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

efficiency_bounded

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)

 200theorem efficiency_bounded (initial final : NuclearConfig)
 201    (h : nuclearCost final ≤ nuclearCost initial) :
 202    0 ≤ transmutation_efficiency initial final ∧
 203    transmutation_efficiency initial final ≤ 1 := by

proof body

Term-mode proof.

 204  unfold transmutation_efficiency
 205  split_ifs with h0
 206  · constructor <;> norm_num
 207  · constructor
 208    · apply div_nonneg
 209      · linarith [nuclear_cost_nonneg final]
 210      · exact nuclear_cost_nonneg initial
 211    · rw [div_le_one (lt_of_le_of_ne (nuclear_cost_nonneg initial) (Ne.symm h0))]
 212      linarith [nuclear_cost_nonneg final]
 213
 214/-- **THEOREM EN-006.14**: Perfect transmutation (to stable state) has 100% efficiency. -/

used by (1)

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

depends on (5)

Lean names referenced from this declaration's body.