Theorems · Theorem · group theory
AddAction.stabilizer_union_eq_left
∀ {G : Type u_1} {α : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G α] {s t : Set α},
Disjoint s t →
AddAction.stabilizer G s ≤ AddAction.stabilizer G t →
AddAction.stabilizer G (s ∪ t) ≤ AddAction.stabilizer G t →
AddAction.stabilizer G (s ∪ t) = AddAction.stabilizer G s- Defined in
- Mathlib.Algebra.Pointwise.Stabilizer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Disjointstatement and proof · cited by 2,201
- le_antisymmproof · cited by 2,068
- AddActionstatement and proof · cited by 820
- AddAction.stabilizerstatement and proof · cited by 112
- Set.disjoint_iff_inter_eq_emptyproof · cited by 49
- le_inf_iffproof · cited by 48
- Set.subset_empty_iffproof · cited by 40
- Set.addActionSetstatement · cited by 39
- Set.union_sdiff_cancel_rightproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.stabilizer_union_eq_rightproof · cited by 0