+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "ground_2/lib/star.ma".
-include "basic_2/syntax/ext2.ma".
-
-(* EXTENSION TO BINDERS OF A RELATION FOR TERMS *****************************)
-
-(* Properties with transitive closure ***************************************)
-
-lemma ext2_tc_pair: ∀R,I,V1,V2. TC … R V1 V2 →
- TC … (ext2 R) (BPair I V1) (BPair I V2).
-#R #I #V1 #V2 #H elim H -H -V2
-/3 width=3 by ext2_pair, step, inj/
-qed.
-
-lemma ext2_tc_inj: ∀R,I1,I2. ext2 R I1 I2 → ext2 (TC … R) I1 I2.
-#R #I1 #I2 * -I1 -I2
-/3 width=1 by ext2_unit, ext2_pair, inj/
-qed.
-
-(* Main properties with transitive closure **********************************)
-
-theorem ext2_tc_step: ∀R,I1,I. ext2 (TC … R) I1 I →
- ∀I2. ext2 R I I2 → ext2 (TC … R) I1 I2.
-#R #I1 #I * -I1 -I
-[ #I #Z #H >(ext2_inv_unit_sn … H) -Z /2 width=1 by ext2_unit/
-| #I #V1 #V #HV1 #Z #H
- elim (ext2_inv_pair_sn … H) -H #V2 #HV2 #H destruct
- /3 width=3 by ext2_pair, step/
-]
-qed-.
-
-(* Advanced properties with transitive closure ******************************)
-
-lemma ext2_tc: ∀R,I1,I2. TC … (ext2 R) I1 I2 → ext2 (TC … R) I1 I2.
-#R #I1 #I2 #H elim H -I2
-/2 width=3 by ext2_tc_step, ext2_tc_inj/
-qed.
-
-(* Advanced inversion lemmas with transitive closure ************************)
-
-lemma ext2_inv_tc: ∀R,I1,I2. ext2 (TC … R) I1 I2 → TC … (ext2 R) I1 I2.
-#R #I1 #I2 * -I1 -I2
-/3 width=1 by ext2_tc_pair, ext2_unit, inj/
-qed-.