Theorems · Theorem · group theory

MulAction.oneEmbedding_isPretransitive_iff

∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {one : Type u_5} [Unique one],
  MulAction.IsPretransitive G (one ↪ α) ↔ MulAction.IsPretransitive G α

An 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: Group MulAction Unique

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Cites7

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

Groupstatement and proof · cited by 6,238
MulActionstatement and proof · cited by 1,294
Function.Embeddingstatement · cited by 988
Uniquestatement and proof · cited by 400
MulAction.IsPretransitivestatement · cited by 94
MulAction.isPretransitive_congrproof · cited by 4
MulActionHom.oneEmbeddingMap_bijectiveproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

MulAction.is_one_pretransitive_iffproof · cited by 7