Mathlib Map

Theorems · Theorem · group theory

AddSubgroup.op_eq_top

∀ {G : Type u_2} [inst : AddGroup G] {S : AddSubgroup G}, S.op = ⊤ ↔ S = ⊤
Defined in
Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas
Cited by
1 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddSubgroup.normal_op · cited by 3AddSubgroup.normal_opTop.top · cited by 9680Top.topAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddOpposite · cited by 452AddOppositeAddSubgroup.op · cited by 57AddSubgroup.opAddSubgroup.op_injective · cited by 2AddSubgroup.op_injectiveAddSubgroup.op_top · cited by 1AddSubgroup.op_topAddSubgroup.op_eq_topCITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.