Theorems · Theorem · group theory
Submonoid.mem_closure_of_mem
∀ {M : Type u_1} [inst : MulOneClass M] {s : Set M} {x : M}, x ∈ s → x ∈ Submonoid.closure s- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Submonoidstatement · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.closurestatement · cited by 167
- Submonoid.subset_closureproof · cited by 46
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Splits.Cproof · cited by 9
- Polynomial.Splits.X_add_Cproof · cited by 6
- Submonoid.fg_of_divisiveproof · cited by 2