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Theorems · Theorem · group theory

normal_of_eq_addCosets

∀ {α : Type u_1} [inst : AddGroup α] (s : AddSubgroup α), (∀ (g : α), g +ᵥ ↑s = AddOpposite.op g +ᵥ ↑s) → s.Normal
Defined in
Mathlib.GroupTheory.Coset.Basic
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
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Around this declaration

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

normal_iff_eq_addCosets · cited by 0normal_iff_eq_addCosetsSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddOpposite · cited by 452AddOppositeSet.vaddSet · cited by 403Set.vaddSetAddOpposite.op · cited by 192AddOpposite.opAddSubgroup.Normal · cited by 183AddSubgroup.Normalmem_leftAddCoset · cited by 4mem_leftAddCosetmem_rightAddCoset_iff · cited by 4mem_rightAddCoset_iffnormal_of_eq_addCosetsCITED BYCITES

Cites11

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Cited by1

Results whose statement or proof uses this declaration.