| 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 | |