Theorems · Theorem · group theory
QuotientGroup.eq_class_eq_leftCoset
∀ {α : Type u_1} [inst : Group α] (s : Subgroup α) (g : α), {x | ↑x = ↑g} = g • ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 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.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.ofPredstatement and proof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Set.extproof · cited by 2,266
- Set.smulSetstatement · cited by 608
- SetLike.mem_coeproof · cited by 302
- QuotientGroup.mkstatement and proof · cited by 196
- Set.mem_ofPred_eqproof · cited by 122
- QuotientGroup.eqproof · cited by 20
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