X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsubstitution%2Fgr2.ma;h=57bb952b4c101f939dafe3df8872501b14128d0a;hb=e76eade57c0454a58b0d58e5484efe9af417847e;hp=562b795301b0533603ca3f20cad3461aee487c7d;hpb=f16bbb93ecb40fa40f736e0b1158e1c7676a640a;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/gr2.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/gr2.ma
index 562b79530..57bb952b4 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/gr2.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/gr2.ma
@@ -12,12 +12,13 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/rat_3.ma".
 include "basic_2/grammar/term_vector.ma".
 
 (* GENERIC RELOCATION WITH PAIRS ********************************************)
 
 inductive at: list2 nat nat → relation nat ≝
-| at_nil: ∀i. at ⟠ i i
+| at_nil: ∀i. at (⟠) i i
 | at_lt : ∀des,d,e,i1,i2. i1 < d →
           at des i1 i2 → at ({d, e} @ des) i1 i2
 | at_ge : ∀des,d,e,i1,i2. d ≤ i1 →
@@ -35,10 +36,10 @@ fact at_inv_nil_aux: ∀des,i1,i2. @⦃i1, des⦄ ≡ i2 → des = ⟠ → i1 =
 | #des #d #e #i1 #i2 #_ #_ #H destruct
 | #des #d #e #i1 #i2 #_ #_ #H destruct
 ]
-qed.
+qed-.
 
 lemma at_inv_nil: ∀i1,i2. @⦃i1, ⟠⦄ ≡ i2 → i1 = i2.
-/2 width=3/ qed-.
+/2 width=3 by at_inv_nil_aux/ qed-.
 
 fact at_inv_cons_aux: ∀des,i1,i2. @⦃i1, des⦄ ≡ i2 →
                       ∀d,e,des0. des = {d, e} @ des0 →
@@ -46,15 +47,15 @@ fact at_inv_cons_aux: ∀des,i1,i2. @⦃i1, des⦄ ≡ i2 →
                       d ≤ i1 ∧ @⦃i1 + e, des0⦄ ≡ i2.
 #des #i1 #i2 * -des -i1 -i2
 [ #i #d #e #des #H destruct
-| #des1 #d1 #e1 #i1 #i2 #Hid1 #Hi12 #d2 #e2 #des2 #H destruct /3 width=1/
-| #des1 #d1 #e1 #i1 #i2 #Hdi1 #Hi12 #d2 #e2 #des2 #H destruct /3 width=1/
+| #des1 #d1 #e1 #i1 #i2 #Hid1 #Hi12 #d2 #e2 #des2 #H destruct /3 width=1 by or_introl, conj/
+| #des1 #d1 #e1 #i1 #i2 #Hdi1 #Hi12 #d2 #e2 #des2 #H destruct /3 width=1 by or_intror, conj/
 ]
-qed.
+qed-.
 
 lemma at_inv_cons: ∀des,d,e,i1,i2. @⦃i1, {d, e} @ des⦄ ≡ i2 →
                    i1 < d ∧ @⦃i1, des⦄ ≡ i2 ∨
                    d ≤ i1 ∧ @⦃i1 + e, des⦄ ≡ i2.
-/2 width=3/ qed-.
+/2 width=3 by at_inv_cons_aux/ qed-.
 
 lemma at_inv_cons_lt: ∀des,d,e,i1,i2. @⦃i1, {d, e} @ des⦄ ≡ i2 →
                       i1 < d → @⦃i1, des⦄ ≡ i2.