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Theorems · Theorem · group theory

AddAction.IsPretransitive.of_embedding

∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {H : Type u_3} {β : Type u_4}
  [inst_2 : AddGroup H] [inst_3 : AddAction H β] {σ : G → H} {f : α →ₑ[σ] β} {n : Type u_5},
  Function.Surjective ⇑f → ∀ [AddAction.IsPretransitive G (n ↪ α)], AddAction.IsPretransitive H (n ↪ β)
Defined in
Mathlib.GroupTheory.GroupAction.MultipleTransitivity
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddActionAddGroupAddActionAddAction.IsPretransitive
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddAction.IsMultiplyPreprimitive.of_bijective_map · cited by 1IsMultiplyPreprimitive.of…DFunLike.coe · cited by 62936DFunLike.coeAddGroup · cited by 4410AddGroupHVAdd.hVAdd · cited by 1820HVAdd.hVAddFunction.Embedding · cited by 988Function.EmbeddingAddAction · cited by 820AddActionDFunLike.ext_iff · cited by 102DFunLike.ext_iffFunction.Embedding.trans · cited by 83Embedding.transAddActionHom · cited by 82AddActionHomAddAction.IsPretransitive · cited by 56AddAction.IsPretransitiveFunction.Embedding.ext · cited by 27Embedding.extFunction.Embedding.trans_apply · cited by 25Embedding.trans_applyFunction.surjInv_eq · cited by 18Function.surjInv_eqFunction.Embedding.ofSurjective · cited by 7Embedding.ofSurjectiveAddAction.IsPretransitive.exists_vadd_eq · cited by 6IsPretransitive.exists_va…AddActionHom.toFun · cited by 6AddActionHom.toFunIsPretransitive.of_embeddingCITED BYCITES

Cites17

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Cited by1

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