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theorem proved term proof

constant_of_preconnected

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formal statement (Lean)

  44theorem constant_of_preconnected {R : V → V → Prop}
  45    (hconn : ∀ u v : V, Relation.ReflTransGen R u v) {f : V → ℝ}
  46    (hadj : ∀ a b, R a b → f a = f b) :
  47    ∀ v w : V, f v = f w := by

proof body

Term-mode proof.

  48  intro v w
  49  exact eq_of_reflTransGen hadj (hconn v w)
  50
  51/-! ### Ratio rigidity (Result 1) -/
  52
  53/-- Edge cost is nonneg for positive fields. -/

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