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Theorems · Theorem · group theory

MulAction.orbit_smul_subset

∀ {M : Type u_1} {α : Type u_3} [inst : Monoid M] [inst_1 : MulAction M α] (m : M) (a : α),
  MulAction.orbit M (m • a) ⊆ MulAction.orbit M a
Defined in
Mathlib.GroupTheory.GroupAction.Defs
Cited by
1 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
Assumes
MonoidMulAction
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Around this declaration

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

MulAction.orbit_smul · cited by 3MulAction.orbit_smulSet · cited by 53352SetMonoid · cited by 3887MonoidMulAction · cited by 1294MulActionSemigroupAction.mul_smul · cited by 291SemigroupAction.mul_smulMulAction.orbit · cited by 114MulAction.orbitSet.range_subset_iff · cited by 99Set.range_subset_iffMulAction.mem_orbit · cited by 10MulAction.mem_orbitMulAction.orbit_smul_subsetCITED BYCITES

Cites7

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Cited by1

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