Theorems · Theorem · group theory
Submonoid.mem_top
∀ {M : Type u_1} [inst : MulOneClass M] (x : M), x ∈ ⊤- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Submonoidstatement · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- Set.mem_univproof · cited by 416
Cited by12
Results whose statement or proof uses this declaration.
- Submonoid.topEquivproof · cited by 4
- CoxeterSystem.simple_induction_leftproof · cited by 1
- Submonoid.eq_top_iff'proof · cited by 1
- Submonoid.subsingleton_iffproof · cited by 1
- CoxeterSystem.simple_inductionproof · cited by 0
- CoxeterSystem.simple_induction_rightproof · cited by 0
- MonoidAlgebra.freeAlgebra_lift_of_surjective_of_closureproof · cited by 0
- Submonoid.dense_inductionproof · cited by 0
- Algebra.GrothendieckGroup.inv_mkstatement · cited by 0
- Submonoid.closure_irreducibleproof · cited by 0
- MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closureproof · cited by 0
- Algebra.GrothendieckGroup.mk_div_mkstatement and proof · cited by 0