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

J_composition_decomposition

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)

 162theorem J_composition_decomposition (a b : ℝ) (ha : 0 < a) (hb : 0 < b) :
 163    J (a * b) + J (a / b) = 2 * J a * J b + 2 * J a + 2 * J b := by

proof body

Term-mode proof.

 164  unfold J Cost.Jcost
 165  have ha0 : a ≠ 0 := ha.ne'
 166  have hb0 : b ≠ 0 := hb.ne'
 167  field_simp [ha0, hb0]
 168  ring
 169
 170/-- Additive regime for independent events.
 171
 172When the interaction term vanishes (`J a * J b = 0`), the pairwise
 173composition law reduces to pure additivity (up to the canonical factor 2). -/

used by (1)

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

depends on (7)

Lean names referenced from this declaration's body.