Theorems · Theorem · group theory
Subgroup.IsComplement.rightCosetEquivalence_equiv_snd
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {T : Set G} (hHT : Subgroup.IsComplement (↑H) T) (g : G),
RightCosetEquivalence (↑H) g ↑(hHT.equiv g).2- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.IsComplementstatement and proof · cited by 94
- mul_inv_cancel_rightproof · cited by 53
- Subgroup.IsComplement.equivstatement and proof · cited by 34
- Subgroup.IsComplement.equiv_snd_eq_inv_mulproof · cited by 8
- RightCosetEquivalencestatement · cited by 4
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