renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / bind.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/bind.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/bind.ma
index 8787d709b1b4d873f889b5945e1af6bdf454fa89..487722c443bad811888ee067cd145f2804e463b7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/bind.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/bind.ma
@@ -21,53 +21,6 @@ inductive bind: Type[0] ≝
 | BPair: bind2 → term → bind
 .
 
-inductive ext2 (R:relation term): relation bind ≝
-| ext2_unit: ∀I. ext2 R (BUnit I) (BUnit I)
-| ext2_pair: ∀I,V1,V2. R V1 V2 → ext2 R (BPair I V1) (BPair I V2)
-.
-
-(* Basic_inversion lemmas **************************************************)
-
-fact ext2_inv_unit_sn_aux: ∀R,Z1,Z2. ext2 R Z1 Z2 →
-                           ∀I. Z1 = BUnit I → Z2 = BUnit I.
-#R #Z1 #Z2 * -Z1 -Z2 #I [2: #V1 #V2 #_ ]
-#J #H destruct //
-qed-.
-
-lemma ext2_inv_unit_sn: ∀R,I,Z2. ext2 R (BUnit I) Z2 → Z2 = BUnit I.
-/2 width=4 by ext2_inv_unit_sn_aux/ qed-.
-
-fact ext2_inv_pair_sn_aux: ∀R,Z1,Z2. ext2 R Z1 Z2 →
-                           ∀I,V1. Z1 = BPair I V1 →
-                           ∃∃V2. R V1 V2 & Z2 = BPair I V2.
-#R #Z1 #Z2 * -Z1 -Z2 #I [2: #V1 #V2 #HV12 ]
-#J #W1 #H destruct /2 width=3 by ex2_intro/
-qed-.
-
-lemma ext2_inv_pair_sn: ∀R,Z2,I,V1. ext2 R (BPair I V1) Z2 →
-                        ∃∃V2. R V1 V2 & Z2 = BPair I V2.
-/2 width=3 by ext2_inv_pair_sn_aux/ qed-.
-
-fact ext2_inv_unit_dx_aux: ∀R,Z1,Z2. ext2 R Z1 Z2 →
-                           ∀I. Z2 = BUnit I → Z1 = BUnit I.
-#R #Z1 #Z2 * -Z1 -Z2 #I [2: #V1 #V2 #_ ]
-#J #H destruct //
-qed-.
-
-lemma ext2_inv_unit_dx: ∀R,I,Z1. ext2 R Z1 (BUnit I) → Z1 = BUnit I.
-/2 width=4 by ext2_inv_unit_dx_aux/ qed-.
-
-fact ext2_inv_pair_dx_aux: ∀R,Z1,Z2. ext2 R Z1 Z2 →
-                           ∀I,V2. Z2 = BPair I V2 →
-                           ∃∃V1. R V1 V2 & Z1 = BPair I V1.
-#R #Z1 #Z2 * -Z1 -Z2 #I [2: #V1 #V2 #HV12 ]
-#J #W2 #H destruct /2 width=3 by ex2_intro/
-qed-.
-
-lemma ext2_inv_pair_dx: ∀R,Z1,I,V2. ext2 R Z1 (BPair I V2) →
-                        ∃∃V1. R V1 V2 & Z1 = BPair I V1.
-/2 width=3 by ext2_inv_pair_dx_aux/ qed-.
-
 (* Basic properties ********************************************************)
 
 lemma eq_bind_dec: ∀I1,I2:bind. Decidable (I1 = I2).
@@ -79,11 +32,3 @@ lemma eq_bind_dec: ∀I1,I2:bind. Decidable (I1 = I2).
 /2 width=1 by or_introl/
 @or_intror #H destruct /2 width=1 by/
 qed-.
-
-lemma ext2_refl: ∀R. reflexive … R → reflexive … (ext2 R).
-#R #HR * /2 width=1 by ext2_pair/
-qed.
-
-lemma ext2_sym: ∀R. symmetric … R → symmetric … (ext2 R).
-#R #HR #T1 #T2 * /3 width=1 by ext2_unit, ext2_pair/
-qed-.