Mathlib Map

Theorems · Theorem · group theory

AddAction.is_zero_pretransitive_iff

∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α],
  AddAction.IsMultiplyPretransitive G α 1 ↔ 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 30 from the axioms · uses propext, Quot.sound
Assumes
AddGroupAddAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddAction.is_zero_preprimitive_iff · cited by 0AddAction.is_zero_preprim…AddGroup · cited by 4410AddGroupAddAction · cited by 820AddActionAddAction.IsPretransitive · cited by 56AddAction.IsPretransitiveAddAction.IsMultiplyPretransitive · cited by 17AddAction.IsMultiplyPretr…AddAction.zeroEmbedding_isPretransitive_iff · cited by 1AddAction.zeroEmbedding_i…AddAction.is_zero_pretransiti…CITED BYCITES

Cites5

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

Cited by1

Results whose statement or proof uses this declaration.