Theorems · Theorem · group theory
AddAction.mem_orbit_symm
∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {a₁ a₂ : α},
a₁ ∈ AddAction.orbit G a₂ ↔ a₂ ∈ AddAction.orbit G a₁- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 1 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddActionstatement and proof · cited by 820
- AddAction.orbitstatement and proof · cited by 86
- AddAction.orbit_eq_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff'proof · cited by 0