English
There exist p,q with p<0<q such that genWeightSpaceChain(M, χ1, χ2, p, q) equals a pair of bottom-weight spaces at p and q.
Русский
Существуют p<0<q такие, что genWeightSpaceChain(M, χ1, χ2, p, q) равна паре нижних весовых пространств при p и q.
LaTeX
$$$\exists p<0, q>0, genWeightSpaceChain(M, χ_1, χ_2, p, q) = ⊥ \land genWeightSpaceChain(M, χ_1, χ_2, p, q) = ⊥$$$
Lean4
/-- This is the largest `n : ℕ` such that `i • α + β` is a weight for all `0 ≤ i ≤ n`. -/
noncomputable def chainTopCoeff : ℕ :=
letI := Classical.propDecidable
if hα : α = 0 then 0
else
Nat.pred <|
Nat.find
(show ∃ n, genWeightSpace M (n • α + β : L → R) = ⊥ from
(eventually_genWeightSpace_smul_add_eq_bot M α β hα).exists)
