universe constraint Type[1] < Type[2].
universe constraint Type[2] < Type[3].
universe constraint Type[3] < Type[4].
+
+(*inductive True : Prop ≝ I : True.
+
+(*lemma fa : ∀X:Prop.X → X.
+#X #p //
+qed.
+
+(* check fa*)
+
+lemma ggr ≝ fa.*)
+
+inductive False : Prop ≝ .
+
+inductive bool : Prop ≝ True : bool | false : bool.
+
+inductive eq (A:Type[1]) (x:A) : A → Prop ≝
+ refl: eq A x x.
+
+lemma provable_True : <A href="cic:/matita/basics/pts/True.ind(1,0,0)">True</A> → eq Prop True True.
+#H %
+qed.*)
\ No newline at end of file