+++ /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 "basic_2/notation/constructors/item0_1.ma".
-include "basic_2/notation/constructors/snitem2_3.ma".
-include "basic_2/notation/constructors/snbind2_4.ma".
-include "basic_2/notation/constructors/snbind2pos_3.ma".
-include "basic_2/notation/constructors/snbind2neg_3.ma".
-include "basic_2/notation/constructors/snflat2_3.ma".
-include "basic_2/notation/constructors/star_1.ma".
-include "basic_2/notation/constructors/lref_1.ma".
-include "basic_2/notation/constructors/gref_1.ma".
-include "basic_2/notation/constructors/snabbr_3.ma".
-include "basic_2/notation/constructors/snabbrpos_2.ma".
-include "basic_2/notation/constructors/snabbrneg_2.ma".
-include "basic_2/notation/constructors/snabst_3.ma".
-include "basic_2/notation/constructors/snabstpos_2.ma".
-include "basic_2/notation/constructors/snabstneg_2.ma".
-include "basic_2/notation/constructors/snappl_2.ma".
-include "basic_2/notation/constructors/sncast_2.ma".
-include "basic_2/syntax/item.ma".
-
-(* TERMS ********************************************************************)
-
-(* terms *)
-inductive term: Type[0] ≝
- | TAtom: item0 → term (* atomic item construction *)
- | TPair: item2 → term → term → term (* binary item construction *)
-.
-
-interpretation "term construction (atomic)"
- 'Item0 I = (TAtom I).
-
-interpretation "term construction (binary)"
- 'SnItem2 I T1 T2 = (TPair I T1 T2).
-
-interpretation "term binding construction (binary)"
- 'SnBind2 p I T1 T2 = (TPair (Bind2 p I) T1 T2).
-
-interpretation "term positive binding construction (binary)"
- 'SnBind2Pos I T1 T2 = (TPair (Bind2 true I) T1 T2).
-
-interpretation "term negative binding construction (binary)"
- 'SnBind2Neg I T1 T2 = (TPair (Bind2 false I) T1 T2).
-
-interpretation "term flat construction (binary)"
- 'SnFlat2 I T1 T2 = (TPair (Flat2 I) T1 T2).
-
-interpretation "sort (term)"
- 'Star s = (TAtom (Sort s)).
-
-interpretation "local reference (term)"
- 'LRef i = (TAtom (LRef i)).
-
-interpretation "global reference (term)"
- 'GRef l = (TAtom (GRef l)).
-
-interpretation "abbreviation (term)"
- 'SnAbbr p T1 T2 = (TPair (Bind2 p Abbr) T1 T2).
-
-interpretation "positive abbreviation (term)"
- 'SnAbbrPos T1 T2 = (TPair (Bind2 true Abbr) T1 T2).
-
-interpretation "negative abbreviation (term)"
- 'SnAbbrNeg T1 T2 = (TPair (Bind2 false Abbr) T1 T2).
-
-interpretation "abstraction (term)"
- 'SnAbst p T1 T2 = (TPair (Bind2 p Abst) T1 T2).
-
-interpretation "positive abstraction (term)"
- 'SnAbstPos T1 T2 = (TPair (Bind2 true Abst) T1 T2).
-
-interpretation "negative abstraction (term)"
- 'SnAbstNeg T1 T2 = (TPair (Bind2 false Abst) T1 T2).
-
-interpretation "application (term)"
- 'SnAppl T1 T2 = (TPair (Flat2 Appl) T1 T2).
-
-interpretation "native type annotation (term)"
- 'SnCast T1 T2 = (TPair (Flat2 Cast) T1 T2).
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was: term_dec *)
-lemma eq_term_dec: ∀T1,T2:term. Decidable (T1 = T2).
-#T1 elim T1 -T1 #I1 [| #V1 #T1 #IHV1 #IHT1 ] * #I2 [2,4: #V2 #T2 ]
-[1,4: @or_intror #H destruct
-| elim (eq_item2_dec I1 I2) #HI
- [ elim (IHV1 V2) -IHV1 #HV
- [ elim (IHT1 T2) -IHT1 /2 width=1 by or_introl/ #HT ]
- ]
- @or_intror #H destruct /2 width=1 by/
-| elim (eq_item0_dec I1 I2) /2 width=1 by or_introl/ #HI
- @or_intror #H destruct /2 width=1 by/
-]
-qed-.
-
-(* Basic inversion lemmas ***************************************************)
-
-fact destruct_tatom_tatom_aux: ∀I1,I2. ⓪{I1} = ⓪{I2} → I1 = I2.
-#I1 #I2 #H destruct //
-qed-.
-
-fact destruct_tpair_tpair_aux: ∀I1,I2,T1,T2,V1,V2. ②{I1}T1.V1 = ②{I2}T2.V2 →
- ∧∧T1 = T2 & I1 = I2 & V1 = V2.
-#I1 #I2 #T1 #T2 #V1 #V2 #H destruct /2 width=1 by and3_intro/
-qed-.
-
-lemma discr_tpair_xy_x: ∀I,T,V. ②{I}V.T = V → ⊥.
-#I #T #V elim V -V
-[ #J #H destruct
-| #J #W #U #IHW #_ #H elim (destruct_tpair_tpair_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
-]
-qed-.
-
-(* Basic_1: was: thead_x_y_y *)
-lemma discr_tpair_xy_y: ∀I,V,T. ②{I}V.T = T → ⊥.
-#I #V #T elim T -T
-[ #J #H destruct
-| #J #W #U #_ #IHU #H elim (destruct_tpair_tpair_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
-]
-qed-.
-
-lemma eq_false_inv_tpair_sn: ∀I,V1,T1,V2,T2.
- (②{I}V1.T1 = ②{I}V2.T2 → ⊥) →
- (V1 = V2 → ⊥) ∨ (V1 = V2 ∧ (T1 = T2 → ⊥)).
-#I #V1 #T1 #V2 #T2 #H
-elim (eq_term_dec V1 V2) /3 width=1 by or_introl/ #HV12 destruct
-@or_intror @conj // #HT12 destruct /2 width=1 by/
-qed-.
-
-lemma eq_false_inv_tpair_dx: ∀I,V1,T1,V2,T2.
- (②{I} V1. T1 = ②{I}V2.T2 → ⊥) →
- (T1 = T2 → ⊥) ∨ (T1 = T2 ∧ (V1 = V2 → ⊥)).
-#I #V1 #T1 #V2 #T2 #H
-elim (eq_term_dec T1 T2) /3 width=1 by or_introl/ #HT12 destruct
-@or_intror @conj // #HT12 destruct /2 width=1 by/
-qed-.
-
-(* Basic_1: removed theorems 3:
- not_void_abst not_abbr_void not_abst_void
-*)
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