fact: Definition Kempe_valid ctu ctr gtr gtu := [/\ ctree_proper h.+1 ctu /\ ctree_sub ctu =1 even_fun et (sub_gt gtr et + sub_gt gtu et), forall et, ctree_mem ctr et -> Kempe_coclosure P (ctrace et) /\ size et = h.+1, forall w, gtree_mem gtr w -> ~ gtree_mem gtu w /\ init_gtree_spec h.+1 w, forall w, gtree_mem gtu w -> init_gtree_spec h.+1 w & forall w, ~ gtree_mem gtu w -> init_gtree_spec h.+1 w -> exists2 et, Kempe_coclosure P (ctrace et) & matchpg Bstack0 et w].
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph) fourcolor(hypermap geometry color chromogram coloring cfmap) fourcolor(cfcolor dyck ctree initctree gtree initgtree) fourcolor(gtreerestrict ctreerestrict)