Theorems · Theorem · group theory
AddSubmonoid.closure_insert_zero
∀ {M : Type u_1} [inst : AddZeroClass M] (s : Set M), AddSubmonoid.closure (insert 0 s) = AddSubmonoid.closure s- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
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Cites9
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 and proof · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- ZeroMemClass.zero_memproof · cited by 162
- sup_eq_rightproof · cited by 53
- Set.insert_eqproof · cited by 47
- AddSubmonoid.closure_unionproof · cited by 10
- AddSubmonoid.closure_singleton_le_iff_memproof · cited by 2
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