- the substitution lemma is proved!

[helm.git] / matita / matita / contribs / lambda-delta / Basic-2 / substitution / lift.ma

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/lift.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/lift.ma
index 0a4e1715abe3d0e7468a7eee4bd59f38fabe60ed..48e37d63096e4926430f43432d94044b5e37920c 100644 (file)
--- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/lift.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/substitution/lift.ma
@@ -16,6 +16,9 @@ include "Basic-2/grammar/term_weight.ma".
 
 (* RELOCATION ***************************************************************)
 
+(* Basic-1: includes:
+            lift_sort lift_lref_lt lift_lref_ge lift_bind lift_flat
+*)
 inductive lift: term → nat → nat → term → Prop ≝
 | lift_sort   : ∀k,d,e. lift (⋆k) d e (⋆k)
 | lift_lref_lt: ∀i,d,e. i < d → lift (#i) d e (#i)
@@ -32,10 +35,12 @@ interpretation "relocation" 'RLift T1 d e T2 = (lift T1 d e T2).
 
 (* Basic properties *********************************************************)
 
+(* Basic-1: was: lift_lref_gt *)
 lemma lift_lref_ge_minus: ∀d,e,i. d + e ≤ i → ↑[d, e] #(i - e) ≡ #i.
 #d #e #i #H >(plus_minus_m_m i e) in ⊢ (? ? ? ? %) /3/
 qed.
 
+(* Basic-1: was: lift_r *)
 lemma lift_refl: ∀T,d. ↑[d, 0] T ≡ T.
 #T elim T -T
 [ * #i // #d elim (lt_or_ge i d) /2/
@@ -54,6 +59,7 @@ lemma lift_total: ∀T1,d,e. ∃T2. ↑[d,e] T1 ≡ T2.
 ]
 qed.
 
+(* Basic-1: was: lift_free (right to left) *)
 lemma lift_split: ∀d1,e2,T1,T2. ↑[d1, e2] T1 ≡ T2 → ∀d2,e1.
                                 d1 ≤ d2 → d2 ≤ d1 + e1 → e1 ≤ e2 →
                                 ∃∃T. ↑[d1, e1] T1 ≡ T & ↑[d2, e2 - e1] T ≡ T2.
@@ -170,6 +176,7 @@ 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: ∀d,e,T1,k. ↑[d,e] T1 ≡ ⋆k → T1 = ⋆k.
 /2 width=5/ qed.
 
@@ -184,16 +191,21 @@ 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: ∀d,e,T1,i. ↑[d,e] T1 ≡ #i →
                       (i < d ∧ T1 = #i) ∨ (d + e ≤ i ∧ T1 = #(i - e)).
 /2/ qed.
 
+(* Basic-1: was: lift_gen_lref_lt *)
 lemma lift_inv_lref2_lt: ∀d,e,T1,i. ↑[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 (plus_lt_false … Hdd)
 qed.
 
+(* Basic-1: was: lift_gen_lref_false *)
+
+(* Basic-1: was: lift_gen_lref_ge *)
 lemma lift_inv_lref2_ge: ∀d,e,T1,i. ↑[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
@@ -213,6 +225,7 @@ fact lift_inv_bind2_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 →
 ]
 qed.
 
+(* Basic-1: was: lift_gen_bind *)
 lemma lift_inv_bind2: ∀d,e,T1,I,V2,U2. ↑[d,e] T1 ≡  𝕓{I} V2. U2 →
                       ∃∃V1,U1. ↑[d,e] V1 ≡ V2 & ↑[d+1,e] U1 ≡ U2 &
                                T1 = 𝕓{I} V1. U1.
@@ -231,7 +244,14 @@ fact lift_inv_flat2_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 →
 ]
 qed.
 
+(* Basic-1: was: lift_gen_flat *)
 lemma lift_inv_flat2: ∀d,e,T1,I,V2,U2. ↑[d,e] T1 ≡  𝕗{I} V2. U2 →
                       ∃∃V1,U1. ↑[d,e] V1 ≡ V2 & ↑[d,e] U1 ≡ U2 &
                                T1 = 𝕗{I} V1. U1.
 /2/ qed.
+
+(* Basic-1: removed theorems 7:
+            lift_head lift_gen_head
+            lift_weight_map lift_weight lift_weight_add lift_weight_add_O
+            lift_tlt_dx
+*)