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(** * Inclusion and extensionality  *)
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(** The inclusion relation is defined as expected: *)

Definition SUB (X : Typ1) (A : Rel X) (a : X) (Y : Typ1) 
  (B : Rel Y) (b : Y) : Prop :=
  forall (Z : Typ1) (C : Rel Z) (c : Z), ELT Z C c X A a -> ELT Z C c Y B b.

Theorem extensionality : forall (X : Typ1) (A : Rel X) (a : X) (Y : Typ1) (B : Rel Y) (b : Y), SUB X A a Y B b -> SUB Y B b X A a -> EQV X A a Y B b.