X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Frelocation%2Fmr2_minus.ma;h=81544fe29e3e7add2a7beab566475537d339a0b9;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=9fd40ad6bfc0a78e6c1347b9522bedb62beb99db;hpb=5102e7f780e83c7fef1d3826f81dfd37ee4028bc;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_minus.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_minus.ma
index 9fd40ad6b..81544fe29 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_minus.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_minus.ma
@@ -20,9 +20,9 @@ include "ground_2/relocation/mr2.ma".
 inductive minuss: nat → relation mr2 ≝
 | minuss_nil: ∀i. minuss i (◊) (◊)
 | minuss_lt : ∀cs1,cs2,l,m,i. i < l → minuss i cs1 cs2 →
-              minuss i ({l, m} @ cs1) ({l - i, m} @ cs2)
+              minuss i (❨l, m❩;cs1) (❨l - i, m❩;cs2)
 | minuss_ge : ∀cs1,cs2,l,m,i. l ≤ i → minuss (m + i) cs1 cs2 →
-              minuss i ({l, m} @ cs1) cs2
+              minuss i (❨l, m❩;cs1) cs2
 .
 
 interpretation "minus (multiple relocation with pairs)"
@@ -30,7 +30,7 @@ interpretation "minus (multiple relocation with pairs)"
 
 (* Basic inversion lemmas ***************************************************)
 
-fact minuss_inv_nil1_aux: ∀cs1,cs2,i. cs1 ▭ i ≡ cs2 → cs1 = ◊ → cs2 = ◊.
+fact minuss_inv_nil1_aux: ∀cs1,cs2,i. cs1 ▭ i ≘ cs2 → cs1 = ◊ → cs2 = ◊.
 #cs1 #cs2 #i * -cs1 -cs2 -i
 [ //
 | #cs1 #cs2 #l #m #i #_ #_ #H destruct
@@ -38,14 +38,14 @@ fact minuss_inv_nil1_aux: ∀cs1,cs2,i. cs1 ▭ i ≡ cs2 → cs1 = ◊ → cs2
 ]
 qed-.
 
-lemma minuss_inv_nil1: ∀cs2,i. ◊ ▭ i ≡ cs2 → cs2 = ◊.
+lemma minuss_inv_nil1: ∀cs2,i. ◊ ▭ i ≘ cs2 → cs2 = ◊.
 /2 width=4 by minuss_inv_nil1_aux/ qed-.
 
-fact minuss_inv_cons1_aux: ∀cs1,cs2,i. cs1 ▭ i ≡ cs2 →
-                           ∀l,m,cs. cs1 = {l, m} @ cs →
-                           l ≤ i ∧ cs ▭ m + i ≡ cs2 ∨
-                           ∃∃cs0. i < l & cs ▭ i ≡ cs0 &
-                                   cs2 = {l - i, m} @ cs0.
+fact minuss_inv_cons1_aux: ∀cs1,cs2,i. cs1 ▭ i ≘ cs2 →
+                           ∀l,m,cs. cs1 = ❨l, m❩;cs →
+                           l ≤ i ∧ cs ▭ m + i ≘ cs2 ∨
+                           ∃∃cs0. i < l & cs ▭ i ≘ cs0 &
+                                   cs2 = ❨l - i, m❩;cs0.
 #cs1 #cs2 #i * -cs1 -cs2 -i
 [ #i #l #m #cs #H destruct
 | #cs1 #cs #l1 #m1 #i1 #Hil1 #Hcs #l2 #m2 #cs2 #H destruct /3 width=3 by ex3_intro, or_intror/
@@ -53,22 +53,22 @@ fact minuss_inv_cons1_aux: ∀cs1,cs2,i. cs1 ▭ i ≡ cs2 →
 ]
 qed-.
 
-lemma minuss_inv_cons1: ∀cs1,cs2,l,m,i. {l, m} @ cs1 ▭ i ≡ cs2 →
-                        l ≤ i ∧ cs1 ▭ m + i ≡ cs2 ∨
-                        ∃∃cs. i < l & cs1 ▭ i ≡ cs &
-                               cs2 = {l - i, m} @ cs.
+lemma minuss_inv_cons1: ∀cs1,cs2,l,m,i. ❨l, m❩;cs1 ▭ i ≘ cs2 →
+                        l ≤ i ∧ cs1 ▭ m + i ≘ cs2 ∨
+                        ∃∃cs. i < l & cs1 ▭ i ≘ cs &
+                               cs2 = ❨l - i, m❩;cs.
 /2 width=3 by minuss_inv_cons1_aux/ qed-.
 
-lemma minuss_inv_cons1_ge: ∀cs1,cs2,l,m,i. {l, m} @ cs1 ▭ i ≡ cs2 →
-                           l ≤ i → cs1 ▭ m + i ≡ cs2.
+lemma minuss_inv_cons1_ge: ∀cs1,cs2,l,m,i. ❨l, m❩;cs1 ▭ i ≘ cs2 →
+                           l ≤ i → cs1 ▭ m + i ≘ cs2.
 #cs1 #cs2 #l #m #i #H
 elim (minuss_inv_cons1 … H) -H * // #cs #Hil #_ #_ #Hli
 elim (lt_le_false … Hil Hli)
 qed-.
 
-lemma minuss_inv_cons1_lt: ∀cs1,cs2,l,m,i. {l, m} @ cs1 ▭ i ≡ cs2 →
+lemma minuss_inv_cons1_lt: ∀cs1,cs2,l,m,i. ❨l, m❩;cs1 ▭ i ≘ cs2 →
                            i < l →
-                           ∃∃cs. cs1 ▭ i ≡ cs & cs2 = {l - i, m} @ cs.
+                           ∃∃cs. cs1 ▭ i ≘ cs & cs2 = ❨l - i, m❩;cs.
 #cs1 #cs2 #l #m #i #H elim (minuss_inv_cons1 … H) -H * /2 width=3 by ex2_intro/
 #Hli #_ #Hil elim (lt_le_false … Hil Hli)
 qed-.