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theorem proved tactic proof

strong_cp_gap

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formal statement (Lean)

 277theorem strong_cp_gap :
 278    1 - Real.cos (Real.pi / 4) > 0.29 := by

proof body

Tactic-mode proof.

 279  have : Real.cos (Real.pi / 4) = Real.sqrt 2 / 2 := Real.cos_pi_div_four
 280  rw [this]
 281  have h_sqrt2 : Real.sqrt 2 < 1.42 := by
 282    rw [show (1.42 : ℝ) = Real.sqrt (1.42 ^ 2) from by
 283      rw [Real.sqrt_sq]; norm_num]
 284    apply Real.sqrt_lt_sqrt
 285    · norm_num
 286    · norm_num
 287  linarith
 288
 289/-- **STRONG CP NUMERICAL CERTIFICATE**.
 290    Combines the structural (8-tick + J-min) and numerical (interval) statements. -/

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