Theorems · Theorem · group theory
Subgroup.closure_prod
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {s : Set G} {t : Set N},
1 ∈ s → 1 ∈ t → Subgroup.closure (s ×ˢ t) = (Subgroup.closure s).prod (Subgroup.closure t)- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- le_antisymmproof · cited by 2,068
- SProd.sprodstatement and proof · cited by 1,750
- Subgroup.closurestatement and proof · cited by 196
- Subgroup.comapproof · cited by 154
- Subgroup.subset_closureproof · cited by 53
- Subgroup.prodstatement and proof · cited by 35
- MonoidHom.inlproof · cited by 32
- MonoidHom.inrproof · cited by 32
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