Theorems · Theorem · group theory
Submonoid.closure_singleton_le_iff_mem
∀ {M : Type u_1} [inst : MulOneClass M] (m : M) (p : Submonoid M), Submonoid.closure {m} ≤ p ↔ m ∈ p- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClass
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
- Submonoidstatement and proof · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- SetLike.mem_coeproof · cited by 302
- Set.singleton_subset_iffproof · cited by 206
- Submonoid.closurestatement · cited by 167
- Submonoid.closure_leproof · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.mem_iSupproof · cited by 0
- Submonoid.closure_insert_oneproof · cited by 0