Theorems · Definition · group theory
Subgroup.subgroupOfEquivOfLe
{G : Type u_7} → [inst : Group G] → {H K : Subgroup G} → H ≤ K → ↥(H.subgroupOf K) ≃* ↥HIf H ≤ K, then H as a subgroup of K is isomorphic to H.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 1,142
- Subgroup.subgroupOfstatement and proof · cited by 122
Cited by13
Results whose statement or proof uses this declaration.
- Subgroup.subgroupOfContinuousMulEquivOfLeproof · cited by 4
- Ideal.card_stabilizer_eq_card_inertia_mul_finrankproof · cited by 2
- IsPGroup.to_sup_of_normal_right'proof · cited by 2
- Sylow.card_normalizer_modEq_cardproof · cited by 1
- Sylow.normalizer_le_centralizer_or_le_commutatorproof · cited by 1
- IsZGroup.of_injectiveproof · cited by 1
- isZGroup_of_coprimeproof · cited by 1
- Subgroup.subgroupOfEquivOfLe.congr_simpstatement and proof · cited by 0
- Subgroup.subgroupOfContinuousMulEquivOfLe_applystatement · cited by 0
- Subgroup.subgroupOfContinuousMulEquivOfLe_toMulEquivstatement · cited by 0
- Subgroup.subgroupOfEquivOfLe_apply_coestatement and proof · cited by 0
- Subgroup.subgroupOfEquivOfLe_symm_apply_coe_coestatement and proof · cited by 0