fact: Definition valid_hub G x := minimal_counter_example G /\ (0 < @dscore G x)%R.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph bigop ssralg ssrnum ssrint) fourcolor(hypermap geometry patch coloring birkhoff embed) fourcolor(quiz quiztree part redpart discharge hubcap) fourcolor(cfmap cfcontract cfreducible configurations)