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Theorems · Theorem · group theory

AddAction.orbitRel_apply

∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {a b : α},
  (AddAction.orbitRel G α) a b ↔ a ∈ AddAction.orbit G b
Defined in
Mathlib.GroupTheory.GroupAction.Defs
Cited by
3 results in Mathlib
Foundations
Depth 66 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.orbitRel.Quotient.orbit_injective · cited by 1Quotient.orbit_injectiveAddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff' · cited by 0Quotient.mem_addSubgroup_…AddAction.orbitRel_addSubgroupOf · cited by 0AddAction.orbitRel_addSub…Set · cited by 53352SetAddGroup · cited by 4410AddGroupAddAction · cited by 820AddActionAddAction.orbit · cited by 86AddAction.orbitAddAction.orbitRel · cited by 47AddAction.orbitRelAddAction.orbitRel_applyCITED BYCITES

Cites5

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Cited by3

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