proposition: Lemma prl_r3_qprop1 i j: gle (psr S) i j -> exists J, [/\ inc J prl_r3_nI, inc i J & inc j J].
proof: Proof. move/prl_prop0 => [iI jI]. move:(prl_r3_nI_stable_union (prl_r3_qprop0 iI) (prl_r3_qprop0 jI)) => h. exists (singleton i +s1 j); split;fprops. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)