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theorem proved tactic proof

affine_log_parameters_forced

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formal statement (Lean)

 166theorem affine_log_parameters_forced
 167    {a b c : ℝ}
 168    (hb : 1 < b)
 169    (h0 : gapAffineLogR a b c 0 = 0)
 170    (h1 : gapAffineLogR a b c 1 = 1)
 171    (hneg1 : gapAffineLogR a b c (-1) = -2) :
 172    b = phi ∧ a = 1 / Real.log phi ∧ c = 0 := by

proof body

Tactic-mode proof.

 173  have hbphi : b = phi := minus_one_step_forces_phi_shift hb h0 h1 hneg1
 174  have h0phi : gapAffineLogR a phi c 0 = 0 := by simpa [hbphi] using h0
 175  have h1phi : gapAffineLogR a phi c 1 = 1 := by simpa [hbphi] using h1
 176  exact ⟨hbphi, unit_step_forces_log_scale h0phi h1phi,
 177         zero_normalization_forces_offset h0phi⟩
 178
 179/-- Under the normalizations, the affine-log family equals the canonical gap. -/

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