From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Mon, 23 May 2005 11:18:45 +0000 (+0000)
Subject: Added andrea.ma
X-Git-Tag: single_binding~27
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=73581a6c15a17eabc3b79a1b379a563d579092a1;p=helm.git

Added andrea.ma
---

diff --git a/helm/matita/tests/andrea.ma b/helm/matita/tests/andrea.ma
new file mode 100644
index 000000000..242e374dd
--- /dev/null
+++ b/helm/matita/tests/andrea.ma
@@ -0,0 +1,35 @@
+inductive True: Prop \def
+I : True.
+
+inductive False: Prop \def .
+
+definition Not: Prop \to Prop \def
+\lambda A:Prop. (A \to False).
+
+theorem absurd : \forall A,C:Prop. A \to Not A \to C.
+cut False.elim Hcut.apply H1.assumption.
+qed.
+
+inductive And (A,B:Prop) : Prop \def
+    conj : A \to B \to (And A B).
+
+theorem proj1: \forall A,B:Prop. (And A B) \to A.
+intro. elim H. assumption.
+qed.
+
+theorem proj2: \forall A,B:Prop. (And A B) \to A.
+intro. elim H. assumption.
+qed.
+
+inductive Or (A,B:Prop) : Prop \def
+     or_introl : A \to (Or A B)
+   | or_intror : B \to (Or A B).
+
+inductive ex (A:Type) (P:A \to Prop) : Prop \def
+    ex_intro: \forall x:A. P x \to ex A P.
+
+inductive ex2 (A:Type) (P,Q:A \to Prop) : Prop \def
+    ex_intro2: \forall x:A. P x \to Q x \to ex2 A P Q.
+
+inductive eq (A:Type) (x:A) : A \to Prop \def
+    refl_equal : eq A x x.