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Theorems · Theorem · group theory

MulAction.orbit_eq_iff

∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {a b : α},
  MulAction.orbit G a = MulAction.orbit G b ↔ a ∈ MulAction.orbit G b
Defined in
Mathlib.GroupTheory.GroupAction.Defs
Cited by
3 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupMulAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

mem_closure_isSwap · cited by 2mem_closure_isSwapswap_mem_closure_isSwap · cited by 1swap_mem_closure_isSwapMulAction.orbitRel.Quotient.mem_subgroup_orbit_iff' · cited by 0Quotient.mem_subgroup_orb…Set · cited by 53352SetGroup · cited by 6238GroupMulAction · cited by 1294MulActionMulAction.orbit · cited by 114MulAction.orbitMulAction.mem_orbit_self · cited by 9MulAction.mem_orbit_selfMulAction.orbit_smul · cited by 3MulAction.orbit_smulMulAction.orbit_eq_iffCITED BYCITES

Cites6

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Cited by3

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