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LeanPool.LeanModularForms.ValenceFormula.RectHomotopy.MainTheorem

Main winding number theorem for the fundamental domain boundary #

The generalized winding number of fdBoundary around interior points equals -1 (clockwise).

theorem RectHomotopyProof.generalizedWindingNumber_fdBoundary_eq_neg_one (p : ) (hp_norm : p > 1) (hp_re : |p.re| < 1 / 2) (hp_im_pos : 0 < p.im) (hp_im : p.im < HHeight) :

For interior points p in the fundamental domain, the generalized winding number of the FD boundary around p equals -1 (clockwise orientation).