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def definition def or abbrev

equalityCost

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  90noncomputable def equalityCost (K : Type*) (weight : ℝ) : K → K → ℝ :=

proof body

Definition body.

  91  fun x y => if x = y then 0 else weight
  92
  93/-! ## The Three Definitional Facts
  94
  95The following three theorems show that an equality-induced cost
  96automatically satisfies three of the four Aristotelian conditions
  97without any structural assumption beyond the type signature.
  98-/
  99
 100/-- **(L1) Identity, derived.** The equality-induced cost satisfies
 101`C(x, x) = 0` definitionally. This is not an axiom; it is the
 102definitional content of "comparing a thing with itself takes no work,"
 103forced by reflexivity of equality. -/

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