Theorems · Theorem · group theory
AddAction.mem_fixedBy_zsmul
∀ {α : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {g : G} {a : α},
a ∈ AddAction.fixedBy α g → ∀ (j : ℤ), a ∈ AddAction.fixedBy α (j • g)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddActionstatement and proof · cited by 820
- one_dvdproof · cited by 37
- AddAction.fixedBystatement and proof · cited by 26
- AddAction.mem_fixedByproof · cited by 12
- AddAction.minimalPeriod_eq_one_iff_fixedByproof · cited by 1
- AddAction.zsmul_vadd_eq_iff_minimalPeriod_dvdproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddAction.fixedBy_subset_fixedBy_zsmulproof · cited by 2
- AddAction.mem_fixedBy_zmultiples_iff_mem_fixedByproof · cited by 0