pith. machine review for the scientific record. sign in
structure definition def or abbrev

RegroupingInvariance

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

  43structure RegroupingInvariance (J : ℝ → ℝ) extends ContextualSubstitutivity J where
  44  symmetric : ∀ u v, combiner u v = combiner v u
  45  zero_boundary : ∀ u, combiner u 0 = 2 * u
  46  unit_diagonal : combiner 1 1 = 6
  47  right_affine : ∀ u, ∃ α β, ∀ v, combiner u v = α * v + β
  48
  49/-- Contextual substitutivity is forced by the ledger's comparison
  50structure: if `J(x₁) = J(x₂)`, then for any `y > 0`,
  51
  52  `J(x₁ y) + J(x₁/y) = J(x₂ y) + J(x₂/y)`
  53
  54because the compound cost depends only on the mismatch, not on the
  55specific ratio realizing it.  Therefore the compound cost descends
  56to a function of `(J(x), J(y))`. -/

used by (3)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (14)

Lean names referenced from this declaration's body.