update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / mr2_minus.ma

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 9fd40ad6bfc0a78e6c1347b9522bedb62beb99db..81544fe29e3e7add2a7beab566475537d339a0b9 100644 (file)
--- 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: â\88\80cs1,cs2,i. cs1 â\96­ i â\89¡ cs2 → cs1 = ◊ → cs2 = ◊.
+fact minuss_inv_nil1_aux: â\88\80cs1,cs2,i. cs1 â\96­ i â\89\98 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: â\88\80cs2,i. â\97\8a â\96­ i â\89¡ cs2 → cs2 = ◊.
+lemma minuss_inv_nil1: â\88\80cs2,i. â\97\8a â\96­ i â\89\98 cs2 → cs2 = ◊.
 /2 width=4 by minuss_inv_nil1_aux/ qed-.
 
-fact minuss_inv_cons1_aux: â\88\80cs1,cs2,i. cs1 â\96­ i â\89¡ cs2 →
-                           ∀l,m,cs. cs1 = {l, m} @ cs →
-                           l â\89¤ i â\88§ cs â\96­ m + i â\89¡ cs2 ∨
-                           â\88\83â\88\83cs0. i < l & cs â\96­ i â\89¡ cs0 &
-                                   cs2 = {l - i, m} @ cs0.
+fact minuss_inv_cons1_aux: â\88\80cs1,cs2,i. cs1 â\96­ i â\89\98 cs2 →
+                           ∀l,m,cs. cs1 = ❨l, m❩;cs →
+                           l â\89¤ i â\88§ cs â\96­ m + i â\89\98 cs2 ∨
+                           â\88\83â\88\83cs0. i < l & cs â\96­ i â\89\98 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 â\89¤ i â\88§ cs1 â\96­ m + i â\89¡ cs2 ∨
-                        â\88\83â\88\83cs. i < l & cs1 â\96­ i â\89¡ cs &
-                               cs2 = {l - i, m} @ cs.
+lemma minuss_inv_cons1: ∀cs1,cs2,l,m,i. ❨l, m❩;cs1 ▭ i ≘ cs2 →
+                        l â\89¤ i â\88§ cs1 â\96­ m + i â\89\98 cs2 ∨
+                        â\88\83â\88\83cs. i < l & cs1 â\96­ i â\89\98 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 â\89¤ i â\86\92 cs1 â\96­ m + i â\89¡ cs2.
+lemma minuss_inv_cons1_ge: ∀cs1,cs2,l,m,i. ❨l, m❩;cs1 ▭ i ≘ cs2 →
+                           l â\89¤ i â\86\92 cs1 â\96­ m + i â\89\98 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 →
-                           â\88\83â\88\83cs. cs1 â\96­ i â\89¡ cs & cs2 = {l - i, m} @ cs.
+                           â\88\83â\88\83cs. cs1 â\96­ i â\89\98 cs & cs2 = â\9d¨l - i, mâ\9d©;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-.