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Theorems · Theorem · group theory

MulAction.nonempty_orbit

∀ {M : Type u_1} {α : Type u_3} [inst : Monoid M] [inst_1 : MulAction M α] (a : α), (MulAction.orbit M a).Nonempty
Defined in
Mathlib.GroupTheory.GroupAction.Defs
Cited by
4 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
MonoidMulAction
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Around this declaration

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

MulAction.IsPartition.of_orbits · cited by 1IsPartition.of_orbitsCategoryTheory.FintypeCat.Action.pretransitive_of_isConnected · cited by 1Action.pretransitive_of_i…isMinimal_iff_isClosed_smul_invariant · cited by 0isMinimal_iff_isClosed_sm…MulAction.orbitRel.Quotient.nonempty_orbit · cited by 0Quotient.nonempty_orbitMonoid · cited by 3887MonoidSet.Nonempty · cited by 2627Set.NonemptyMulAction · cited by 1294MulActionMulAction.orbit · cited by 114MulAction.orbitSet.range_nonempty · cited by 84Set.range_nonemptyMulAction.nonempty_orbitCITED BYCITES

Cites5

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Cited by4

Results whose statement or proof uses this declaration.