Section e1_diese_def.
Variables (r : C) (h : r --> a).
Hypothesis p : Equalizer_eq k h.
Definition E_tau (x : PA k) :=
match x as x' return (Carrier (r --> FPA x')) with
| PA1 => h
| PA2 => h o k (Witness l)
end.
Definition E_NT := Build_Cone E_tau_cone_law.
Definition E1_diese : r --> E1_ob := Lim_diese l E_NT.
End e1_diese_def.

Lemma Prf_E1_law3 : Equalizer_law3 E1_mor E1_diese.