proposition: Lemma path_correct_upd_dist: forall (g: @DijkGG size inf) src i m dist prev newcost p2m, vvalid g i -> vvalid g m -> Zlength dist = size -> m <> i -> path_correct g prev (upd_Znth i dist newcost) src m p2m -> path_correct g prev dist src m p2m.
proof: Proof. intros. destruct H3 as [? [? [? [? ?]]]]. split3; [| |split3]; trivial. apply (vvalid_meaning g) in H. apply (vvalid_meaning g) in H0. rewrite upd_Znth_diff in H6; lia. Qed.
imports: CertiGraph.dijkstra.dijkstra_env CertiGraph.dijkstra.MathDijkGraph CertiGraph.dijkstra.dijkstra_spec_pure