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e320e82 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | import OAI.Combinatorics.EditDistance.AlphabetLower
import OAI.Combinatorics.EditDistance.AlphabetSupremum
import OAI.Combinatorics.EditDistance.WholeMaps
namespace OAI
/-!
# Two-sided exponential bounds for edit-distance distortion
-/
universe u
theorem edit_distance_main : EditDistortion.MainClaim.{u} := by
obtain ⟨c,hc,dL,hL⟩ := EditLower.all_lower_clauses.{u}
obtain ⟨dU,hU⟩ := Filter.eventually_atTop.mp EditUpper.eventual_upper.{u}
refine ⟨c,32,hc,by norm_num,max dL dU,?_⟩
intro d hd
obtain ⟨hl,hw,hs⟩ := hL d ((le_max_left _ _).trans hd)
obtain ⟨hu,hsu⟩ := hU d ((le_max_right _ _).trans hd)
exact ⟨fun A inst hA => ⟨hl A hA,hu A hA⟩,hw,hs,hsu⟩
end OAI
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