Theorems · Theorem · group theory
AddAction.IsBlock.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 = BAlias of the forward direction of AddAction.isBlock_iff_vadd_eq_of_nonempty.
- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 2,627
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.vaddSetstatement · cited by 403
- AddAction.IsBlockstatement · cited by 65
- AddAction.isBlock_iff_vadd_eq_of_nonemptyproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.IsBlock.stabilizer_leproof · cited by 1