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theorem proved tactic proof

bright_fringes

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formal statement (Lean)

 147theorem bright_fringes (setup : DoubleSlitSetup) (n : ℤ) :
 148    intensity setup (n * fringeSpacing setup) = 4 := by

proof body

Tactic-mode proof.

 149  unfold intensity phaseDifference pathDifference fringeSpacing
 150  have hd : setup.d ≠ 0 := ne_of_gt setup.d_pos
 151  have hL : setup.L ≠ 0 := ne_of_gt setup.L_pos
 152  have hlam : setup.lambda ≠ 0 := ne_of_gt setup.lambda_pos
 153  have h1 : 2 * π * (setup.d * (↑n * (setup.lambda * setup.L / setup.d)) / setup.L) / setup.lambda / 2
 154          = n * π := by field_simp [hd, hL, hlam]
 155  simp only [h1, cos_int_mul_pi_sq, mul_one]
 156
 157/-- **THEOREM**: Dark fringes occur at y = (n + 1/2) × Δy with zero intensity.
 158    At these positions, the phase difference is (2n+1)π, giving cos²((2n+1)π/2) = 0. -/

depends on (17)

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