Theorems · Theorem · group theory

AddAction.zeroEmbedding_isPretransitive_iff

∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {zero : Type u_5} [Unique zero],
  AddAction.IsPretransitive G (zero ↪ α) ↔ AddAction.IsPretransitive G α

An additive action is 1-pretransitive iff it is pretransitive.

Defined in: Mathlib.GroupTheory.GroupAction.MultipleTransitivity
Cited by: 1 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Quot.sound
Assumes: AddGroup AddAction Unique

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Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

AddGroupstatement and proof · cited by 4,410
Function.Embeddingstatement · cited by 988
AddActionstatement and proof · cited by 820
Uniquestatement and proof · cited by 400
AddAction.IsPretransitivestatement · cited by 56
AddAction.isPretransitive_congrproof · cited by 4
AddActionHom.zeroEmbeddingMap_bijectiveproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

AddAction.is_zero_pretransitive_iffproof · cited by 1