- we introduced the pointer_step rc in the perspective of proving

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/grammar/term.ma b/matita/matita/contribs/lambda_delta/basic_2/grammar/term.ma
index 6e8370d497251de2cfd69bfba097e5418823bb77..5ccb5e4accdf9482813b9fe5c8ecb203c46608b9 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/grammar/term.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/grammar/term.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/grammar/item.ma".
+include "basic_2/grammar/item.ma".
 
 (* TERMS ********************************************************************)
 
@@ -29,7 +29,13 @@ interpretation "term construction (binary)"
    'SnItem2 I T1 T2 = (TPair I T1 T2).
 
 interpretation "term binding construction (binary)"
-   'SnBind2 I T1 T2 = (TPair (Bind2 I) T1 T2).
+   'SnBind2 a I T1 T2 = (TPair (Bind2 a 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).
@@ -44,10 +50,22 @@ interpretation "global reference (term)"
    'GRef p = (TAtom (GRef p)).
 
 interpretation "abbreviation (term)"
-   'SnAbbr T1 T2 = (TPair (Bind2 Abbr) T1 T2).
+   'SnAbbr a T1 T2 = (TPair (Bind2 a 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 T1 T2 = (TPair (Bind2 Abst) T1 T2).
+   'SnAbst a T1 T2 = (TPair (Bind2 a 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).
@@ -62,7 +80,7 @@ axiom term_eq_dec: ∀T1,T2:term. Decidable (T1 = T2).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma discr_tpair_xy_x: ∀I,T,V. ②{I} V. T = V → False.
+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 destruct
@@ -72,7 +90,7 @@ lemma discr_tpair_xy_x: ∀I,T,V. ②{I} V. T = V → False.
 qed-.
 
 (* Basic_1: was: thead_x_y_y *)
-lemma discr_tpair_xy_y: ∀I,V,T. ②{I} V. T = T → False.
+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 destruct
@@ -82,26 +100,26 @@ lemma discr_tpair_xy_y: ∀I,V,T. ②{I} V. T = T → False.
 qed-.
 
 lemma eq_false_inv_tpair_sn: ∀I,V1,T1,V2,T2.
-                             (②{I} V1. T1 = ②{I} V2. T2 → False) →
-                             (V1 = V2 → False) ∨ (V1 = V2 ∧ (T1 = T2 → False)).
+                             (②{I} V1. T1 = ②{I} V2. T2 → ⊥) →
+                             (V1 = V2 → ⊥) ∨ (V1 = V2 ∧ (T1 = T2 → ⊥)).
 #I #V1 #T1 #V2 #T2 #H
 elim (term_eq_dec V1 V2) /3 width=1/ #HV12 destruct
 @or_intror @conj // #HT12 destruct /2 width=1/ 
 qed-.
 
 lemma eq_false_inv_tpair_dx: ∀I,V1,T1,V2,T2.
-                             (②{I} V1. T1 = ②{I} V2. T2 → False) →
-                             (T1 = T2 → False) ∨ (T1 = T2 ∧ (V1 = V2 → False)).
+                             (②{I} V1. T1 = ②{I} V2. T2 → ⊥) →
+                             (T1 = T2 → ⊥) ∨ (T1 = T2 ∧ (V1 = V2 → ⊥)).
 #I #V1 #T1 #V2 #T2 #H
 elim (term_eq_dec T1 T2) /3 width=1/ #HT12 destruct
 @or_intror @conj // #HT12 destruct /2 width=1/
 qed-.
 
-lemma eq_false_inv_beta: ∀V1,V2,W1,W2,T1,T2.
-                         (ⓐV1. ⓛW1. T1 = ⓐV2. ⓛW2 .T2 →False) →
-                         (W1 = W2 → False) ∨
-                         (W1 = W2 ∧ (ⓓV1. T1 = ⓓV2. T2 → False)).
-#V1 #V2 #W1 #W2 #T1 #T2 #H
+lemma eq_false_inv_beta: ∀a,V1,V2,W1,W2,T1,T2.
+                         (ⓐV1. ⓛ{a}W1. T1 = ⓐV2. ⓛ{a}W2 .T2 → ⊥) →
+                         (W1 = W2 → ⊥) ∨
+                         (W1 = W2 ∧ (ⓓ{a}V1. T1 = ⓓ{a}V2. T2 → ⊥)).
+#a #V1 #V2 #W1 #W2 #T1 #T2 #H
 elim (eq_false_inv_tpair_sn … H) -H
 [ #HV12 elim (term_eq_dec W1 W2) /3 width=1/
   #H destruct @or_intror @conj // #H destruct /2 width=1/