proposition: Lemma permutation_exists1 n i: natp n -> i <c n -> exists2 f, inc f (permutations n) & Vf f \0c = i.
proof: Proof. move => nN lin. move /(NltP nN): (cle_ltT (cle0x (proj31_1 lin)) lin) => oE. move /(NltP nN):lin => iI. move:(transposition_prop nN iI oE) => [pa _ pb _ _];ex_tac. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)