proposition: Lemma equalizer_twoarrow_nt_hypothesis : forall a u v y, equalizer_hypothesis a u v y -> twoarrow_nt_hypothesis a (id a (source y)) (id a (source y)) u v y (comp a u y).
proof: Proof. ir. uh H; ee. uh H; ee. assert (ob a (source y)). rww ob_source. assert (ob a (target y)). rww ob_target. uhg; ee. uh H0; ee; am. app mor_id. app mor_id. am. am. am. rww mor_comp. rww source_id. sy; am. rww source_comp. rww target_id. rww target_comp. tv. tv. am. am. rww assoc. rww right_id. app mor_id. rww target_id. rww assoc. rww right_id. app mor_id. rww target_id. Qed.
imports: Arith colimits little_cat fc_limits cardinal