X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fgrammar%2Flenv.ma;h=80738ebbde5c366fa3ec33662696af5898d44aa0;hb=7d99a19985ae7ca20845d0a875e32f23ba06e536;hp=c34238632d50c18f97f9044bb0295291fa3a3b04;hpb=a2092f7ba4c7c566ea90653ff57e4623ab94d8d5;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/grammar/lenv.ma b/matita/matita/contribs/lambdadelta/basic_2/grammar/lenv.ma
index c34238632..80738ebbd 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/grammar/lenv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/grammar/lenv.ma
@@ -40,12 +40,22 @@ interpretation "abstraction (local environment)"
 
 (* Basic properties *********************************************************)
 
-axiom eq_lenv_dec: ∀L1,L2:lenv. Decidable (L1 = L2).
+lemma eq_lenv_dec: ∀L1,L2:lenv. Decidable (L1 = L2).
+#L1 elim L1 -L1 [| #L1 #I1 #V1 #IHL1 ] * [2,4: #L2 #I2 #V2 ]
+[1,4: @or_intror #H destruct
+| elim (eq_bind2_dec I1 I2) #HI
+  [ elim (eq_term_dec V1 V2) #HV
+    [ elim (IHL1 L2) -IHL1 /2 width=1 by or_introl/ #HL ]
+  ]
+  @or_intror #H destruct /2 width=1 by/
+| /2 width=1 by or_introl/
+]
+qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma destruct_lpair_lpair: ∀I1,I2,L1,L2,V1,V2. L1.ⓑ{I1}V1 = L2.ⓑ{I2}V2 →
-                            ∧∧L1 = L2 & I1 = I2 & V1 = V2.
+fact destruct_lpair_lpair_aux: ∀I1,I2,L1,L2,V1,V2. L1.ⓑ{I1}V1 = L2.ⓑ{I2}V2 →
+                               ∧∧L1 = L2 & I1 = I2 & V1 = V2.
 #I1 #I2 #L1 #L2 #V1 #V2 #H destruct /2 width=1 by and3_intro/
 qed-.
 
@@ -53,6 +63,9 @@ lemma discr_lpair_x_xy: ∀I,V,L. L = L.ⓑ{I}V → ⊥.
 #I #V #L elim L -L
 [ #H destruct
 | #L #J #W #IHL #H
-  elim (destruct_lpair_lpair … H) -H #H1 #H2 #H3 destruct /2 width=1 by/ (**) (* destruct lemma needed *)
+  elim (destruct_lpair_lpair_aux … H) -H #H1 #H2 #H3 destruct /2 width=1 by/ (**) (* destruct lemma needed *)
 ]
 qed-.
+
+lemma discr_lpair_xy_x: ∀I,V,L. L.ⓑ{I}V = L→ ⊥.
+/2 width=4 by discr_lpair_x_xy/ qed-.