Theorems · Theorem · group theory

AddAction.IsBlock.ncard_block_add_ncard_orbit_eq

∀ {G : Type u_1} [inst : AddGroup G] {X : Type u_2} [inst_1 : AddAction G X] [AddAction.IsPretransitive G X]
  {B : Set X}, AddAction.IsBlock G B → B.Nonempty → B.ncard * (AddAction.orbit G B).ncard = Nat.card X

The cardinality of the ambient space is the product of the cardinality of a block by the cardinality of the set of translates of that block

Defined in

Mathlib.GroupTheory.GroupAction.Blocks

Cited by

4 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionAddAction.IsPretransitive