pith. machine review for the scientific record. sign in
theorem proved term proof

jcost_pos_away_from_one

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)

  65theorem jcost_pos_away_from_one (x : ℝ) (hx : x > 0) (hne : x ≠ 1) :
  66    Jcost x > 0 := by

proof body

Term-mode proof.

  67  rw [jcost_squared_form x hx]
  68  apply div_pos
  69  · have : x - 1 ≠ 0 := sub_ne_zero.mpr hne
  70    positivity
  71  · positivity
  72
  73/-- **THEOREM IC-005.5**: J-cost is symmetric: J(x) = J(1/x).
  74    This means the RS cost landscape has a reflection symmetry,
  75    ensuring the optimization problem is well-conditioned. -/

used by (3)

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

depends on (11)

Lean names referenced from this declaration's body.