Theorems · Theorem · group theory
Sylow.subtype.congr_simp
∀ {p : ℕ} {G : Type u_1} [inst : Group G] (P P_1 : Sylow p G) (e_P : P = P_1) {N : Subgroup G} (h : ↑P ≤ N),
P.subtype h = P_1.subtype ⋯- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
Cites5
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
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- Sylow.subtypestatement and proof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Sylow.conj_eq_normalizer_conj_of_mem_centralizerproof · cited by 1