Theorems · Theorem · group theory
AddSubgroup.mk_goursatFst_eq_iff_mk_goursatSnd_eq
∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] {I : AddSubgroup (G × H)},
Function.Surjective (Prod.fst ∘ ⇑I.subtype) →
Function.Surjective (Prod.snd ∘ ⇑I.subtype) → ∀ {x y : G × H}, x ∈ I → y ∈ I → (↑x.1 = ↑y.1 ↔ ↑x.2 = ↑y.2)- Defined in
- Mathlib.GroupTheory.Goursat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement · cited by 3,230
- zero_addproof · cited by 2,366
- HasQuotient.Quotientstatement · cited by 2,301
- sub_selfproof · cited by 996
- QuotientAddGroup.mkstatement and proof · cited by 348
- sub_add_cancelproof · cited by 344
- AddMemClass.add_memproof · cited by 229
- AddSubgroup.Normalproof · cited by 183
- AddSubgroup.subtypestatement and proof · cited by 82
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.goursat_surjectiveproof · cited by 2