Theorems · Theorem · group theory
AddAction.mem_addSubgroup_orbit_iff
∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {H : AddSubgroup G} {x : α}
{a b : ↑(AddAction.orbit G x)}, a ∈ AddAction.orbit (↥H) b ↔ ↑a ∈ AddAction.orbit ↥H ↑b- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HVAdd.hVAddproof · cited by 1,820
- AddActionstatement and proof · cited by 820
- AddAction.orbitstatement and proof · cited by 86
- AddAction.mem_orbitproof · cited by 14
- AddAction.addSubgroup_vadd_defproof · cited by 2
- AddAction.orbit.coe_vaddproof · cited by 1
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