Theorems · Theorem · group theory
AddSubmonoid.mem_closure_of_mem
∀ {M : Type u_1} [inst : AddZeroClass M] {s : Set M} {x : M}, x ∈ s → x ∈ AddSubmonoid.closure s- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- AddZeroClass
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
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- AddSubmonoid.closurestatement · cited by 224
- AddSubmonoid.subset_closureproof · cited by 63
Cited by6
Results whose statement or proof uses this declaration.
- AddSubmonoid.fg_of_subtractiveproof · cited by 2
- IsLinearSet.closureproof · cited by 1
- IsLinearSet.exists_fg_eq_subtypeValproof · cited by 1
- IsLinearSet.isProperSemilinearSetproof · cited by 1
- AddSubmonoid.closure_isSquareproof · cited by 0
- NonUnitalStarRingHom.map_le_map_of_map_starproof · cited by 0