Section in_sig.
Variables T1 T2 T3 : Type.
Variables (D1 : {pred T1}) (D2 : {pred T2})  (D3 : {pred T3}).
Variable P1 : T1 -> Prop.
Variable P2 : T1 -> T2 -> Prop.
Variable P3 : T1 -> T2 -> T3 -> Prop.

Lemma in1_sig : {in D1, {all1 P1}} -> forall x : sig D1, P1 (sval x).
Section MonoHomoMorphismTheory.