Theorems · Theorem · group theory
AddSubgroup.closure_singleton_zero
∀ {G : Type u_1} [inst : AddGroup G], AddSubgroup.closure {0} = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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 · cited by 53,352
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.closurestatement and proof · cited by 156
- zsmul_zeroproof · cited by 14
- AddSubgroup.eq_bot_iff_forallproof · cited by 11
- AddSubgroup.mem_closure_singletonproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.cyclic_of_isolated_zeroproof · cited by 2
- Finset.nsmul_right_strictMonoproof · cited by 0