Theorems · Theorem · group theory
AddAction.IsPartition.of_orbits
∀ {G : Type u_1} [inst : AddGroup G] {X : Type u_2} [inst_1 : AddAction G X],
Setoid.IsPartition (Set.range fun a => AddAction.orbit G a)Orbits of an element form a partition
- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- AddGroupstatement and proof · cited by 4,410
- AddActionstatement and proof · cited by 820
- AddAction.orbitstatement and proof · cited by 86
- Set.Nonempty.ne_emptyproof · cited by 65
- Setoid.IsPartitionstatement · cited by 18
- AddAction.mem_orbit_selfproof · cited by 10
- AddAction.nonempty_orbitproof · cited by 5
- Set.PairwiseDisjoint.isPartition_of_exists_of_ne_emptyproof · cited by 2
- AddAction.orbit.pairwiseDisjointproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.IsBlockSystem.of_normalproof · cited by 0