Theorems · Theorem · number theory
IsHeckeTriple.le_commensurator_left
∀ {G : Type u_1} [inst : Group G] {Δ : Submonoid G} {H₁ : Subgroup G} (H₂ : Subgroup G) [h : IsHeckeTriple Δ H₁ H₂],
Δ ≤ (Subgroup.Commensurable.commensurator H₁).toSubmonoidThe submonoid Δ lies in the commensurator of the left subgroup.
- Defined in
- Mathlib.NumberTheory.HeckeRing.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupIsHeckeTriple
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Submonoidstatement and proof · cited by 3,086
- Subgroup.toSubmonoidstatement and proof · cited by 114
- IsHeckeTriplestatement and proof · cited by 14
- Subgroup.Commensurable.commensuratorstatement · cited by 7
- IsHeckeTriple.le_commensurator_rightproof · cited by 4
- IsHeckeTriple.commensurableproof · cited by 3
- Subgroup.Commensurable.eqproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsHeckeTriple.diag_leftproof · cited by 0
- IsHeckeTriple.mem_commensurator_leftproof · cited by 0