proposition: Lemma show_is_fiprod : forall a u v y1 y2 , fiprod_hypothesis a u v y1 y2 -> (forall z z', mor a z -> mor a z' -> source y1 = target z -> source y1 = target z' -> comp a y1 z = comp a y1 z' -> comp a y2 z = comp a y2 z' -> z = z') -> (forall z1 z2, fiprod_hypothesis a u v z1 z2 -> (exists w, (mor a w & source y1 = target w & comp a y1 w = z1 & comp a y2 w = z2))) -> is_fiprod a u v y1 y2.
proof: Proof. ir. uhg; ee. am. uhg. ee. rww is_uni_fiprod_cone. rww is_versal_fiprod_cone. Qed.
imports: Arith colimits little_cat fc_limits cardinal