syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / ext2.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/ext2.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/ext2.ma
deleted file mode 100644 (file)
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--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/ext2.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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 "basic_2/syntax/bind.ma".
-
-(* EXTENSION TO BINDERS OF A RELATION FOR TERMS *****************************)
-
-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-.
-
-(* Advanced inversion lemmas ***********************************************)
-
-lemma ext2_inv_unit: ∀R,I1,I2. ext2 R (BUnit I1) (BUnit I2) → I1 = I2.
-#R #I1 #I2 #H lapply (ext2_inv_unit_sn … H) -H
-#H destruct //
-qed-.
-
-lemma ext2_inv_pair: ∀R,I1,I2,V1,V2. ext2 R (BPair I1 V1) (BPair I2 V2) →
-                     I1 = I2 ∧ R V1 V2.
-#R #I1 #I2 #V1 #V2 #H elim (ext2_inv_pair_sn … H) -H
-#V #HV #H destruct /2 width=1 by conj/
-qed-.
-
-(* Basic properties ********************************************************)
-
-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-.
-
-lemma ext2_dec: ∀R. (∀T1,T2. Decidable (R T1 T2)) →
-                ∀I1,I2. Decidable (ext2 R I1 I2).
-#R #HR * #I1 [2: #T1 ] * #I2 [2,4: #T2 ]
-[ elim (eq_bind2_dec I1 I2) #HI12 destruct
-  [ elim (HR T1 T2) -HR #HT12 /3 width=1 by ext2_pair, or_introl/ ]
-  @or_intror #H elim (ext2_inv_pair … H) -H /2 width=1 by/
-| @or_intror #H lapply (ext2_inv_unit_sn … H) -H
-  #H destruct
-| @or_intror #H lapply (ext2_inv_unit_dx … H) -H
-  #H destruct
-| elim (eq_bind1_dec I1 I2) #HI12 destruct
-  /4 width=2 by ext2_inv_unit, ext2_unit, or_intror, or_introl/
-]
-qed-.