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Theorems · Theorem · group theory

AddAction.orbit_eq_univ

∀ (M : Type u) [inst : AddMonoid M] {α : Type v} [inst_1 : AddAction M α] [AddAction.IsPretransitive M α] (a : α),
  AddAction.orbit M a = Set.univ
Defined in
Mathlib.GroupTheory.GroupAction.Basic
Cited by
1 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
AddMonoidAddActionAddAction.IsPretransitive
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Around this declaration

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

AddAction.index_stabilizer_of_transitive · cited by 1AddAction.index_stabilize…Set · cited by 53352SetSet.univ · cited by 3945Set.univAddMonoid · cited by 2864AddMonoidAddAction · cited by 820AddActionAddAction.orbit · cited by 86AddAction.orbitFunction.Surjective.range_eq · cited by 70Surjective.range_eqAddAction.IsPretransitive · cited by 56AddAction.IsPretransitiveAddAction.surjective_vadd · cited by 2AddAction.surjective_vaddAddAction.orbit_eq_univCITED BYCITES

Cites8

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Cited by1

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