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theorem proved term proof

gamma_ge_one

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formal statement (Lean)

  40theorem gamma_ge_one (v c : ℝ) (hc : 0 < c) (hv : |v| < c) :
  41    1 ≤ c / Real.sqrt (c^2 - v^2) := by

proof body

Term-mode proof.

  42  rw [le_div_iff (Real.sqrt_pos.mpr (by nlinarith [sq_nonneg v, sq_abs v, abs_lt.mp hv]))]
  43  rw [one_mul]
  44  apply Real.le_sqrt.mpr
  45  constructor
  46  · positivity
  47  · nlinarith [sq_abs v, abs_lt.mp hv]
  48
  49/-- J-cost at rapidity: J(cosh θ) = cosh θ - 1 = γ - 1 ≥ 0. -/

depends on (3)

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