openAI-math-dataset / lean /OAI /Probability /CriticalPercolation /Classification /AlgebraicDescent.lean
| import Mathlib | |
| namespace OAI | |
| section | |
| section | |
| noncomputable section | |
| open Set Function | |
| open scoped Classical | |
| namespace CriticalPercolation | |
| universe u | |
| inductive AlgebraicDescent : (N : Type u) → [Group N] → Prop | |
| | finite (N : Type u) [Group N] [Finite N] : AlgebraicDescent N | |
| | cyclic (N : Type u) [Group N] | |
| (φ : N →* Multiplicative ℤ) (hφ : Surjective φ) | |
| (hf : (φ.ker : Set N).Finite) : AlgebraicDescent N | |
| | plane (N : Type u) [Group N] | |
| (φ : N →* Multiplicative (ℤ×ℤ)) (hφ : Surjective φ) | |
| (lower : ∀ J : Subgroup N, J≤φ.ker → AlgebraicDescent J) : AlgebraicDescent N | |
| end CriticalPercolation | |
| end | |
| end | |
| end | |
| end OAI | |