- predefined_virtuals: an addition

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / unfold / gr2.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2.ma
index b8dab57aea8efc8659e9fd1c15028e9fd7a248af..1168e52dffd4860f5a76601ea844c1f7c9068cd5 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/gr2.ma
@@ -19,9 +19,9 @@ include "basic_2/grammar/term_vector.ma".
 inductive at: list2 nat nat → relation nat ≝
 | 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 des i1 i2 → at ({d, e} @ des) i1 i2
 | at_ge : ∀des,d,e,i1,i2. d ≤ i1 →
-          at des (i1 + e) i2 → at ({d, e} :: des) i1 i2
+          at des (i1 + e) i2 → at ({d, e} @ des) i1 i2
 .
 
 interpretation "application (generic relocation with pairs)"
@@ -41,7 +41,7 @@ lemma at_inv_nil: ∀i1,i2. @[i1] ⟠ ≡ i2 → i1 = i2.
 /2 width=3/ qed-.
 
 fact at_inv_cons_aux: ∀des,i1,i2. @[i1] des ≡ i2 →
-                      ∀d,e,des0. des = {d, e} :: des0 →
+                      ∀d,e,des0. des = {d, e} @ des0 →
                       i1 < d ∧ @[i1] des0 ≡ i2 ∨
                       d ≤ i1 ∧ @[i1 + e] des0 ≡ i2.
 #des #i1 #i2 * -des -i1 -i2
@@ -51,12 +51,12 @@ fact at_inv_cons_aux: ∀des,i1,i2. @[i1] des ≡ i2 →
 ]
 qed.
 
-lemma at_inv_cons: ∀des,d,e,i1,i2. @[i1] {d, e} :: des ≡ i2 →
+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-.
 
-lemma at_inv_cons_lt: ∀des,d,e,i1,i2. @[i1] {d, e} :: des ≡ i2 →
+lemma at_inv_cons_lt: ∀des,d,e,i1,i2. @[i1] {d, e} @ des ≡ i2 →
                       i1 < d → @[i1] des ≡ i2.
 #des #d #e #i1 #e2 #H
 elim (at_inv_cons … H) -H * // #Hdi1 #_ #Hi1d
@@ -64,7 +64,7 @@ lapply (le_to_lt_to_lt … Hdi1 Hi1d) -Hdi1 -Hi1d #Hd
 elim (lt_refl_false … Hd)
 qed-.
 
-lemma at_inv_cons_ge: ∀des,d,e,i1,i2. @[i1] {d, e} :: des ≡ i2 →
+lemma at_inv_cons_ge: ∀des,d,e,i1,i2. @[i1] {d, e} @ des ≡ i2 →
                       d ≤ i1 → @[i1 + e] des ≡ i2.
 #des #d #e #i1 #e2 #H
 elim (at_inv_cons … H) -H * // #Hi1d #_ #Hdi1