Theorems · Theorem · group theory
AddSubgroup.zmultiples_eq_closure
∀ {G : Type u_1} [inst : AddGroup G] (g : G), AddSubgroup.zmultiples g = AddSubgroup.closure {g}- Cited by
- 9 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement · cited by 493
- AddSubgroup.closurestatement · cited by 156
- AddSubgroup.extproof · cited by 75
- AddSubgroup.mem_closure_singletonproof · cited by 6
Cited by9
Results whose statement or proof uses this declaration.
- Real.Angle.angle_eq_iff_two_pi_dvd_subproof · cited by 8
- AddSubgroup.zmultiples_leproof · cited by 7
- AddMonoidHom.map_zmultiplesproof · cited by 6
- AddSubgroup.dense_xor_cyclicproof · cited by 3
- AddSubgroup.toAddSubmonoid_zmultiplesproof · cited by 1
- dense_addSubgroupClosure_pair_iffproof · cited by 1
- AddSubgroup.discrete_iff_addCyclicproof · cited by 1
- Int.zmultiples_supproof · cited by 0
- AddCircle.denseRange_zsmul_coe_iffproof · cited by 0