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Theorems · Theorem · group theory

AddSubgroup.mem_mk

∀ {G : Type u_1} [inst : AddGroup G] {s : AddSubmonoid G} {x : G} (h_neg : ∀ {x : G}, x ∈ s.carrier → -x ∈ s.carrier),
  x ∈ { toAddSubmonoid := s, neg_mem' := h_neg } ↔ x ∈ s
Defined in
Mathlib.Algebra.Group.Subgroup.Defs
Cited by
3 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
AddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ArchimedeanClass.mem_addSubgroup_iff · cited by 3ArchimedeanClass.mem_addS…AddMonoidHom.ker_eq_top_iff · cited by 2AddMonoidHom.ker_eq_top_i…FiniteArchimedeanClass.addSubgroup_eq_bot · cited by 0FiniteArchimedeanClass.ad…Set · cited by 53352SetAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.toAddSubsemigroup · cited by 198AddSubmonoid.toAddSubsemi…AddSubsemigroup.carrier · cited by 198AddSubsemigroup.carrierAddSubgroup.mem_mkCITED BYCITES

Cites6

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Cited by3

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