Theorems · Theorem · group theory
Subgroup.mk_goursatFst_eq_iff_mk_goursatSnd_eq
∀ {G : Type u_1} {H : Type u_2} [inst : Group G] [inst_1 : Group H] {I : Subgroup (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.
Cites17
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
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- HasQuotient.Quotientstatement · cited by 2,301
- Subgroup.Normalproof · cited by 334
- QuotientGroup.mkstatement and proof · cited by 196
- Subgroup.subtypestatement and proof · cited by 185
- MulMemClass.mul_memproof · cited by 173
- div_mul_cancelproof · cited by 33
- div_self'proof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.goursat_surjectiveproof · cited by 1