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Theorems · Theorem · group theory

AddSubmonoid.mem_closure_neg

∀ {G : Type u_2} [inst : AddGroup G] (s : Set G) (x : G), x ∈ AddSubmonoid.closure (-s) ↔ -x ∈ AddSubmonoid.closure s
Defined in
Mathlib.Algebra.Group.Submonoid.Pointwise
Cited by
1 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroup
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Around this declaration

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

AddSubgroup.closure_toAddSubmonoid · cited by 6AddSubgroup.closure_toAdd…Set · cited by 53352SetAddGroup · cited by 4410AddGroupAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.closure · cited by 224AddSubmonoid.closureSet.neg · cited by 168Set.negAddSubmonoid.mem_neg · cited by 2AddSubmonoid.mem_negAddSubmonoid.closure_neg · cited by 1AddSubmonoid.closure_negAddSubmonoid.mem_closure_negCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.