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Theorems · Theorem · group theory

AddSubgroup.mem_ofAddUnits_of_isAddUnit_of_addUnit_mem

∀ {M : Type u_1} [inst : AddMonoid M] (S : AddSubgroup (AddUnits M)) {x : M} (h₁ : IsAddUnit x),
  h₁.addUnit ∈ S → x ∈ S.ofAddUnits
Defined in
Mathlib.Algebra.Group.Submonoid.Units
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice
Assumes
AddMonoid
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Around this declaration

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

AddSubgroup.mem_ofAddUnits_iff_exists_isAddUnit · cited by 0AddSubgroup.mem_ofAddUnit…AddSubgroup · cited by 3232AddSubgroupAddMonoid · cited by 2864AddMonoidAddSubmonoid · cited by 1178AddSubmonoidAddUnits · cited by 325AddUnitsIsAddUnit · cited by 215IsAddUnitIsAddUnit.addUnit · cited by 30IsAddUnit.addUnitAddSubgroup.ofAddUnits · cited by 30AddSubgroup.ofAddUnitsIsAddUnit.addUnit_spec · cited by 1IsAddUnit.addUnit_specAddSubgroup.mem_ofAddUnits · cited by 1AddSubgroup.mem_ofAddUnitsAddSubgroup.mem_ofAddUnits_of…CITED BYCITES

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Cited by1

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