Theorems · Theorem · group theory
AddAction.isBlock_iff_vadd_eq_of_nonempty
∀ {G : Type u_1} [inst : AddGroup G] {X : Type u_2} [inst_1 : AddAction G X] {B : Set X},
AddAction.IsBlock G B ↔ ∀ ⦃g : G⦄, ((g +ᵥ B) ∩ B).Nonempty → g +ᵥ B = B- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- Set.Nonemptystatement and proof · cited by 2,627
- Disjointproof · cited by 2,201
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.vaddSetstatement · cited by 403
- AddAction.IsBlockstatement · cited by 65
- not_imp_commproof · cited by 56
- Set.not_disjoint_iff_nonempty_interproof · cited by 29
- AddAction.isBlock_iff_disjoint_vadd_of_neproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- AddAction.isBlock_iff_vadd_eq_of_memproof · cited by 2
- AddAction.IsBlock.of_subsetproof · cited by 1
- AddAction.IsBlock.vadd_eq_of_nonemptyproof · cited by 1
- AddAction.IsBlock.of_orbitproof · cited by 0