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Theorems · Theorem · group theory

AddSubmonoid.mem_mk

∀ {M : Type u_1} [inst : AddZeroClass M] {s : AddSubsemigroup M} {x : M} (h_zero : 0 ∈ s.carrier),
  x ∈ { toAddSubsemigroup := s, zero_mem' := h_zero } ↔ x ∈ s
Defined in
Mathlib.Algebra.Group.Submonoid.Defs
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
AddZeroClass
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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…FiniteArchimedeanClass.addSubgroup_eq_bot · cited by 0FiniteArchimedeanClass.ad…Set · cited by 53352SetAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddSubsemigroup · cited by 262AddSubsemigroupAddSubsemigroup.carrier · cited by 198AddSubsemigroup.carrierAddSubmonoid.mem_mkCITED BYCITES

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Cited by2

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