proposition: Lemma uniq_predom_augment s z x : uniq (predom s) -> uniq (predom (augment s z x)).
proof: Proof. elim: s => [|[z' x'] s IHs] //=. by case: eqVneq => [->|neq_xx'] //= /andP [/mem_augment ->]. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order generic_quotient) mathcomp(ssralg ssrnum ssrint)