Theorems · Theorem · group theory
QuotientAddGroup.preimage_image_mk_eq_add
∀ {α : Type u_1} [inst : AddGroup α] (N : AddSubgroup α) (s : Set α),
QuotientAddGroup.mk ⁻¹' QuotientAddGroup.mk '' s = s + ↑N- Defined in
- Mathlib.GroupTheory.Coset.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 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.
Cites17
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 · cited by 4,946
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Set.iUnionproof · cited by 2,483
- HasQuotient.Quotientstatement · cited by 2,301
- Set.image_congrproof · cited by 533
- Set.iUnion_congr_Propproof · cited by 374
- QuotientAddGroup.mkstatement · cited by 348
- Set.addstatement · cited by 338
Cited by3
Results whose statement or proof uses this declaration.
- QuotientAddGroup.preimage_mk_zeroproof · cited by 2
- QuotientAddGroup.isClosedMap_coeproof · cited by 0
- QuotientAddGroup.dense_image_mkproof · cited by 0