proposition: Lemma prl_singleton_I S: singletonp (psI S) -> projective_limit S = (productb (psE S)).
proof: Proof. move => [k Iv]. set_extens t; first by case/Zo_P. move => tp; apply/Zo_P;split => // i j lij. move:(prl_prop0 lij) => [iI jI]. move:(iI) jI; rewrite Iv => /set1_P ik /set1_P jk. rewrite jk - ik (prl_prop5 iI) //. by move/setXb_P:tp => [pa pb pc]; apply: pc; rewrite ps_domain_E. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)