Theorems · Theorem · group theory
Subgroup.isCoatom_map
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) (f : G ≃* ↥H) {K : Subgroup G},
IsCoatom (Subgroup.map (↑f) K) ↔ IsCoatom K- Defined in
- Mathlib.Algebra.Group.Subgroup.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulEquivstatement and proof · cited by 1,142
- Subgroup.mapstatement · cited by 301
- MonoidHomClass.toMonoidHomstatement · cited by 294
- IsCoatomstatement · cited by 114
- MulEquiv.mapSubgroupproof · cited by 11
- OrderIso.isCoatom_iffproof · cited by 7
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