Theorems · Theorem · group theory
QuotientAddGroup.forall_mk
∀ {α : Type u_1} [inst : AddGroup α] {s : AddSubgroup α} {C : α ⧸ s → Prop}, (∀ (x : α ⧸ s), C x) ↔ ∀ (x : α), C ↑x- Defined in
- Mathlib.GroupTheory.Coset.Defs
- Cited by
- 6 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.forallproof · cited by 214
- QuotientAddGroup.mk_surjectiveproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.index_eq_two_iffproof · cited by 5
- AddSubgroup.leftCoset_cover_const_iff_surjOnproof · cited by 3
- AddSubgroup.upperCentralSeriesStep_eq_comap_centerproof · cited by 1
- QuotientAddGroup.comap_comap_centerproof · cited by 1
- QuotientAddGroup.nhds_zero_hasBasisproof · cited by 0