Theorems · Theorem · group theory
orbit_addSubgroup_eq_self_of_mem
∀ {α : Type u_1} [inst : AddGroup α] (s : AddSubgroup α) {a : α}, a ∈ s → AddAction.orbit (↥s) a = ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddAction.orbitstatement · cited by 86
- rightAddCoset_mem_rightAddCosetproof · cited by 1
- orbit_addSubgroup_eq_rightCosetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- orbit_addSubgroup_zero_eq_selfproof · cited by 1