Theorems · Theorem · group theory
Subgroup.normalClosure_empty
∀ {G : Type u_1} [inst : Group G], Subgroup.normalClosure ∅ = ⊥The normal closure of an empty set is the trivial subgroup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Subgroup.normalClosurestatement and proof · cited by 35
- Subgroup.closure_emptyproof · cited by 3
- Subgroup.normalClosure_eq_selfproof · cited by 2
- Subgroup.normalClosure_closure_eq_normalClosureproof · cited by 1
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