Theorems · Theorem · group theory
AddAction.isPretransitive_congr
∀ {M : Type u_3} {N : Type u_4} {α : Type u_5} {β : Type u_6} [inst : AddMonoid M] [inst_1 : AddMonoid N]
[inst_2 : AddAction M α] [inst_3 : AddAction N β] {φ : M → N} {f : α →ₑ[φ] β},
Function.Surjective φ → Function.Bijective ⇑f → (AddAction.IsPretransitive M α ↔ AddAction.IsPretransitive N β)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- AddMonoidstatement and proof · cited by 2,864
- HVAdd.hVAddproof · cited by 1,820
- Function.Bijectivestatement and proof · cited by 863
- AddActionstatement and proof · cited by 820
- Function.Bijective.injectiveproof · cited by 115
- Function.Bijective.surjectiveproof · cited by 114
- AddActionHomstatement and proof · cited by 82
- AddAction.IsPretransitivestatement and proof · cited by 56
- AddActionSemiHomClass.map_vaddₛₗproof · cited by 8
- AddAction.IsPretransitive.exists_vadd_eqproof · cited by 6
- AddAction.IsPretransitive.of_surjective_mapproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- AddAction.isPreprimitive_congrproof · cited by 4
- AddAction.IsPretransitive.of_embedding_congrproof · cited by 2
- AddAction.zeroEmbedding_isPretransitive_iffproof · cited by 1
- SubAddAction.ofStabilizer.isPretransitive_iff_of_addConjproof · cited by 1