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Theorems · Theorem · group theory

AddAction.orbit.eq_or_disjoint

∀ {G : Type u_1} [inst : AddGroup G] {X : Type u_2} [inst_1 : AddAction G X] (a b : X),
  AddAction.orbit G a = AddAction.orbit G b ∨ Disjoint (AddAction.orbit G a) (AddAction.orbit G b)
Defined in
Mathlib.GroupTheory.GroupAction.Blocks
Cited by
2 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddAction
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Around this declaration

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

AddAction.orbit.pairwiseDisjoint · cited by 1orbit.pairwiseDisjointAddAction.IsBlock.orbit_of_normal · cited by 1IsBlock.orbit_of_normalSet · cited by 53352SetAddGroup · cited by 4410AddGroupDisjoint · cited by 2201DisjointAddAction · cited by 820AddActionem · cited by 115emAddAction.orbit · cited by 86AddAction.orbitSet.not_disjoint_iff · cited by 30Set.not_disjoint_iffAddAction.orbit_eq_iff · cited by 4AddAction.orbit_eq_ifforbit.eq_or_disjointCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.