proposition: Lemma source_eqz_dotted : forall a u v y, has_coequalizer a u v -> coequalizer_hypothesis a u v y -> source (coeqz_dotted a u v y) = target (coequalizer a u v).
proof: Proof. ir. rwi has_coeq_has_eq H. rwi coeq_hyp_eq_hyp H0. uf coeqz_dotted. rw source_flip. rw target_eqz_dotted. uf coequalizer. rw target_flip. tv. apply mor_arrow_like with (opp a). app mor_equalizer. am. am. apply mor_arrow_like with (opp a). app mor_eqz_dotted. uh H0; ee. uh H1; ee; am. uh H0; ee. uh H1; ee; am. Qed.
imports: Arith colimits little_cat fc_limits cardinal