Mathlib Map

Theorems · Theorem · group theory

MulAction.smul_mem_of_set_mem_fixedBy

∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {s : Set α} {g : G},
  s ∈ MulAction.fixedBy (Set α) g → ∀ {x : α}, g • x ∈ s ↔ x ∈ s
Defined in
Mathlib.GroupTheory.GroupAction.FixedPoints
Cited by
1 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
GroupMulAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

orbit_fixingSubgroup_compl_subset · cited by 0orbit_fixingSubgroup_comp…Set · cited by 53352SetGroup · cited by 6238GroupMulAction · cited by 1294MulActionSet.mulActionSet · cited by 95Set.mulActionSetMulAction.fixedBy · cited by 36MulAction.fixedByMulAction.set_mem_fixedBy_iff · cited by 1MulAction.set_mem_fixedBy…MulAction.smul_mem_of_set_mem…CITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.