Theorems · Theorem · group theory
AddAction.orbitRel.Quotient.orbit_injective
∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α],
Function.Injective AddAction.orbitRel.Quotient.orbit- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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 · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddActionstatement and proof · cited by 820
- Quotient.eq''proof · cited by 44
- Quotient.out_eq'proof · cited by 35
- Quotient.out_eqproof · cited by 27
- AddAction.orbitRel.Quotientstatement and proof · cited by 17
- AddAction.orbitRel.Quotient.orbitstatement and proof · cited by 15
- AddAction.orbitRel.Quotient.orbit_eq_orbit_outproof · cited by 4
- AddAction.orbit_eq_iffproof · cited by 4
- AddAction.orbitRel_applyproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.orbitRel.Quotient.orbit_injproof · cited by 0