+(* default inhabitance predicates *******************************************)
+
+definition true_f ≝ λX:Type. λ_:X. True.
+
+definition false_f ≝ λX:Type. λ_:X. False.
+
+(* default foreward compatibilities *****************************************)
+
+theorem const_fw: ∀A:Prop. ∀X:Type. ∀P:X→X→Prop. ∀x1,x2. A → P x1 x2 → A.
+intros; autobatch.
+qed.
+
+definition true_fw ≝ const_fw True.
+
+definition false_fw ≝ const_fw False.
+
+(* default backward compatibilities *****************************************)
+
+theorem const_bw: ∀A:Prop. ∀X:Type. ∀P:X→X→Prop. ∀x1,x2. A → P x2 x1 → A.
+intros; autobatch.
+qed.
+
+definition true_bw ≝ const_bw True.
+
+definition false_bw ≝ const_bw False.