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theorem proved tactic proof

three_point_forces_canonical_gap

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formal statement (Lean)

 197theorem three_point_forces_canonical_gap
 198    {a b c : ℝ}
 199    (hb : 1 < b)
 200    (h0 : gapAffineLogR a b c 0 = 0)
 201    (h1 : gapAffineLogR a b c 1 = 1)
 202    (hneg1 : gapAffineLogR a b c (-1) = -2) :
 203    ∀ Z : ℤ, gapAffineLog a b c Z = RSBridge.gap Z := by

proof body

Tactic-mode proof.

 204  have hbphi : b = phi := minus_one_step_forces_phi_shift hb h0 h1 hneg1
 205  have h0phi : gapAffineLogR a phi c 0 = 0 := by simpa [hbphi] using h0
 206  have h1phi : gapAffineLogR a phi c 1 = 1 := by simpa [hbphi] using h1
 207  intro Z
 208  simpa [hbphi] using affine_log_collapses_to_gap h0phi h1phi Z
 209
 210/-- Certificate structure for the three-point closure. -/

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