Theorems · Theorem · group theory
QuotientAddGroup.image_coe_inj
∀ {G : Type u_1} [inst : AddGroup G] (N : AddSubgroup G) [nN : N.Normal] {s t : Set G},
QuotientAddGroup.mk '' s = QuotientAddGroup.mk '' t ↔ ↑N + s = ↑N + t- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- QuotientAddGroup.mkstatement and proof · cited by 348
- Set.addstatement · cited by 338
- AddSubgroup.Normalstatement and proof · cited by 183
- QuotientAddGroup.mk_surjectiveproof · cited by 11
- Function.Surjective.preimage_injectiveproof · cited by 2
- QuotientAddGroup.preimage_image_coeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.stabilizer_image_coe_quotientproof · cited by 0