Theorems · Theorem · group theory
AddAction.isBlock_iff_disjoint_vadd_of_ne
∀ {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 → Disjoint (g +ᵥ B) B- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 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
- Disjointstatement and proof · cited by 2,201
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.vaddSetstatement · cited by 403
- zero_vaddproof · cited by 95
- AddAction.IsBlockstatement and proof · cited by 65
- vadd_vaddproof · cited by 40
- neg_vadd_eq_iffproof · cited by 13
- Set.disjoint_vadd_set_rightproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- AddAction.isBlock_iff_vadd_eq_of_nonemptyproof · cited by 4
- AddAction.isBlock_iff_vadd_eq_or_disjointproof · cited by 3
- AddAction.IsBlock.disjoint_vadd_of_neproof · cited by 0