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Theorems · Definition · group theory

AddSubmonoid.neg

{G : Type u_2} → [inst : AddGroup G] → Neg (AddSubmonoid G)

The additive submonoid with every element negated.

Defined in
Mathlib.Algebra.Group.Submonoid.Pointwise
Cited by
16 results in Mathlib
Foundations
Depth 14 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.

AddSubmonoid.mem_neg · cited by 2AddSubmonoid.mem_negAddSubmonoid.neg_le · cited by 1AddSubmonoid.neg_leAddSubmonoid.coe_neg · cited by 1AddSubmonoid.coe_negAddSubmonoid.closure_neg · cited by 1AddSubmonoid.closure_negAddSubmonoid.leftNeg_eq_neg · cited by 0AddSubmonoid.leftNeg_eq_n…Submodule.neg_toAddSubmonoid · cited by 0Submodule.neg_toAddSubmon…AddSubmonoid.support_toAddSubmonoid · cited by 0AddSubmonoid.support_toAd…AddSubmonoid.neg_bot · cited by 0AddSubmonoid.neg_botAddSubmonoid.neg_iInf · cited by 0AddSubmonoid.neg_iInfAddSubmonoid.neg_iSup · cited by 0AddSubmonoid.neg_iSupAddSubmonoid.neg_inf · cited by 0AddSubmonoid.neg_infAddSubmonoid.neg_le_neg · cited by 0AddSubmonoid.neg_le_negAddSubmonoid.neg_sup · cited by 0AddSubmonoid.neg_supAddSubmonoid.neg_top · cited by 0AddSubmonoid.neg_topAddSubmonoid.mk_add_mk_neg_eq_zero · cited by 0AddSubmonoid.mk_add_mk_ne…SetLike.coe · cited by 8199SetLike.coeAddGroup · cited by 4410AddGroupAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.negCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.