Theorems · Theorem · group theory
AddSubmonoid.closure_sdiff_singleton_zero
∀ {M : Type u_1} [inst : AddZeroClass M] (s : Set M), AddSubmonoid.closure (s \ {0}) = AddSubmonoid.closure s- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SetLike.mem_coeproof · cited by 302
- AddSubmonoid.closurestatement and proof · cited by 224
- Set.singleton_subset_iffproof · cited by 206
- ZeroMemClass.zero_memproof · cited by 162
- AddSubmonoid.closure_sdiff_eq_closureproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.closure_addIrreducibleproof · cited by 0