proposition: Theorem grec1up_init n : n < size init -> grec1up n = take n.+1 init.
proof: Proof. by rewrite /grec1up /grec1down -subn_eq0; move/eqP ->; rewrite revK. Qed.
imports: Coq(ZArith Rfunctions NaryFunctions Lia) mathcomp.ssreflect(ssreflect ssrbool ssrfun eqtype ssrnat seq fintype bigop tuple) MathComp