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Learning.pullCount_congr🔗

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Minimal Lean file

pullCount_congr🔗

LemmaLearning.pullCount_congr
Details

No docstring.

🔗theorem
Learning.pullCount_congr.{u_1, u_3} {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {a : 𝓐} {n : ℕ} {ω ω' : Ω}
  (h_eq : ∀ i ≤ n, A i ω = A i ω') :
  pullCount A a (n + 1) ω = pullCount A a (n + 1) ω'
Learning.pullCount_congr.{u_1, u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {a : 𝓐}
  {n : ℕ} {ω ω' : Ω}
  (h_eq : ∀ i ≤ n, A i ω = A i ω') :
  pullCount A a (n + 1) ω =
    pullCount A a (n + 1) ω'

Code

lemma pullCount_congr {ω' : Ω} (h_eq : ∀ i ≤ n, A i ω = A i ω') :
    pullCount A a (n + 1) ω = pullCount A a (n + 1) ω'
Type uses (1)
Used by (1)

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Proof
by
  unfold pullCount
  congr 1 with s
  simp only [mem_filter, mem_range, and_congr_right_iff]
  intro hs
  rw [Nat.lt_add_one_iff] at hs
  rw [h_eq s hs]

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)

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