notational change of lift, drop, and gget

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lift.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lift.ma
index f8848629202d42750d885d59d179636b93995ace..d6537046caf4051af2f50853896f467d95f232ed 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lift.ma
@@ -38,14 +38,14 @@ interpretation "relocation" 'RLift d e T1 T2 = (lift d e T1 T2).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lift_inv_O2_aux: â\88\80d,e,T1,T2. â\87§[d, e] T1 ≡ T2 → e = 0 → T1 = T2.
+fact lift_inv_O2_aux: â\88\80d,e,T1,T2. â¬\86[d, e] T1 ≡ T2 → e = 0 → T1 = T2.
 #d #e #T1 #T2 #H elim H -d -e -T1 -T2 /3 width=1 by eq_f2/
 qed-.
 
-lemma lift_inv_O2: â\88\80d,T1,T2. â\87§[d, 0] T1 ≡ T2 → T1 = T2.
+lemma lift_inv_O2: â\88\80d,T1,T2. â¬\86[d, 0] T1 ≡ T2 → T1 = T2.
 /2 width=4 by lift_inv_O2_aux/ qed-.
 
-fact lift_inv_sort1_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 → ∀k. T1 = ⋆k → T2 = ⋆k.
+fact lift_inv_sort1_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 → ∀k. T1 = ⋆k → T2 = ⋆k.
 #d #e #T1 #T2 * -d -e -T1 -T2 //
 [ #i #d #e #_ #k #H destruct
 | #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct
@@ -53,10 +53,10 @@ fact lift_inv_sort1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀k. T1 = ⋆k 
 ]
 qed-.
 
-lemma lift_inv_sort1: â\88\80d,e,T2,k. â\87§[d,e] ⋆k ≡ T2 → T2 = ⋆k.
+lemma lift_inv_sort1: â\88\80d,e,T2,k. â¬\86[d,e] ⋆k ≡ T2 → T2 = ⋆k.
 /2 width=5 by lift_inv_sort1_aux/ qed-.
 
-fact lift_inv_lref1_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 → ∀i. T1 = #i →
+fact lift_inv_lref1_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 → ∀i. T1 = #i →
                          (i < d ∧ T2 = #i) ∨ (d ≤ i ∧ T2 = #(i + e)).
 #d #e #T1 #T2 * -d -e -T1 -T2
 [ #k #d #e #i #H destruct
@@ -68,23 +68,23 @@ fact lift_inv_lref1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀i. T1 = #i →
 ]
 qed-.
 
-lemma lift_inv_lref1: â\88\80d,e,T2,i. â\87§[d,e] #i ≡ T2 →
+lemma lift_inv_lref1: â\88\80d,e,T2,i. â¬\86[d,e] #i ≡ T2 →
                       (i < d ∧ T2 = #i) ∨ (d ≤ i ∧ T2 = #(i + e)).
 /2 width=3 by lift_inv_lref1_aux/ qed-.
 
-lemma lift_inv_lref1_lt: â\88\80d,e,T2,i. â\87§[d,e] #i ≡ T2 → i < d → T2 = #i.
+lemma lift_inv_lref1_lt: â\88\80d,e,T2,i. â¬\86[d,e] #i ≡ T2 → i < d → T2 = #i.
 #d #e #T2 #i #H elim (lift_inv_lref1 … H) -H * //
 #Hdi #_ #Hid lapply (le_to_lt_to_lt … Hdi Hid) -Hdi -Hid #Hdd
 elim (lt_refl_false … Hdd)
 qed-.
 
-lemma lift_inv_lref1_ge: â\88\80d,e,T2,i. â\87§[d,e] #i ≡ T2 → d ≤ i → T2 = #(i + e).
+lemma lift_inv_lref1_ge: â\88\80d,e,T2,i. â¬\86[d,e] #i ≡ T2 → d ≤ i → T2 = #(i + e).
 #d #e #T2 #i #H elim (lift_inv_lref1 … H) -H * //
 #Hid #_ #Hdi lapply (le_to_lt_to_lt … Hdi Hid) -Hdi -Hid #Hdd
 elim (lt_refl_false … Hdd)
 qed-.
 
-fact lift_inv_gref1_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 → ∀p. T1 = §p → T2 = §p.
+fact lift_inv_gref1_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 → ∀p. T1 = §p → T2 = §p.
 #d #e #T1 #T2 * -d -e -T1 -T2 //
 [ #i #d #e #_ #k #H destruct
 | #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct
@@ -92,12 +92,12 @@ fact lift_inv_gref1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀p. T1 = §p →
 ]
 qed-.
 
-lemma lift_inv_gref1: â\88\80d,e,T2,p. â\87§[d,e] §p ≡ T2 → T2 = §p.
+lemma lift_inv_gref1: â\88\80d,e,T2,p. â¬\86[d,e] §p ≡ T2 → T2 = §p.
 /2 width=5 by lift_inv_gref1_aux/ qed-.
 
-fact lift_inv_bind1_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 →
+fact lift_inv_bind1_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 →
                          ∀a,I,V1,U1. T1 = ⓑ{a,I} V1.U1 →
-                         â\88\83â\88\83V2,U2. â\87§[d,e] V1 â\89¡ V2 & â\87§[d+1,e] U1 ≡ U2 &
+                         â\88\83â\88\83V2,U2. â¬\86[d,e] V1 â\89¡ V2 & â¬\86[d+1,e] U1 ≡ U2 &
                                   T2 = ⓑ{a,I} V2. U2.
 #d #e #T1 #T2 * -d -e -T1 -T2
 [ #k #d #e #a #I #V1 #U1 #H destruct
@@ -109,14 +109,14 @@ fact lift_inv_bind1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 →
 ]
 qed-.
 
-lemma lift_inv_bind1: â\88\80d,e,T2,a,I,V1,U1. â\87§[d,e] ⓑ{a,I} V1. U1 ≡ T2 →
-                      â\88\83â\88\83V2,U2. â\87§[d,e] V1 â\89¡ V2 & â\87§[d+1,e] U1 ≡ U2 &
+lemma lift_inv_bind1: â\88\80d,e,T2,a,I,V1,U1. â¬\86[d,e] ⓑ{a,I} V1. U1 ≡ T2 →
+                      â\88\83â\88\83V2,U2. â¬\86[d,e] V1 â\89¡ V2 & â¬\86[d+1,e] U1 ≡ U2 &
                                T2 = ⓑ{a,I} V2. U2.
 /2 width=3 by lift_inv_bind1_aux/ qed-.
 
-fact lift_inv_flat1_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 →
+fact lift_inv_flat1_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 →
                          ∀I,V1,U1. T1 = ⓕ{I} V1.U1 →
-                         â\88\83â\88\83V2,U2. â\87§[d,e] V1 â\89¡ V2 & â\87§[d,e] U1 ≡ U2 &
+                         â\88\83â\88\83V2,U2. â¬\86[d,e] V1 â\89¡ V2 & â¬\86[d,e] U1 ≡ U2 &
                                   T2 = ⓕ{I} V2. U2.
 #d #e #T1 #T2 * -d -e -T1 -T2
 [ #k #d #e #I #V1 #U1 #H destruct
@@ -128,12 +128,12 @@ fact lift_inv_flat1_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 →
 ]
 qed-.
 
-lemma lift_inv_flat1: â\88\80d,e,T2,I,V1,U1. â\87§[d,e] ⓕ{I} V1. U1 ≡ T2 →
-                      â\88\83â\88\83V2,U2. â\87§[d,e] V1 â\89¡ V2 & â\87§[d,e] U1 ≡ U2 &
+lemma lift_inv_flat1: â\88\80d,e,T2,I,V1,U1. â¬\86[d,e] ⓕ{I} V1. U1 ≡ T2 →
+                      â\88\83â\88\83V2,U2. â¬\86[d,e] V1 â\89¡ V2 & â¬\86[d,e] U1 ≡ U2 &
                                T2 = ⓕ{I} V2. U2.
 /2 width=3 by lift_inv_flat1_aux/ qed-.
 
-fact lift_inv_sort2_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 → ∀k. T2 = ⋆k → T1 = ⋆k.
+fact lift_inv_sort2_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 → ∀k. T2 = ⋆k → T1 = ⋆k.
 #d #e #T1 #T2 * -d -e -T1 -T2 //
 [ #i #d #e #_ #k #H destruct
 | #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct
@@ -142,10 +142,10 @@ fact lift_inv_sort2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀k. T2 = ⋆k 
 qed-.
 
 (* Basic_1: was: lift_gen_sort *)
-lemma lift_inv_sort2: â\88\80d,e,T1,k. â\87§[d,e] T1 ≡ ⋆k → T1 = ⋆k.
+lemma lift_inv_sort2: â\88\80d,e,T1,k. â¬\86[d,e] T1 ≡ ⋆k → T1 = ⋆k.
 /2 width=5 by lift_inv_sort2_aux/ qed-.
 
-fact lift_inv_lref2_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 → ∀i. T2 = #i →
+fact lift_inv_lref2_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 → ∀i. T2 = #i →
                          (i < d ∧ T1 = #i) ∨ (d + e ≤ i ∧ T1 = #(i - e)).
 #d #e #T1 #T2 * -d -e -T1 -T2
 [ #k #d #e #i #H destruct
@@ -158,12 +158,12 @@ fact lift_inv_lref2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀i. T2 = #i →
 qed-.
 
 (* Basic_1: was: lift_gen_lref *)
-lemma lift_inv_lref2: â\88\80d,e,T1,i. â\87§[d,e] T1 ≡ #i →
+lemma lift_inv_lref2: â\88\80d,e,T1,i. â¬\86[d,e] T1 ≡ #i →
                       (i < d ∧ T1 = #i) ∨ (d + e ≤ i ∧ T1 = #(i - e)).
 /2 width=3 by lift_inv_lref2_aux/ qed-.
 
 (* Basic_1: was: lift_gen_lref_lt *)
-lemma lift_inv_lref2_lt: â\88\80d,e,T1,i. â\87§[d,e] T1 ≡ #i → i < d → T1 = #i.
+lemma lift_inv_lref2_lt: â\88\80d,e,T1,i. â¬\86[d,e] T1 ≡ #i → i < d → T1 = #i.
 #d #e #T1 #i #H elim (lift_inv_lref2 … H) -H * //
 #Hdi #_ #Hid lapply (le_to_lt_to_lt … Hdi Hid) -Hdi -Hid #Hdd
 elim (lt_inv_plus_l … Hdd) -Hdd #Hdd
@@ -171,7 +171,7 @@ elim (lt_refl_false … Hdd)
 qed-.
 
 (* Basic_1: was: lift_gen_lref_false *)
-lemma lift_inv_lref2_be: â\88\80d,e,T1,i. â\87§[d,e] T1 ≡ #i →
+lemma lift_inv_lref2_be: â\88\80d,e,T1,i. â¬\86[d,e] T1 ≡ #i →
                          d ≤ i → i < d + e → ⊥.
 #d #e #T1 #i #H elim (lift_inv_lref2 … H) -H *
 [ #H1 #_ #H2 #_ | #H2 #_ #_ #H1 ]
@@ -180,14 +180,14 @@ elim (lt_refl_false … H)
 qed-.
 
 (* Basic_1: was: lift_gen_lref_ge *)
-lemma lift_inv_lref2_ge: â\88\80d,e,T1,i. â\87§[d,e] T1 ≡ #i → d + e ≤ i → T1 = #(i - e).
+lemma lift_inv_lref2_ge: â\88\80d,e,T1,i. â¬\86[d,e] T1 ≡ #i → d + e ≤ i → T1 = #(i - e).
 #d #e #T1 #i #H elim (lift_inv_lref2 … H) -H * //
 #Hid #_ #Hdi lapply (le_to_lt_to_lt … Hdi Hid) -Hdi -Hid #Hdd
 elim (lt_inv_plus_l … Hdd) -Hdd #Hdd
 elim (lt_refl_false … Hdd)
 qed-.
 
-fact lift_inv_gref2_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 → ∀p. T2 = §p → T1 = §p.
+fact lift_inv_gref2_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 → ∀p. T2 = §p → T1 = §p.
 #d #e #T1 #T2 * -d -e -T1 -T2 //
 [ #i #d #e #_ #k #H destruct
 | #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct
@@ -195,12 +195,12 @@ fact lift_inv_gref2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 → ∀p. T2 = §p →
 ]
 qed-.
 
-lemma lift_inv_gref2: â\88\80d,e,T1,p. â\87§[d,e] T1 ≡ §p → T1 = §p.
+lemma lift_inv_gref2: â\88\80d,e,T1,p. â¬\86[d,e] T1 ≡ §p → T1 = §p.
 /2 width=5 by lift_inv_gref2_aux/ qed-.
 
-fact lift_inv_bind2_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 →
+fact lift_inv_bind2_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 →
                          ∀a,I,V2,U2. T2 = ⓑ{a,I} V2.U2 →
-                         â\88\83â\88\83V1,U1. â\87§[d,e] V1 â\89¡ V2 & â\87§[d+1,e] U1 ≡ U2 &
+                         â\88\83â\88\83V1,U1. â¬\86[d,e] V1 â\89¡ V2 & â¬\86[d+1,e] U1 ≡ U2 &
                                   T1 = ⓑ{a,I} V1. U1.
 #d #e #T1 #T2 * -d -e -T1 -T2
 [ #k #d #e #a #I #V2 #U2 #H destruct
@@ -213,14 +213,14 @@ fact lift_inv_bind2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 →
 qed-.
 
 (* Basic_1: was: lift_gen_bind *)
-lemma lift_inv_bind2: â\88\80d,e,T1,a,I,V2,U2. â\87§[d,e] T1 ≡ ⓑ{a,I} V2. U2 →
-                      â\88\83â\88\83V1,U1. â\87§[d,e] V1 â\89¡ V2 & â\87§[d+1,e] U1 ≡ U2 &
+lemma lift_inv_bind2: â\88\80d,e,T1,a,I,V2,U2. â¬\86[d,e] T1 ≡ ⓑ{a,I} V2. U2 →
+                      â\88\83â\88\83V1,U1. â¬\86[d,e] V1 â\89¡ V2 & â¬\86[d+1,e] U1 ≡ U2 &
                                T1 = ⓑ{a,I} V1. U1.
 /2 width=3 by lift_inv_bind2_aux/ qed-.
 
-fact lift_inv_flat2_aux: â\88\80d,e,T1,T2. â\87§[d,e] T1 ≡ T2 →
+fact lift_inv_flat2_aux: â\88\80d,e,T1,T2. â¬\86[d,e] T1 ≡ T2 →
                          ∀I,V2,U2. T2 = ⓕ{I} V2.U2 →
-                         â\88\83â\88\83V1,U1. â\87§[d,e] V1 â\89¡ V2 & â\87§[d,e] U1 ≡ U2 &
+                         â\88\83â\88\83V1,U1. â¬\86[d,e] V1 â\89¡ V2 & â¬\86[d,e] U1 ≡ U2 &
                                   T1 = ⓕ{I} V1. U1.
 #d #e #T1 #T2 * -d -e -T1 -T2
 [ #k #d #e #I #V2 #U2 #H destruct
@@ -233,12 +233,12 @@ fact lift_inv_flat2_aux: ∀d,e,T1,T2. ⇧[d,e] T1 ≡ T2 →
 qed-.
 
 (* Basic_1: was: lift_gen_flat *)
-lemma lift_inv_flat2: â\88\80d,e,T1,I,V2,U2. â\87§[d,e] T1 ≡  ⓕ{I} V2. U2 →
-                      â\88\83â\88\83V1,U1. â\87§[d,e] V1 â\89¡ V2 & â\87§[d,e] U1 ≡ U2 &
+lemma lift_inv_flat2: â\88\80d,e,T1,I,V2,U2. â¬\86[d,e] T1 ≡  ⓕ{I} V2. U2 →
+                      â\88\83â\88\83V1,U1. â¬\86[d,e] V1 â\89¡ V2 & â¬\86[d,e] U1 ≡ U2 &
                                T1 = ⓕ{I} V1. U1.
 /2 width=3 by lift_inv_flat2_aux/ qed-.
 
-lemma lift_inv_pair_xy_x: â\88\80d,e,I,V,T. â\87§[d, e] ②{I} V. T ≡ V → ⊥.
+lemma lift_inv_pair_xy_x: â\88\80d,e,I,V,T. â¬\86[d, e] ②{I} V. T ≡ V → ⊥.
 #d #e #J #V elim V -V
 [ * #i #T #H
   [ lapply (lift_inv_sort2 … H) -H #H destruct
@@ -253,7 +253,7 @@ lemma lift_inv_pair_xy_x: ∀d,e,I,V,T. ⇧[d, e] ②{I} V. T ≡ V → ⊥.
 qed-.
 
 (* Basic_1: was: thead_x_lift_y_y *)
-lemma lift_inv_pair_xy_y: â\88\80I,T,V,d,e. â\87§[d, e] ②{I} V. T ≡ T → ⊥.
+lemma lift_inv_pair_xy_y: â\88\80I,T,V,d,e. â¬\86[d, e] ②{I} V. T ≡ T → ⊥.
 #J #T elim T -T
 [ * #i #V #d #e #H
   [ lapply (lift_inv_sort2 … H) -H #H destruct
@@ -269,33 +269,33 @@ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lift_fwd_pair1: â\88\80I,T2,V1,U1,d,e. â\87§[d,e] ②{I}V1.U1 ≡ T2 →
-                      â\88\83â\88\83V2,U2. â\87§[d,e] V1 ≡ V2 & T2 = ②{I}V2.U2.
+lemma lift_fwd_pair1: â\88\80I,T2,V1,U1,d,e. â¬\86[d,e] ②{I}V1.U1 ≡ T2 →
+                      â\88\83â\88\83V2,U2. â¬\86[d,e] V1 ≡ V2 & T2 = ②{I}V2.U2.
 * [ #a ] #I #T2 #V1 #U1 #d #e #H
 [ elim (lift_inv_bind1 … H) -H /2 width=4 by ex2_2_intro/
 |  elim (lift_inv_flat1 … H) -H /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
-lemma lift_fwd_pair2: â\88\80I,T1,V2,U2,d,e. â\87§[d,e] T1 ≡ ②{I}V2.U2 →
-                      â\88\83â\88\83V1,U1. â\87§[d,e] V1 ≡ V2 & T1 = ②{I}V1.U1.
+lemma lift_fwd_pair2: â\88\80I,T1,V2,U2,d,e. â¬\86[d,e] T1 ≡ ②{I}V2.U2 →
+                      â\88\83â\88\83V1,U1. â¬\86[d,e] V1 ≡ V2 & T1 = ②{I}V1.U1.
 * [ #a ] #I #T1 #V2 #U2 #d #e #H
 [ elim (lift_inv_bind2 … H) -H /2 width=4 by ex2_2_intro/
 |  elim (lift_inv_flat2 … H) -H /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
-lemma lift_fwd_tw: â\88\80d,e,T1,T2. â\87§[d, e] T1 ≡ T2 → ♯{T1} = ♯{T2}.
+lemma lift_fwd_tw: â\88\80d,e,T1,T2. â¬\86[d, e] T1 ≡ T2 → ♯{T1} = ♯{T2}.
 #d #e #T1 #T2 #H elim H -d -e -T1 -T2 normalize //
 qed-.
 
-lemma lift_simple_dx: â\88\80d,e,T1,T2. â\87§[d, e] T1 ≡ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
+lemma lift_simple_dx: â\88\80d,e,T1,T2. â¬\86[d, e] T1 ≡ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
 #d #e #T1 #T2 #H elim H -d -e -T1 -T2 //
 #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #H
 elim (simple_inv_bind … H)
 qed-.
 
-lemma lift_simple_sn: â\88\80d,e,T1,T2. â\87§[d, e] T1 ≡ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
+lemma lift_simple_sn: â\88\80d,e,T1,T2. â¬\86[d, e] T1 ≡ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
 #d #e #T1 #T2 #H elim H -d -e -T1 -T2 //
 #a #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #H
 elim (simple_inv_bind … H)
@@ -304,22 +304,22 @@ qed-.
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: lift_lref_gt *)
-lemma lift_lref_ge_minus: â\88\80d,e,i. d + e â\89¤ i â\86\92 â\87§[d, e] #(i - e) ≡ #i.
+lemma lift_lref_ge_minus: â\88\80d,e,i. d + e â\89¤ i â\86\92 â¬\86[d, e] #(i - e) ≡ #i.
 #d #e #i #H >(plus_minus_m_m i e) in ⊢ (? ? ? ? %); /3 width=2 by lift_lref_ge, le_plus_to_minus_r, le_plus_b/
 qed.
 
-lemma lift_lref_ge_minus_eq: â\88\80d,e,i,j. d + e â\89¤ i â\86\92 j = i - e â\86\92 â\87§[d, e] #j ≡ #i.
+lemma lift_lref_ge_minus_eq: â\88\80d,e,i,j. d + e â\89¤ i â\86\92 j = i - e â\86\92 â¬\86[d, e] #j ≡ #i.
 /2 width=1/ qed-.
 
 (* Basic_1: was: lift_r *)
-lemma lift_refl: â\88\80T,d. â\87§[d, 0] T ≡ T.
+lemma lift_refl: â\88\80T,d. â¬\86[d, 0] T ≡ T.
 #T elim T -T
 [ * #i // #d elim (lt_or_ge i d) /2 width=1 by lift_lref_lt, lift_lref_ge/
 | * /2 width=1 by lift_bind, lift_flat/
 ]
 qed.
 
-lemma lift_total: â\88\80T1,d,e. â\88\83T2. â\87§[d,e] T1 ≡ T2.
+lemma lift_total: â\88\80T1,d,e. â\88\83T2. â¬\86[d,e] T1 ≡ T2.
 #T1 elim T1 -T1
 [ * #i /2 width=2/ #d #e elim (lt_or_ge i d) /3 width=2 by lift_lref_lt, lift_lref_ge, ex_intro/
 | * [ #a ] #I #V1 #T1 #IHV1 #IHT1 #d #e
@@ -331,9 +331,9 @@ lemma lift_total: ∀T1,d,e. ∃T2. ⇧[d,e] T1 ≡ T2.
 qed.
 
 (* Basic_1: was: lift_free (right to left) *)
-lemma lift_split: â\88\80d1,e2,T1,T2. â\87§[d1, e2] T1 ≡ T2 →
+lemma lift_split: â\88\80d1,e2,T1,T2. â¬\86[d1, e2] T1 ≡ T2 →
                   ∀d2,e1. d1 ≤ d2 → d2 ≤ d1 + e1 → e1 ≤ e2 →
-                  â\88\83â\88\83T. â\87§[d1, e1] T1 â\89¡ T & â\87§[d2, e2 - e1] T ≡ T2.
+                  â\88\83â\88\83T. â¬\86[d1, e1] T1 â\89¡ T & â¬\86[d2, e2 - e1] T ≡ T2.
 #d1 #e2 #T1 #T2 #H elim H -d1 -e2 -T1 -T2
 [ /3 width=3/
 | #i #d1 #e2 #Hid1 #d2 #e1 #Hd12 #_ #_
@@ -352,7 +352,7 @@ lemma lift_split: ∀d1,e2,T1,T2. ⇧[d1, e2] T1 ≡ T2 →
 qed.
 
 (* Basic_1: was only: dnf_dec2 dnf_dec *)
-lemma is_lift_dec: â\88\80T2,d,e. Decidable (â\88\83T1. â\87§[d,e] T1 ≡ T2).
+lemma is_lift_dec: â\88\80T2,d,e. Decidable (â\88\83T1. â¬\86[d,e] T1 ≡ T2).
 #T1 elim T1 -T1
 [ * [1,3: /3 width=2 by lift_sort, lift_gref, ex_intro, or_introl/ ] #i #d #e
   elim (lt_or_ge i d) #Hdi