`Learning.pullCount_action_eq_pullCount_add_one`🔗

This page has the declaration's own card below, then its dependency graph, then a card for each dependency (type dependencies first, then the rest of the transitive closure). For a theorem, the graph and the dependency cards only follow its statement's dependencies (its proof is replaced by sorry, so what it proves doesn't depend on how); for everything else, both the type and the body/value are followed, since their content is part of what later declarations build on.

Minimal Lean file

`pullCount_action_eq_pullCount_add_one`🔗

LemmaLearning.pullCount_action_eq_pullCount_add_one

Details

No docstring.

theorem

Learning.pullCount_action_eq_pullCount_add_one.{u_1, u_3} {𝓐 : Type u_1}
  {Ω : Type u_3} [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} (t : ℕ) (ω : Ω) :
  pullCount A (A t ω) (t + 1) ω = pullCount A (A t ω) t ω + 1
Learning.pullCount_action_eq_pullCount_add_one.{u_1,
    u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} (t : ℕ)
  (ω : Ω) :
  pullCount A (A t ω) (t + 1) ω =
    pullCount A (A t ω) t ω + 1

Code

lemma pullCount_action_eq_pullCount_add_one (t : ℕ) (ω : Ω) :
    pullCount A (A t ω) (t + 1) ω = pullCount A (A t ω) t ω + 1

Type uses (1)

pullCount

Used by (7)

Actions: Source · Open Issue

Proof

by
  simp [pullCount, range_add_one, filter_insert]

Dependency graph

Type dependencies (1)

`pullCount`🔗

DefinitionLearning.pullCount

Details

Number of times action a was chosen up to time t (excluding t).

def

Learning.pullCount.{u_1, u_3} {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] (A : ℕ → Ω → 𝓐) (a : 𝓐) (t : ℕ) (ω : Ω) : ℕ
Learning.pullCount.{u_1, u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] (A : ℕ → Ω → 𝓐) (a : 𝓐)
  (t : ℕ) (ω : Ω) : ℕ

Code

noncomputable
def pullCount (A : ℕ → Ω → 𝓐) (a : 𝓐) (t : ℕ) (ω : Ω) : ℕ :=
  #(filter (fun s ↦ A s ω = a) (range t))

Used by (146)

Actions: Source · Open Issue

Learning.pullCount_action_eq_pullCount_add_one🔗

pullCount_action_eq_pullCount_add_one🔗

pullCount🔗

`Learning.pullCount_action_eq_pullCount_add_one`🔗

`pullCount_action_eq_pullCount_add_one`🔗

`pullCount`🔗