proposition: Lemma sub_symconnectP {g} : reflect (symmetric g /\ subrel (symconnect g) g) (rstclosed g).
proof: Proof. apply: (iffP symconnect_eqP) => [gP|[gsym gsub] x y]. by split=> x y; rewrite -?gP// symconnect_sym. by apply/idP/idP => [/gsub//|gxy]; rewrite /symconnect !connect1// gsym. Qed.
imports: mathcomp(all_ssreflect) extra