Theorems · Theorem · group theory
QuotientAddGroup.exists_mk
∀ {α : Type u_1} [inst : AddGroup α] {s : AddSubgroup α} {C : α ⧸ s → Prop}, (∃ x, C x) ↔ ∃ x, C ↑x- Defined in
- Mathlib.GroupTheory.Coset.Defs
- 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement and proof · cited by 2,301
- QuotientAddGroup.mkstatement · cited by 348
- Function.Surjective.existsproof · cited by 53
- QuotientAddGroup.mk_surjectiveproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.index_eq_two_iffproof · cited by 5