fact: Definition lift_perm_fun n i j (s : 'S_n) k := if @unlift n.+1 i k is Some k' then @lift n.+1 j (s k') else j.
imports: ssreflect ssrbool ssrfun eqtype ssrnat seq choice fintype finfun bigops ssralg groups perm zmodp morphisms Ring RingClass bigopsClass Setoid Morphisms