Theorems · Theorem · group theory
mem_rightAddCoset_iff
∀ {α : Type u_1} [inst : AddGroup α] {s : Set α} {x : α} (a : α), x ∈ AddOpposite.op a +ᵥ s ↔ x + -a ∈ s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddOppositestatement · cited by 452
- Set.vaddSetstatement · cited by 403
- AddOpposite.opstatement and proof · cited by 192
- neg_add_cancel_rightproof · cited by 75
- add_neg_cancel_rightproof · cited by 65
Cited by4
Results whose statement or proof uses this declaration.
- eq_addCosets_of_normalproof · cited by 1
- rightAddCoset_mem_rightAddCosetproof · cited by 1
- normal_of_eq_addCosetsproof · cited by 1
- rightAddCoset_eq_iffproof · cited by 0