proposition: Lemma noid_inl_class_eq x y: inc x noid_inl_sum -> inc y noid_inl_sum -> (class noid_inl_equiv x = class noid_inl_equiv y <-> noid_inl_equiv_rel x y).
proof: Proof. have [ha hb] := noid_inl_equiv_esr. move => xE yE; move: (xE)(yE); rewrite - hb => xsr ysr. split => xx. by move/(related_equiv_P ha): (And3 xsr ysr xx) => /graph_on_P1 []. by apply/(class_eq1 ha); apply/graph_on_P1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)