- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / lifts.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts.ma
index 8d3d9ccd510a9ba5491c07417739e8b2728a0187..d4a5a61cc02c187af047cd1896390e4b4886c8dd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts.ma
@@ -20,8 +20,8 @@ include "basic_2/multiple/mr2_plus.ma".
 
 inductive lifts: list2 nat nat → relation term ≝
 | lifts_nil : ∀T. lifts (◊) T T
-| lifts_cons: ∀T1,T,T2,des,d,e.
-              ⬆[d,e] T1 ≡ T → lifts des T T2 → lifts ({d, e} @ des) T1 T2
+| lifts_cons: ∀T1,T,T2,des,l,m.
+              ⬆[l,m] T1 ≡ T → lifts des T T2 → lifts ({l, m} @ des) T1 T2
 .
 
 interpretation "generic relocation (term)"
@@ -31,30 +31,30 @@ interpretation "generic relocation (term)"
 
 fact lifts_inv_nil_aux: ∀T1,T2,des. ⬆*[des] T1 ≡ T2 → des = ◊ → T1 = T2.
 #T1 #T2 #des * -T1 -T2 -des //
-#T1 #T #T2 #d #e #des #_ #_ #H destruct
+#T1 #T #T2 #l #m #des #_ #_ #H destruct
 qed-.
 
 lemma lifts_inv_nil: ∀T1,T2. ⬆*[◊] T1 ≡ T2 → T1 = T2.
 /2 width=3 by lifts_inv_nil_aux/ qed-.
 
 fact lifts_inv_cons_aux: ∀T1,T2,des. ⬆*[des] T1 ≡ T2 →
-                         ∀d,e,tl. des = {d, e} @ tl →
-                         ∃∃T. ⬆[d, e] T1 ≡ T & ⬆*[tl] T ≡ T2.
+                         ∀l,m,tl. des = {l, m} @ tl →
+                         ∃∃T. ⬆[l, m] T1 ≡ T & ⬆*[tl] T ≡ T2.
 #T1 #T2 #des * -T1 -T2 -des
-[ #T #d #e #tl #H destruct
-| #T1 #T #T2 #des #d #e #HT1 #HT2 #hd #he #tl #H destruct
+[ #T #l #m #tl #H destruct
+| #T1 #T #T2 #des #l #m #HT1 #HT2 #l0 #m0 #tl #H destruct
   /2 width=3 by ex2_intro/
 qed-.
 
-lemma lifts_inv_cons: ∀T1,T2,d,e,des. ⬆*[{d, e} @ des] T1 ≡ T2 →
-                      ∃∃T. ⬆[d, e] T1 ≡ T & ⬆*[des] T ≡ T2.
+lemma lifts_inv_cons: ∀T1,T2,l,m,des. ⬆*[{l, m} @ des] T1 ≡ T2 →
+                      ∃∃T. ⬆[l, m] T1 ≡ T & ⬆*[des] T ≡ T2.
 /2 width=3 by lifts_inv_cons_aux/ qed-.
 
 (* Basic_1: was: lift1_sort *)
 lemma lifts_inv_sort1: ∀T2,k,des. ⬆*[des] ⋆k ≡ T2 → T2 = ⋆k.
 #T2 #k #des elim des -des
 [ #H <(lifts_inv_nil … H) -H //
-| #d #e #des #IH #H
+| #l #m #des #IH #H
   elim (lifts_inv_cons … H) -H #X #H
   >(lift_inv_sort1 … H) -H /2 width=1 by/
 ]
@@ -65,9 +65,9 @@ lemma lifts_inv_lref1: ∀T2,des,i1. ⬆*[des] #i1 ≡ T2 →
                        ∃∃i2. @⦃i1, des⦄ ≡ i2 & T2 = #i2.
 #T2 #des elim des -des
 [ #i1 #H <(lifts_inv_nil … H) -H /2 width=3 by at_nil, ex2_intro/
-| #d #e #des #IH #i1 #H
+| #l #m #des #IH #i1 #H
   elim (lifts_inv_cons … H) -H #X #H1 #H2
-  elim (lift_inv_lref1 … H1) -H1 * #Hdi1 #H destruct
+  elim (lift_inv_lref1 … H1) -H1 * #Hli1 #H destruct
   elim (IH … H2) -IH -H2 /3 width=3 by at_lt, at_ge, ex2_intro/
 ]
 qed-.
@@ -75,7 +75,7 @@ qed-.
 lemma lifts_inv_gref1: ∀T2,p,des. ⬆*[des] §p ≡ T2 → T2 = §p.
 #T2 #p #des elim des -des
 [ #H <(lifts_inv_nil … H) -H //
-| #d #e #des #IH #H
+| #l #m #des #IH #H
   elim (lifts_inv_cons … H) -H #X #H
   >(lift_inv_gref1 … H) -H /2 width=1 by/
 ]
@@ -88,10 +88,10 @@ lemma lifts_inv_bind1: ∀a,I,T2,des,V1,U1. ⬆*[des] ⓑ{a,I} V1. U1 ≡ T2 →
 #a #I #T2 #des elim des -des
 [ #V1 #U1 #H
   <(lifts_inv_nil … H) -H /2 width=5 by ex3_2_intro, lifts_nil/
-| #d #e #des #IHdes #V1 #U1 #H
+| #l #m #des #IHcs #V1 #U1 #H
   elim (lifts_inv_cons … H) -H #X #H #HT2
   elim (lift_inv_bind1 … H) -H #V #U #HV1 #HU1 #H destruct
-  elim (IHdes … HT2) -IHdes -HT2 #V2 #U2 #HV2 #HU2 #H destruct
+  elim (IHcs … HT2) -IHcs -HT2 #V2 #U2 #HV2 #HU2 #H destruct
   /3 width=5 by ex3_2_intro, lifts_cons/
 ]
 qed-.
@@ -103,10 +103,10 @@ lemma lifts_inv_flat1: ∀I,T2,des,V1,U1. ⬆*[des] ⓕ{I} V1. U1 ≡ T2 →
 #I #T2 #des elim des -des
 [ #V1 #U1 #H
   <(lifts_inv_nil … H) -H /2 width=5 by ex3_2_intro, lifts_nil/
-| #d #e #des #IHdes #V1 #U1 #H
+| #l #m #des #IHcs #V1 #U1 #H
   elim (lifts_inv_cons … H) -H #X #H #HT2
   elim (lift_inv_flat1 … H) -H #V #U #HV1 #HU1 #H destruct
-  elim (IHdes … HT2) -IHdes -HT2 #V2 #U2 #HV2 #HU2 #H destruct
+  elim (IHcs … HT2) -IHcs -HT2 #V2 #U2 #HV2 #HU2 #H destruct
   /3 width=5 by ex3_2_intro, lifts_cons/
 ]
 qed-.
@@ -128,7 +128,7 @@ lemma lifts_bind: ∀a,I,T2,V1,V2,des. ⬆*[des] V1 ≡ V2 →
                   ⬆*[des] ⓑ{a,I} V1. T1 ≡ ⓑ{a,I} V2. T2.
 #a #I #T2 #V1 #V2 #des #H elim H -V1 -V2 -des
 [ #V #T1 #H >(lifts_inv_nil … H) -H //
-| #V1 #V #V2 #des #d #e #HV1 #_ #IHV #T1 #H
+| #V1 #V #V2 #des #l #m #HV1 #_ #IHV #T1 #H
   elim (lifts_inv_cons … H) -H /3 width=3 by lift_bind, lifts_cons/
 ]
 qed.
@@ -138,13 +138,13 @@ lemma lifts_flat: ∀I,T2,V1,V2,des. ⬆*[des] V1 ≡ V2 →
                   ⬆*[des] ⓕ{I} V1. T1 ≡ ⓕ{I} V2. T2.
 #I #T2 #V1 #V2 #des #H elim H -V1 -V2 -des
 [ #V #T1 #H >(lifts_inv_nil … H) -H //
-| #V1 #V #V2 #des #d #e #HV1 #_ #IHV #T1 #H
+| #V1 #V #V2 #des #l #m #HV1 #_ #IHV #T1 #H
   elim (lifts_inv_cons … H) -H /3 width=3 by lift_flat, lifts_cons/
 ]
 qed.
 
 lemma lifts_total: ∀des,T1. ∃T2. ⬆*[des] T1 ≡ T2.
 #des elim des -des /2 width=2 by lifts_nil, ex_intro/
-#d #e #des #IH #T1 elim (lift_total T1 d e)
+#l #m #des #IH #T1 elim (lift_total T1 l m)
 #T #HT1 elim (IH T) -IH /3 width=4 by lifts_cons, ex_intro/
 qed.