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

warWindow_ordered

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)

  63theorem warWindow_ordered : warWindowLow < warWindowHigh := by

proof body

Term-mode proof.

  64  unfold warWindowLow warWindowHigh
  65  -- phi⁻¹ < phi since phi > 1 implies phi * phi > 1 > phi * phi⁻¹ = 1... direct:
  66  have hphi_sq : phi ^ 2 = phi + 1 := phi_sq_eq
  67  rw [inv_eq_one_div]
  68  rw [div_lt_iff₀ phi_pos]
  69  nlinarith [phi_gt_onePointFive]
  70
  71/-- At the φ-boundary, J-cost equals the canonical recognition quantum. -/

used by (1)

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

depends on (10)

Lean names referenced from this declaration's body.