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Learning.pullCount_lt_of_forall_ne🔗

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Minimal Lean file

pullCount_lt_of_forall_ne🔗

LemmaLearning.pullCount_lt_of_forall_ne
Details

No docstring.

🔗theorem
Learning.pullCount_lt_of_forall_ne.{u_1, u_3} {𝓐 : Type u_1}
  {Ω : Type u_3} [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {a : 𝓐} {n t : ℕ}
  {ω : Ω} (h_lt : ∀ (s : ℕ), pullCount A a (s + 1) ω ≠ t) (ht : t ≠ 0) :
  pullCount A a n ω < t
Learning.pullCount_lt_of_forall_ne.{u_1,
    u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {a : 𝓐}
  {n t : ℕ} {ω : Ω}
  (h_lt :
    ∀ (s : ℕ),
      pullCount A a (s + 1) ω ≠ t)
  (ht : t ≠ 0) : pullCount A a n ω < t

Code

lemma pullCount_lt_of_forall_ne (h_lt : ∀ s, pullCount A a (s + 1) ω ≠ t) (ht : t ≠ 0) :
    pullCount A a n ω < t
Type uses (1)
Body uses (2)
Used by (1)

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Proof
by
  induction n with
  | zero => simpa using ht.bot_lt
  | succ n hn =>
    specialize h_lt n
    rw [pullCount_add_one] at h_lt ⊢
    grind

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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