- lambda_delta: programmed renaming to lambdadelta

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / grammar / tstc.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/grammar/tstc.ma b/matita/matita/contribs/lambda_delta/basic_2/grammar/tstc.ma
deleted file mode 100644 (file)
index 78a9b49..0000000
--- a/matita/matita/contribs/lambda_delta/basic_2/grammar/tstc.ma
+++ /dev/null
@@ -1,107 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/grammar/term_simple.ma".
-
-(* SAME TOP TERM CONSTRUCTOR ************************************************)
-
-inductive tstc: relation term ≝
-   | tstc_atom: ∀I. tstc (⓪{I}) (⓪{I})
-   | tstc_pair: ∀I,V1,V2,T1,T2. tstc (②{I} V1. T1) (②{I} V2. T2)
-.
-
-interpretation "same top constructor (term)" 'Iso T1 T2 = (tstc T1 T2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact tstc_inv_atom1_aux: ∀T1,T2. T1 ≃ T2 → ∀I. T1 = ⓪{I} → T2 = ⓪{I}.
-#T1 #T2 * -T1 -T2 //
-#J #V1 #V2 #T1 #T2 #I #H destruct
-qed.
-
-(* Basic_1: was: iso_gen_sort iso_gen_lref *)
-lemma tstc_inv_atom1: ∀I,T2. ⓪{I} ≃ T2 → T2 = ⓪{I}.
-/2 width=3/ qed-.
-
-fact tstc_inv_pair1_aux: ∀T1,T2. T1 ≃ T2 → ∀I,W1,U1. T1 = ②{I}W1.U1 →
-                         ∃∃W2,U2. T2 = ②{I}W2. U2.
-#T1 #T2 * -T1 -T2
-[ #J #I #W1 #U1 #H destruct
-| #J #V1 #V2 #T1 #T2 #I #W1 #U1 #H destruct /2 width=3/
-]
-qed.
-
-(* Basic_1: was: iso_gen_head *)
-lemma tstc_inv_pair1: ∀I,W1,U1,T2. ②{I}W1.U1 ≃ T2 →
-                      ∃∃W2,U2. T2 = ②{I}W2. U2.
-/2 width=5/ qed-.
-
-fact tstc_inv_atom2_aux: ∀T1,T2. T1 ≃ T2 → ∀I. T2 = ⓪{I} → T1 = ⓪{I}.
-#T1 #T2 * -T1 -T2 //
-#J #V1 #V2 #T1 #T2 #I #H destruct
-qed.
-
-lemma tstc_inv_atom2: ∀I,T1. T1 ≃ ⓪{I} → T1 = ⓪{I}.
-/2 width=3/ qed-.
-
-fact tstc_inv_pair2_aux: ∀T1,T2. T1 ≃ T2 → ∀I,W2,U2. T2 = ②{I}W2.U2 →
-                         ∃∃W1,U1. T1 = ②{I}W1. U1.
-#T1 #T2 * -T1 -T2
-[ #J #I #W2 #U2 #H destruct
-| #J #V1 #V2 #T1 #T2 #I #W2 #U2 #H destruct /2 width=3/
-]
-qed.
-
-lemma tstc_inv_pair2: ∀I,T1,W2,U2. T1 ≃ ②{I}W2.U2 →
-                      ∃∃W1,U1. T1 = ②{I}W1. U1.
-/2 width=5/ qed-.
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was: iso_refl *)
-lemma tstc_refl: ∀T. T ≃ T.
-#T elim T -T //
-qed.
-
-lemma tstc_sym: ∀T1,T2. T1 ≃ T2 → T2 ≃ T1.
-#T1 #T2 #H elim H -T1 -T2 //
-qed.
-
-lemma tstc_dec: ∀T1,T2. Decidable (T1 ≃ T2).
-* #I1 [2: #V1 #T1 ] * #I2 [2,4: #V2 #T2 ]
-[ elim (item2_eq_dec I1 I2) #HI12
-  [ destruct /2 width=1/
-  | @or_intror #H
-    elim (tstc_inv_pair1 … H) -H #V #T #H destruct /2 width=1/
-  ]
-| @or_intror #H
-  lapply (tstc_inv_atom1 … H) -H #H destruct
-| @or_intror #H
-  lapply (tstc_inv_atom2 … H) -H #H destruct
-| elim (item0_eq_dec I1 I2) #HI12
-  [ destruct /2 width=1/
-  | @or_intror #H
-    lapply (tstc_inv_atom2 … H) -H #H destruct /2 width=1/
-  ]
-]
-qed.
-
-lemma simple_tstc_repl_dx: ∀T1,T2. T1 ≃ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
-#T1 #T2 * -T1 -T2 //
-#I #V1 #V2 #T1 #T2 #H
-elim (simple_inv_pair … H) -H #J #H destruct //
-qed. (**) (* remove from index *)
-
-lemma simple_tstc_repl_sn: ∀T1,T2. T1 ≃ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
-/3 width=3/ qed-.