Learning.exists_pullCount_eq_of_le🔗

Learning.exists_pullCount_eq_of_le.{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} (hnm : t ≤ pullCount A a (n + 1) ω) (ht : t ≠ 0) :
  ∃ s, pullCount A a (s + 1) ω = t
Learning.exists_pullCount_eq_of_le.{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}
  (hnm : t ≤ pullCount A a (n + 1) ω)
  (ht : t ≠ 0) :
  ∃ s, pullCount A a (s + 1) ω = t

lemma exists_pullCount_eq_of_le (hnm : t ≤ pullCount A a (n + 1) ω) (ht : t ≠ 0) :
    ∃ s, pullCount A a (s + 1) ω = t

by
  by_contra! h_contra
  refine lt_irrefl (pullCount A a (n + 1) ω) ?_
  refine lt_of_lt_of_le ?_ hnm
  exact pullCount_lt_of_forall_ne h_contra ht

Meaning unchanged since v4.33.0-rc1-29-gce231eb, the oldest revision on record (2026-07-30).

Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file · open it in the Lean web editor.

Dependency graph

Audit surface: 1 project declarations, 15 external constants

✓ Proved: no sorry anywhere in its closure

This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.