Theorems · Theorem · group theory
AddAction.isBlock_iff_vadd_eq_of_mem
∀ {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⦄ ⦃a : X⦄, a ∈ B → g +ᵥ a ∈ B → g +ᵥ B = B- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 2 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.
Cites10
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
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.vaddSetstatement · cited by 403
- AddAction.IsBlockstatement · cited by 65
- Set.mem_inter_iffproof · cited by 50
- exists_exists_and_eq_andproof · cited by 10
- Set.mem_vadd_setproof · cited by 7
- AddAction.isBlock_iff_vadd_eq_of_nonemptyproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- AddAction.IsBlock.vadd_eq_of_memproof · cited by 1
- AddAction.isPreprimitive_of_is_two_pretransitiveproof · cited by 1