- bug fix in the induction for the closure property

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/grammar/term.ma b/matita/matita/contribs/lambdadelta/basic_2/grammar/term.ma
index 5ccb5e4accdf9482813b9fe5c8ecb203c46608b9..5b62fa9405e497856ec2bb5f429080d7be44b016 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/grammar/term.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/grammar/term.ma
@@ -12,6 +12,23 @@
 (*                                                                        *)
 (**************************************************************************)
 
+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/grammar/item.ma".
 
 (* TERMS ********************************************************************)
@@ -76,7 +93,7 @@ interpretation "native type annotation (term)"
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: term_dec *)
-axiom term_eq_dec: ∀T1,T2:term. Decidable (T1 = T2).
+axiom eq_term_dec: ∀T1,T2:term. Decidable (T1 = T2).
 
 (* Basic inversion lemmas ***************************************************)
 
@@ -103,33 +120,18 @@ 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 (term_eq_dec V1 V2) /3 width=1/ #HV12 destruct
-@or_intror @conj // #HT12 destruct /2 width=1/ 
+elim (eq_term_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 → ⊥) →
                              (T1 = T2 → ⊥) ∨ (T1 = T2 ∧ (V1 = V2 → ⊥)).
 #I #V1 #T1 #V2 #T2 #H
-elim (term_eq_dec T1 T2) /3 width=1/ #HT12 destruct
+elim (eq_term_dec T1 T2) /3 width=1/ #HT12 destruct
 @or_intror @conj // #HT12 destruct /2 width=1/
 qed-.
 
-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/
-| * #H1 #H2 destruct
-  elim (eq_false_inv_tpair_sn … H2) -H2 /3 width=1/
-  * #H #HT12 destruct
-  @or_intror @conj // #H destruct /2 width=1/
-]
-qed.
-
 (* Basic_1: removed theorems 3:
             not_void_abst not_abbr_void not_abst_void
 *)