Theorems · Theorem · group theory

MulAction.isPretransitive_of_is_two_pretransitive

∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α]
  [h2 : MulAction.IsMultiplyPretransitive G α 2], MulAction.IsPretransitive G α

A 2-pretransitive action is pretransitive.

Defined in: Mathlib.GroupTheory.GroupAction.MultipleTransitivity
Cited by: 1 results in Mathlib
Foundations: Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction MulAction.IsMultiplyPretransitive

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Cites6

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
one_smulproof · cited by 1,374
MulActionstatement and proof · cited by 1,294
MulAction.IsPretransitivestatement · cited by 94
MulAction.IsMultiplyPretransitivestatement and proof · cited by 33
MulAction.is_two_pretransitive_iffproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

MulAction.isPreprimitive_of_is_two_pretransitiveproof · cited by 3