Theorems · Theorem · group theory
QuotientAddGroup.eq_class_eq_leftCoset
∀ {α : Type u_1} [inst : AddGroup α] (s : AddSubgroup α) (g : α), {x | ↑x = ↑g} = g +ᵥ ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Set.ofPredstatement and proof · cited by 6,101
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- Set.extproof · cited by 2,266
- HVAdd.hVAddstatement · cited by 1,820
- Set.vaddSetstatement · cited by 403
- QuotientAddGroup.mkstatement and proof · cited by 348
- SetLike.mem_coeproof · cited by 302
- Set.mem_ofPred_eqproof · cited by 122
Cited by1
Results whose statement or proof uses this declaration.
- QuotientAddGroup.orbit_eq_out_vaddproof · cited by 1