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theorem proved term proof

planck_positive

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formal statement (Lean)

 102theorem planck_positive (ν T : ℝ) (hν : 0 < ν) (hT : 0 < T) :
 103    0 < planck_radiance ν T := by

proof body

Term-mode proof.

 104  unfold planck_radiance
 105  apply div_pos
 106  · positivity
 107  · have harg : 0 < ν / T := div_pos hν hT
 108    linarith [Real.one_lt_exp_iff.mpr harg]
 109
 110/-- CMB photons follow the Planck spectrum at T = T₀. -/

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