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theorem proved term proof

gamow_energy_increases_with_T

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formal statement (Lean)

  45theorem gamow_energy_increases_with_T (Z₁Z₂ μ T₁ T₂ : ℝ)
  46    (hZ : 0 < Z₁Z₂) (hμ : 0 < μ) (hT₁ : 0 < T₁) (h : T₁ < T₂) :
  47    gamow_energy T₁ Z₁Z₂ μ < gamow_energy T₂ Z₁Z₂ μ := by

proof body

Term-mode proof.

  48  unfold gamow_energy
  49  apply mul_lt_mul_of_pos_left _ (by positivity)
  50  apply Real.rpow_lt_rpow (by positivity) (div_lt_div_of_pos_right h (by norm_num)) (by norm_num)
  51
  52/-! ## Stellar Structure Scaling Relations -/
  53
  54/-- **VIRIAL TEMPERATURE**: T_c ∝ GM m_p / (k_B R)
  55    From the virial theorem applied to a stellar interior. -/

depends on (8)

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