Research proof index

The preimage of m under succSuccAbove i j hij given that m is not equal to i or j. -/ def predPredAbove (i j : Fin (n + 1 + 1)) (hij : i ≠ j) (m : Fin (n + 1 + 1)) (hm : m ≠ i ∧ m ≠ j) : Fin n := if h1 : m.1 < i.1 ∧ m.1 < j.1 then ⟨m, by grind⟩ else if h2 : m.1 - 1 < i.1 ∧ j.1 ≤ m.1 then ⟨m - 1, by grind⟩ else if h3 : i.1 - 1 ≤ m.1 ∧ m.1 < j.1 t...