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theorem proved tactic proof

alpha_W_gt_alpha

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formal statement (Lean)

  62theorem alpha_W_gt_alpha : alpha < alpha_W := by

proof body

Tactic-mode proof.

  63  unfold alpha_W
  64  rw [lt_div_iff₀ sin2_theta_positive]
  65  calc alpha * sin2_theta_W_rs
  66      < alpha * 1 := by {
  67        apply mul_lt_mul_of_pos_left _ alpha_pos_aux
  68        linarith [sin2_theta_lt_half]
  69      }
  70    _ = alpha := mul_one _
  71
  72/-- sin²θ_W > 0 (needed for division). -/

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