Theorems · Theorem · group theory
QuotientAddGroup.preimage_image_coe
∀ {G : Type u_1} [inst : AddGroup G] (N : AddSubgroup G) [nN : N.Normal] (s : Set G),
QuotientAddGroup.mk ⁻¹' QuotientAddGroup.mk '' s = ↑N + s- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 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.
Cites15
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 and proof · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- 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
- sub_selfproof · cited by 996
- QuotientAddGroup.mkstatement and proof · cited by 348
- sub_add_cancelproof · cited by 344
- Set.addstatement · cited by 338
Cited by1
Results whose statement or proof uses this declaration.
- QuotientAddGroup.image_coe_injproof · cited by 1