proposition: Lemma is_connected_coequalizer_graph : is_connected Coequalizer_graph.
proof: Proof. use (is_connected_pointed Coequalizer_graph (● 0)%stn). intro v. induction v as [v v2]. induction v as [|v Hv]. - exists 0. apply subtypePath; [intro; apply propproperty|]. reflexivity. - induction v as [|v Hv2]; [|induction (nopathsfalsetotrue v2)]. exists 1. exists (● 1)%stn. split. * do 2 apply inl. exact tt. * apply subtypePath; [intro; apply propproperty|]. reflexivity. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.EqDiag UniMath.CategoryTheory.Limits.Coequalizers