fact: Definition next_round_dec n (h: Hydra) : (h = head) + {h' : Hydra & {R1 h h'} + {R2 n h h'}}.
imports: Coq(Arith Lia List Relation_Operators Operators_Properties Peano_dec Wellfounded.Inverse_Image Wellfounded.Inclusion) hydras(More_Arith Epsilon0 Hessenberg Simple_LexProd MoreLibHyps)