proposition: Lemma prelift_augment s k x : prelift (augment s k x) = k *: f x + prelift s.
proof: Proof. elim: s => [|[k' x'] s IHs] //=. by rewrite prelift_seq1 prelift_nil addr0. have [->|ne_xx'] := eqVneq x x'. by rewrite !prelift_cons scalerDl addrA. by rewrite !prelift_cons IHs addrCA. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order generic_quotient) mathcomp(ssralg ssrnum ssrint)