- we introduced the pointer_step rc in the perspective of proving

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / unfold / gr2_minus.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2_minus.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2_minus.ma
index 5e3144c93bf24766564bb3ada5170069b9dc117a..6138548cde489a0f34bd2c6d464b1cde337f3cde 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2_minus.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2_minus.ma
@@ -12,16 +12,16 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/unfold/gr2.ma".
+include "basic_2/unfold/gr2.ma".
 
 (* GENERIC RELOCATION WITH PAIRS ********************************************)
 
 inductive minuss: nat → relation (list2 nat nat) ≝
 | minuss_nil: ∀i. minuss i ⟠ ⟠ 
 | minuss_lt : ∀des1,des2,d,e,i. i < d → minuss i des1 des2 →
-              minuss i ({d, e} :: des1) ({d - i, e} :: des2)
+              minuss i ({d, e} @ des1) ({d - i, e} @ des2)
 | minuss_ge : ∀des1,des2,d,e,i. d ≤ i → minuss (e + i) des1 des2 →
-              minuss i ({d, e} :: des1) des2
+              minuss i ({d, e} @ des1) des2
 .
 
 interpretation "minus (generic relocation with pairs)"
@@ -41,10 +41,10 @@ lemma minuss_inv_nil1: ∀des2,i. ⟠ ▭ i ≡ des2 → des2 = ⟠.
 /2 width=4/ qed-.
 
 fact minuss_inv_cons1_aux: ∀des1,des2,i. des1 ▭ i ≡ des2 →
-                           ∀d,e,des. des1 = {d, e} :: des →
+                           ∀d,e,des. des1 = {d, e} @ des →
                            d ≤ i ∧ des ▭ e + i ≡ des2 ∨
                            ∃∃des0. i < d & des ▭ i ≡ des0 &
-                                   des2 = {d - i, e} :: des0.
+                                   des2 = {d - i, e} @ des0.
 #des1 #des2 #i * -des1 -des2 -i
 [ #i #d #e #des #H destruct 
 | #des1 #des #d1 #e1 #i1 #Hid1 #Hdes #d2 #e2 #des2 #H destruct /3 width=3/
@@ -52,13 +52,13 @@ fact minuss_inv_cons1_aux: ∀des1,des2,i. des1 ▭ i ≡ des2 →
 ]
 qed.
 
-lemma minuss_inv_cons1: ∀des1,des2,d,e,i. {d, e} :: des1 ▭ i ≡ des2 →
+lemma minuss_inv_cons1: ∀des1,des2,d,e,i. {d, e} @ des1 ▭ i ≡ des2 →
                         d ≤ i ∧ des1 ▭ e + i ≡ des2 ∨
                         ∃∃des. i < d & des1 ▭ i ≡ des &
-                               des2 = {d - i, e} :: des.
+                               des2 = {d - i, e} @ des.
 /2 width=3/ qed-.
 
-lemma minuss_inv_cons1_ge: ∀des1,des2,d,e,i. {d, e} :: des1 ▭ i ≡ des2 →
+lemma minuss_inv_cons1_ge: ∀des1,des2,d,e,i. {d, e} @ des1 ▭ i ≡ des2 →
                            d ≤ i → des1 ▭ e + i ≡ des2.
 #des1 #des2 #d #e #i #H
 elim (minuss_inv_cons1 … H) -H * // #des #Hid #_ #_ #Hdi
@@ -66,9 +66,9 @@ lapply (lt_to_le_to_lt … Hid Hdi) -Hid -Hdi #Hi
 elim (lt_refl_false … Hi)
 qed-.
 
-lemma minuss_inv_cons1_lt: ∀des1,des2,d,e,i. {d, e} :: des1 ▭ i ≡ des2 →
+lemma minuss_inv_cons1_lt: ∀des1,des2,d,e,i. {d, e} @ des1 ▭ i ≡ des2 →
                            i < d → 
-                           ∃∃des. des1 ▭ i ≡ des & des2 = {d - i, e} :: des.
+                           ∃∃des. des1 ▭ i ≡ des & des2 = {d - i, e} @ des.
 #des1 #des2 #d #e #i #H
 elim (minuss_inv_cons1 … H) -H * /2 width=3/ #Hdi #_ #Hid
 lapply (lt_to_le_to_lt … Hid Hdi) -Hid -Hdi #Hi