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

ScaleInvarianceCert

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)

  60structure ScaleInvarianceCert where
  61  rcl : ∀ {x y : ℝ}, 0 < x → 0 < y →
  62    Jcost (x * y) + Jcost (x / y) = 2 * Jcost x * Jcost y + 2 * Jcost x + 2 * Jcost y
  63  scale_cost_bound : ∀ {c x : ℝ}, 0 < c → 0 < x →
  64    Jcost (c * x) ≤ 2 * Jcost c * Jcost x + 2 * Jcost c + 2 * Jcost x
  65  free_at_unit : ∀ {x : ℝ}, 0 < x → Jcost (1 * x) = Jcost x
  66  log_symmetric : ∀ {x : ℝ}, 0 < x → Jcost x = Jcost x⁻¹
  67
  68/-- Scale-invariance selection certificate. -/

used by (1)

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