Theorems · Theorem · group theory
AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff
∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {H : AddSubgroup G}
{x : AddAction.orbitRel.Quotient G α} {a b : ↑x.orbit}, ↑a ∈ AddAction.orbit ↥H ↑b ↔ a ∈ AddAction.orbit (↥H) b- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HVAdd.hVAddproof · cited by 1,820
- AddActionstatement and proof · cited by 820
- AddAction.orbitstatement and proof · cited by 86
- AddAction.orbitRel.Quotientstatement and proof · cited by 17
- AddAction.orbitRel.Quotient.orbitstatement and proof · cited by 15
- AddAction.mem_orbitproof · cited by 14
- AddAction.addSubgroup_vadd_defproof · cited by 2
- AddAction.orbitRel.Quotient.orbit.coe_vaddproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff'proof · cited by 0
- AddAction.orbitRel.Quotient.addSubgroup_quotient_eq_iffproof · cited by 0