proposition: Lemma eqzmap_extensionality : forall a b, is_cone a -> is_cone b -> cone_source a = twoarrow_cat -> socle a = socle b -> eqzmap a = eqzmap b -> a = b.
proof: Proof. ir. assert (cone_source b = twoarrow_cat). uf cone_source. wr H2. am. util (equalizer_cone_eq2 (c:= a)). am. am. util (equalizer_cone_eq2 (c:= b)). am. am. rw H5; rw H6. assert (eqzfirst a = eqzfirst b). uf eqzfirst. rww H2. assert (eqzsecond a = eqzsecond b). uf eqzsecond. rw H2. reflexivity. rw H3; rw H7; rw H8. assert (cone_target a = cone_target b). uf cone_target. rww H2. rw H9. reflexivity. Qed.
imports: Arith colimits little_cat fc_limits cardinal