hNeg : rankDelta (mark (Utilities.Certificate.SubdivisionGraph.Spec.graph B) u v) D < 0)
:
A negative marked second difference on a theta graph has, after deleting the first marked chip, a unique vertex-chip representative.