X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Ffrees_drops.ma;h=fe24eadf5d0496b0dce3a9145e2e441f55e4174b;hp=59c6b3ff47f9d7d56e91bf69fc64c70331c6b25c;hb=222044da28742b24584549ba86b1805a87def070;hpb=75f395f0febd02de8e0f881d918a8812b1425c8d

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma
index 59c6b3ff4..fe24eadf5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma
@@ -21,7 +21,7 @@ include "basic_2/static/frees_fqup.ma".
 (* Advanced properties ******************************************************)
 
 lemma frees_atom_drops: ∀b,L,i. ⬇*[b, 𝐔❴i❵] L ≘ ⋆ →
-                        ∀f. 𝐈⦃f⦄ → L ⊢ 𝐅*⦃#i⦄ ≘ ↑*[i]⫯f.
+                        ∀f. 𝐈⦃f⦄ → L ⊢ 𝐅*⦃#i⦄ ≘ ⫯*[i]↑f.
 #b #L elim L -L /2 width=1 by frees_atom/
 #L #I #IH *
 [ #H lapply (drops_fwd_isid … H ?) -H // #H destruct
@@ -30,7 +30,7 @@ lemma frees_atom_drops: ∀b,L,i. ⬇*[b, 𝐔❴i❵] L ≘ ⋆ →
 qed.
 
 lemma frees_pair_drops: ∀f,K,V. K ⊢ 𝐅*⦃V⦄ ≘ f → 
-                        ∀i,I,L. ⬇*[i] L ≘ K.ⓑ{I}V → L ⊢ 𝐅*⦃#i⦄ ≘ ↑*[i] ⫯f.
+                        ∀i,I,L. ⬇*[i] L ≘ K.ⓑ{I}V → L ⊢ 𝐅*⦃#i⦄ ≘ ⫯*[i] ↑f.
 #f #K #V #Hf #i elim i -i
 [ #I #L #H lapply (drops_fwd_isid … H ?) -H /2 width=1 by frees_pair/
 | #i #IH #I #L #H elim (drops_inv_succ … H) -H /3 width=2 by frees_lref/
@@ -38,7 +38,7 @@ lemma frees_pair_drops: ∀f,K,V. K ⊢ 𝐅*⦃V⦄ ≘ f →
 qed.
 
 lemma frees_unit_drops: ∀f.  𝐈⦃f⦄ → ∀I,K,i,L. ⬇*[i] L ≘ K.ⓤ{I} →
-                       L ⊢ 𝐅*⦃#i⦄ ≘ ↑*[i] ⫯f.
+                       L ⊢ 𝐅*⦃#i⦄ ≘ ⫯*[i] ↑f.
 #f #Hf #I #K #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H /2 width=1 by frees_unit/
 | #i #IH #Y #H elim (drops_inv_succ … H) -H
@@ -47,7 +47,7 @@ lemma frees_unit_drops: ∀f.  𝐈⦃f⦄ → ∀I,K,i,L. ⬇*[i] L ≘ K.ⓤ{I
 qed.
 (*
 lemma frees_sort_pushs: ∀f,K,s. K ⊢ 𝐅*⦃⋆s⦄ ≘ f →
-                        ∀i,L. ⬇*[i] L ≘ K → L ⊢ 𝐅*⦃⋆s⦄ ≘ ↑*[i] f.
+                        ∀i,L. ⬇*[i] L ≘ K → L ⊢ 𝐅*⦃⋆s⦄ ≘ ⫯*[i] f.
 #f #K #s #Hf #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H //
 | #i #IH #L #H elim (drops_inv_succ … H) -H /3 width=1 by frees_sort/
@@ -55,7 +55,7 @@ lemma frees_sort_pushs: ∀f,K,s. K ⊢ 𝐅*⦃⋆s⦄ ≘ f →
 qed.
 *)
 lemma frees_lref_pushs: ∀f,K,j. K ⊢ 𝐅*⦃#j⦄ ≘ f →
-                        ∀i,L. ⬇*[i] L ≘ K → L ⊢ 𝐅*⦃#(i+j)⦄ ≘ ↑*[i] f.
+                        ∀i,L. ⬇*[i] L ≘ K → L ⊢ 𝐅*⦃#(i+j)⦄ ≘ ⫯*[i] f.
 #f #K #j #Hf #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H //
 | #i #IH #L #H elim (drops_inv_succ … H) -H
@@ -64,7 +64,7 @@ lemma frees_lref_pushs: ∀f,K,j. K ⊢ 𝐅*⦃#j⦄ ≘ f →
 qed.
 (*
 lemma frees_gref_pushs: ∀f,K,l. K ⊢ 𝐅*⦃§l⦄ ≘ f →
-                        ∀i,L. ⬇*[i] L ≘ K → L ⊢ 𝐅*⦃§l⦄ ≘ ↑*[i] f.
+                        ∀i,L. ⬇*[i] L ≘ K → L ⊢ 𝐅*⦃§l⦄ ≘ ⫯*[i] f.
 #f #K #l #Hf #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H //
 | #i #IH #L #H elim (drops_inv_succ … H) -H /3 width=1 by frees_gref/
@@ -74,10 +74,10 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 lemma frees_inv_lref_drops: ∀L,i,f. L ⊢ 𝐅*⦃#i⦄ ≘ f →
-                            ∨∨ ∃∃g. ⬇*[Ⓕ, 𝐔❴i❵] L ≘ ⋆ & 𝐈⦃g⦄ & f = ↑*[i] ⫯g
+                            ∨∨ ∃∃g. ⬇*[Ⓕ, 𝐔❴i❵] L ≘ ⋆ & 𝐈⦃g⦄ & f = ⫯*[i] ↑g
                              | ∃∃g,I,K,V. K ⊢ 𝐅*⦃V⦄ ≘ g &
-                                          ⬇*[i] L ≘ K.ⓑ{I}V & f = ↑*[i] ⫯g
-                             | ∃∃g,I,K. ⬇*[i] L ≘ K.ⓤ{I} & 𝐈⦃g⦄ & f = ↑*[i] ⫯g.
+                                          ⬇*[i] L ≘ K.ⓑ{I}V & f = ⫯*[i] ↑g
+                             | ∃∃g,I,K. ⬇*[i] L ≘ K.ⓤ{I} & 𝐈⦃g⦄ & f = ⫯*[i] ↑g.
 #L elim L -L
 [ #i #g | #L #I #IH * [ #g cases I -I [ #I | #I #V ] -IH | #i #g ] ] #H
 [ elim (frees_inv_atom … H) -H #f #Hf #H destruct
@@ -155,7 +155,7 @@ lemma frees_lifts: ∀b,f1,K,T. K ⊢ 𝐅*⦃T⦄ ≘ f1 →
 qed-.
 
 lemma frees_lifts_SO: ∀b,L,K. ⬇*[b, 𝐔❴1❵] L ≘ K → ∀T,U. ⬆*[1] T ≘ U →
-                      ∀f. K ⊢ 𝐅*⦃T⦄ ≘ f → L ⊢ 𝐅*⦃U⦄ ≘ ↑f.
+                      ∀f. K ⊢ 𝐅*⦃T⦄ ≘ f → L ⊢ 𝐅*⦃U⦄ ≘ ⫯f.
 #b #L #K #HLK #T #U #HTU #f #Hf
 @(frees_lifts b … Hf … HTU) //  (**) (* auto fails *)
 qed.
@@ -191,10 +191,10 @@ lemma frees_inv_lifts: ∀b,f2,L,U. L ⊢ 𝐅*⦃U⦄ ≘ f2 →
 /3 width=7 by frees_eq_repl_back, coafter_inj/
 qed-.
 
-(* Note: this is used by lfxs_conf and might be modified *)
+(* Note: this is used by rex_conf and might be modified *)
 lemma frees_inv_drops_next: ∀f1,L1,T1. L1 ⊢ 𝐅*⦃T1⦄ ≘ f1 →
                             ∀I2,L2,V2,n. ⬇*[n] L1 ≘ L2.ⓑ{I2}V2 →
-                            ∀g1. ⫯g1 = ⫱*[n] f1 →
+                            ∀g1. ↑g1 = ⫱*[n] f1 →
                             ∃∃g2. L2 ⊢ 𝐅*⦃V2⦄ ≘ g2 & g2 ⊆ g1.
 #f1 #L1 #T1 #H elim H -f1 -L1 -T1
 [ #f1 #L1 #s #Hf1 #I2 #L2 #V2 #n #_ #g1 #H1 -I2 -L1 -s