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lemma proved tactic proof

display_speed_eq_c_of_nonzero

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formal statement (Lean)

  24lemma display_speed_eq_c_of_nonzero (U : RSUnits)
  25  (hτ : tau_rec_display U ≠ 0) : (lambda_kin_display U) / (tau_rec_display U) = U.c := by

proof body

Tactic-mode proof.

  26  have h := lambda_kin_from_tau_rec U
  27  calc
  28    (lambda_kin_display U) / (tau_rec_display U)
  29        = (U.c * tau_rec_display U) / (tau_rec_display U) := by rw [h]
  30    _   = U.c * (tau_rec_display U / tau_rec_display U) := by rw [mul_div_assoc]
  31    _   = U.c * 1 := by rw [div_self hτ]
  32    _   = U.c := by rw [mul_one]
  33
  34/-! Strengthen display-speed equality: remove nonzero hypothesis by proving positivity. -/

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