Theorems · Theorem · group theory
Monoid.PushoutI.NormalWord.transversal_nonempty
∀ {ι : Type u_1} {G : ι → Type u_2} {H : Type u_3} [inst : (i : ι) → Group (G i)] [inst_1 : Group H]
(φ : (i : ι) → H →* G i), (∀ (i : ι), Function.Injective ⇑(φ i)) → Nonempty (Monoid.PushoutI.NormalWord.Transversal φ)- Defined in
- Mathlib.GroupTheory.PushoutI
- Cited by
- 3 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.
Cites9
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
- Setproof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- MonoidHom.rangeproof · cited by 314
- Subgroup.IsComplementproof · cited by 94
- Monoid.PushoutI.NormalWord.Transversalstatement · cited by 45
- Subgroup.exists_isComplement_rightproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Monoid.PushoutI.Reduced.eq_empty_of_mem_rangeproof · cited by 1
- Monoid.PushoutI.of_injectiveproof · cited by 0
- Monoid.PushoutI.base_injectiveproof · cited by 0