Theorems · Theorem · group theory
Subgroup.normalClosure_eq_bot_iff
∀ {G : Type u_1} [inst : Group G] {s : Set G}, Subgroup.normalClosure s = ⊥ ↔ s ⊆ {1}- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Bot.botstatement · cited by 4,720
- Subgroupstatement · cited by 3,593
- eq_bot_iffproof · cited by 159
- Subgroup.normalClosurestatement · cited by 35
- Subgroup.normalClosure_subset_iffproof · cited by 2
- Subgroup.coe_botproof · cited by 1
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