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def definition def or abbrev

rank

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formal statement (Lean)

  30noncomputable def rank [Fintype State] [DecidableEq State]
  31    (J : State → ℝ) (x : State) : ℕ :=

proof body

Definition body.

  32  Finset.card { y ∈ Finset.univ | J y < J x }
  33
  34/-- Strictly monotone transforms preserve strict ordering, hence ranks. -/

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