lambda: some refactoring + support for subsets of subterms started

[helm.git] / matita / matita / contribs / lambda / term.ma

diff --git a/matita/matita/contribs/lambda/term.ma b/matita/matita/contribs/lambda/term.ma
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--- a/matita/matita/contribs/lambda/term.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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* Initial invocation: - Patience on us to gain peace and perfection! - *)
-
-include "preamble.ma".
-
-(* TERM STRUCTURE ***********************************************************)
-
-(* Policy: term metavariables : A, B, C, D, M, N
-           depth metavariables: i, j
-*)
-inductive term: Type[0] ≝
-| VRef: nat  → term        (* variable reference by depth *)
-| Abst: term → term        (* function formation          *)
-| Appl: term → term → term (* function application        *)
-.
-
-interpretation "term construction (variable reference by index)"
-   'VariableReferenceByIndex i = (VRef i).
-
-interpretation "term construction (abstraction)"
-   'Abstraction A = (Abst A).
-
-interpretation "term construction (application)"
-   'Application C A = (Appl C A).
-
-notation "hvbox( # term 90 i )"
- non associative with precedence 90
- for @{ 'VariableReferenceByIndex $i }.
-
-notation "hvbox( 𝛌  . term 46 A )"
-   non associative with precedence 46
-   for @{ 'Abstraction $A }.
-
-notation "hvbox( @ term 46 C . break term 46 A )"
-   non associative with precedence 46
-   for @{ 'Application $C $A }.
-
-definition compatible_abst: predicate (relation term) ≝ λR.
-                            ∀A1,A2. R A1 A2 → R (𝛌.A1) (𝛌.A2).
-
-definition compatible_sn: predicate (relation term) ≝ λR.
-                          ∀A,B1,B2. R B1 B2 → R (@B1.A) (@B2.A).
-
-definition compatible_dx: predicate (relation term) ≝ λR.
-                          ∀B,A1,A2. R A1 A2 → R (@B.A1) (@B.A2).
-
-definition compatible_appl: predicate (relation term) ≝ λR.
-                            ∀B1,B2. R B1 B2 → ∀A1,A2. R A1 A2 →
-                            R (@B1.A1) (@B2.A2).
-
-lemma star_compatible_abst: ∀R. compatible_abst R → compatible_abst (star … R).
-#R #HR #A1 #A2 #H elim H -A2 // /3 width=3/
-qed.
-
-lemma star_compatible_sn: ∀R. compatible_sn R → compatible_sn (star … R).
-#R #HR #A #B1 #B2 #H elim H -B2 // /3 width=3/
-qed.
-
-lemma star_compatible_dx: ∀R. compatible_dx R → compatible_dx (star … R).
-#R #HR #B #A1 #A2 #H elim H -A2 // /3 width=3/
-qed.
-
-lemma star_compatible_appl: ∀R. reflexive ? R →
-                            compatible_appl R → compatible_appl (star … R).
-#R #H1R #H2R #B1 #B2 #H elim H -B2 /3 width=1/ /3 width=5/
-qed.