Theorems · Theorem · group theory
Submonoid.mem_closure_inv
∀ {G : Type u_2} [inst : Group G] (s : Set G) (x : G), x ∈ Submonoid.closure s⁻¹ ↔ x⁻¹ ∈ Submonoid.closure s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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 and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Submonoidstatement and proof · cited by 3,086
- Submonoid.closurestatement and proof · cited by 167
- Set.invstatement · cited by 132
- Submonoid.mem_invproof · cited by 2
- Submonoid.closure_invproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.closure_toSubmonoidproof · cited by 9