renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / frees_drops.ma

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 f24e507850a21470569138388286bcde62428fc5..fe24eadf5d0496b0dce3a9145e2e441f55e4174b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/frees_drops.ma
@@ -20,8 +20,8 @@ include "basic_2/static/frees_fqup.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma frees_atom_drops: â\88\80b,L,i. â¬\87*[b, ð\9d\90\94â\9d´iâ\9dµ] L â\89¡ ⋆ →
-                        â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L â\8a¢ ð\9d\90\85*â¦\83#iâ¦\84 â\89¡ â\86\91*[i]⫯f.
+lemma frees_atom_drops: â\88\80b,L,i. â¬\87*[b, ð\9d\90\94â\9d´iâ\9dµ] L â\89\98 ⋆ →
+                        â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L â\8a¢ ð\9d\90\85*â¦\83#iâ¦\84 â\89\98 ⫯*[i]â\86\91f.
 #b #L elim L -L /2 width=1 by frees_atom/
 #L #I #IH *
 [ #H lapply (drops_fwd_isid … H ?) -H // #H destruct
@@ -29,16 +29,16 @@ lemma frees_atom_drops: ∀b,L,i. ⬇*[b, 𝐔❴i❵] L ≡ ⋆ →
 ]
 qed.
 
-lemma frees_pair_drops: â\88\80f,K,V. K â\8a¢ ð\9d\90\85*â¦\83Vâ¦\84 â\89¡ f → 
-                        â\88\80i,I,L. â¬\87*[i] L â\89¡ K.â\93\91{I}V â\86\92 L â\8a¢ ð\9d\90\85*â¦\83#iâ¦\84 â\89¡ â\86\91*[i] ⫯f.
+lemma frees_pair_drops: â\88\80f,K,V. K â\8a¢ ð\9d\90\85*â¦\83Vâ¦\84 â\89\98 f → 
+                        â\88\80i,I,L. â¬\87*[i] L â\89\98 K.â\93\91{I}V â\86\92 L â\8a¢ ð\9d\90\85*â¦\83#iâ¦\84 â\89\98 ⫯*[i] â\86\91f.
 #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/
 ]
 qed.
 
-lemma frees_unit_drops: â\88\80f.  ð\9d\90\88â¦\83fâ¦\84 â\86\92 â\88\80I,K,i,L. â¬\87*[i] L â\89¡ K.ⓤ{I} →
-                       L â\8a¢ ð\9d\90\85*â¦\83#iâ¦\84 â\89¡ â\86\91*[i] ⫯f.
+lemma frees_unit_drops: â\88\80f.  ð\9d\90\88â¦\83fâ¦\84 â\86\92 â\88\80I,K,i,L. â¬\87*[i] L â\89\98 K.ⓤ{I} →
+                       L â\8a¢ ð\9d\90\85*â¦\83#iâ¦\84 â\89\98 ⫯*[i] â\86\91f.
 #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
@@ -46,16 +46,16 @@ lemma frees_unit_drops: ∀f.  𝐈⦃f⦄ → ∀I,K,i,L. ⬇*[i] L ≡ K.ⓤ{I
 ]
 qed.
 (*
-lemma frees_sort_pushs: â\88\80f,K,s. K â\8a¢ ð\9d\90\85*â¦\83â\8b\86sâ¦\84 â\89¡ f →
-                        â\88\80i,L. â¬\87*[i] L â\89¡ K â\86\92 L â\8a¢ ð\9d\90\85*â¦\83â\8b\86sâ¦\84 â\89¡ â\86\91*[i] f.
+lemma frees_sort_pushs: â\88\80f,K,s. K â\8a¢ ð\9d\90\85*â¦\83â\8b\86sâ¦\84 â\89\98 f →
+                        â\88\80i,L. â¬\87*[i] L â\89\98 K â\86\92 L â\8a¢ ð\9d\90\85*â¦\83â\8b\86sâ¦\84 â\89\98 ⫯*[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/
 ]
 qed.
 *)
-lemma frees_lref_pushs: â\88\80f,K,j. K â\8a¢ ð\9d\90\85*â¦\83#jâ¦\84 â\89¡ f →
-                        â\88\80i,L. â¬\87*[i] L â\89¡ K â\86\92 L â\8a¢ ð\9d\90\85*â¦\83#(i+j)â¦\84 â\89¡ â\86\91*[i] f.
+lemma frees_lref_pushs: â\88\80f,K,j. K â\8a¢ ð\9d\90\85*â¦\83#jâ¦\84 â\89\98 f →
+                        â\88\80i,L. â¬\87*[i] L â\89\98 K â\86\92 L â\8a¢ ð\9d\90\85*â¦\83#(i+j)â¦\84 â\89\98 ⫯*[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
@@ -63,8 +63,8 @@ lemma frees_lref_pushs: ∀f,K,j. K ⊢ 𝐅*⦃#j⦄ ≡ f →
 ]
 qed.
 (*
-lemma frees_gref_pushs: â\88\80f,K,l. K â\8a¢ ð\9d\90\85*â¦\83§lâ¦\84 â\89¡ f →
-                        â\88\80i,L. â¬\87*[i] L â\89¡ K â\86\92 L â\8a¢ ð\9d\90\85*â¦\83§lâ¦\84 â\89¡ â\86\91*[i] f.
+lemma frees_gref_pushs: â\88\80f,K,l. K â\8a¢ ð\9d\90\85*â¦\83§lâ¦\84 â\89\98 f →
+                        â\88\80i,L. â¬\87*[i] L â\89\98 K â\86\92 L â\8a¢ ð\9d\90\85*â¦\83§lâ¦\84 â\89\98 ⫯*[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/
@@ -73,11 +73,11 @@ qed.
 *)
 (* Advanced inversion lemmas ************************************************)
 
-lemma frees_inv_lref_drops: â\88\80L,i,f. L â\8a¢ ð\9d\90\85*â¦\83#iâ¦\84 â\89¡ f →
-                            â\88¨â\88¨ â\88\83â\88\83g. â¬\87*[â\92», ð\9d\90\94â\9d´iâ\9dµ] L â\89¡ â\8b\86 & ð\9d\90\88â¦\83gâ¦\84 & f = â\86\91*[i] ⫯g
-                             | â\88\83â\88\83g,I,K,V. K â\8a¢ ð\9d\90\85*â¦\83Vâ¦\84 â\89¡ g &
-                                          â¬\87*[i] L â\89¡ K.â\93\91{I}V & f = â\86\91*[i] ⫯g
-                             | â\88\83â\88\83g,I,K. â¬\87*[i] L â\89¡ K.â\93¤{I} & ð\9d\90\88â¦\83gâ¦\84 & f = â\86\91*[i] ⫯g.
+lemma frees_inv_lref_drops: â\88\80L,i,f. L â\8a¢ ð\9d\90\85*â¦\83#iâ¦\84 â\89\98 f →
+                            â\88¨â\88¨ â\88\83â\88\83g. â¬\87*[â\92», ð\9d\90\94â\9d´iâ\9dµ] L â\89\98 â\8b\86 & ð\9d\90\88â¦\83gâ¦\84 & f = ⫯*[i] â\86\91g
+                             | â\88\83â\88\83g,I,K,V. K â\8a¢ ð\9d\90\85*â¦\83Vâ¦\84 â\89\98 g &
+                                          â¬\87*[i] L â\89\98 K.â\93\91{I}V & f = ⫯*[i] â\86\91g
+                             | â\88\83â\88\83g,I,K. â¬\87*[i] L â\89\98 K.â\93¤{I} & ð\9d\90\88â¦\83gâ¦\84 & f = ⫯*[i] â\86\91g.
 #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
@@ -97,9 +97,9 @@ qed-.
 
 (* Properties with generic slicing for local environments *******************)
 
-lemma frees_lifts: â\88\80b,f1,K,T. K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ f1 →
-                   â\88\80f,L. â¬\87*[b, f] L â\89¡ K â\86\92 â\88\80U. â¬\86*[f] T â\89¡ U →
-                   â\88\80f2. f ~â\8a\9a f1 â\89¡ f2 â\86\92 L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89¡ f2.
+lemma frees_lifts: â\88\80b,f1,K,T. K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 f1 →
+                   â\88\80f,L. â¬\87*[b, f] L â\89\98 K â\86\92 â\88\80U. â¬\86*[f] T â\89\98 U →
+                   â\88\80f2. f ~â\8a\9a f1 â\89\98 f2 â\86\92 L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89\98 f2.
 #b #f1 #K #T #H lapply (frees_fwd_isfin … H) elim H -f1 -K -T
 [ #f1 #K #s #Hf1 #_ #f #L #HLK #U #H2 #f2 #H3
   lapply (coafter_isid_inv_dx … H3 … Hf1) -f1 #Hf2
@@ -154,47 +154,48 @@ lemma frees_lifts: ∀b,f1,K,T. K ⊢ 𝐅*⦃T⦄ ≡ f1 →
 ]
 qed-.
 
-lemma frees_lifts_SO: â\88\80b,L,K. â¬\87*[b, ð\9d\90\94â\9d´1â\9dµ] L â\89¡ K â\86\92 â\88\80T,U. â¬\86*[1] T â\89¡ U →
-                      â\88\80f. K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ f â\86\92 L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89¡ â\86\91f.
+lemma frees_lifts_SO: â\88\80b,L,K. â¬\87*[b, ð\9d\90\94â\9d´1â\9dµ] L â\89\98 K â\86\92 â\88\80T,U. â¬\86*[1] T â\89\98 U →
+                      â\88\80f. K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 f â\86\92 L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89\98 ⫯f.
 #b #L #K #HLK #T #U #HTU #f #Hf
 @(frees_lifts b … Hf … HTU) //  (**) (* auto fails *)
 qed.
 
 (* Forward lemmas with generic slicing for local environments ***************)
 
-lemma frees_fwd_coafter: â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89¡ f2 →
-                         â\88\80f,K. â¬\87*[b, f] L â\89¡ K â\86\92 â\88\80T. â¬\86*[f] T â\89¡ U →
-                         â\88\80f1. K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ f1 â\86\92 f ~â\8a\9a f1 â\89¡ f2.
+lemma frees_fwd_coafter: â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89\98 f2 →
+                         â\88\80f,K. â¬\87*[b, f] L â\89\98 K â\86\92 â\88\80T. â¬\86*[f] T â\89\98 U →
+                         â\88\80f1. K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 f1 â\86\92 f ~â\8a\9a f1 â\89\98 f2.
 /4 width=11 by frees_lifts, frees_mono, coafter_eq_repl_back0/ qed-.
 
 (* Inversion lemmas with generic slicing for local environments *************)
 
-lemma frees_inv_lifts_ex: â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89¡ f2 →
-                          â\88\80f,K. â¬\87*[b, f] L â\89¡ K â\86\92 â\88\80T. â¬\86*[f] T â\89¡ U →
-                          â\88\83â\88\83f1. f ~â\8a\9a f1 â\89¡ f2 & K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ f1.
+lemma frees_inv_lifts_ex: â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89\98 f2 →
+                          â\88\80f,K. â¬\87*[b, f] L â\89\98 K â\86\92 â\88\80T. â¬\86*[f] T â\89\98 U →
+                          â\88\83â\88\83f1. f ~â\8a\9a f1 â\89\98 f2 & K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 f1.
 #b #f2 #L #U #Hf2 #f #K #HLK #T elim (frees_total K T)
 /3 width=9 by frees_fwd_coafter, ex2_intro/
 qed-.
 
-lemma frees_inv_lifts_SO: â\88\80b,f,L,U. L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89¡ f →
-                          â\88\80K. â¬\87*[b, ð\9d\90\94â\9d´1â\9dµ] L â\89¡ K â\86\92 â\88\80T. â¬\86*[1] T â\89¡ U →
-                          K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ ⫱f.
+lemma frees_inv_lifts_SO: â\88\80b,f,L,U. L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89\98 f →
+                          â\88\80K. â¬\87*[b, ð\9d\90\94â\9d´1â\9dµ] L â\89\98 K â\86\92 â\88\80T. â¬\86*[1] T â\89\98 U →
+                          K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 ⫱f.
 #b #f #L #U #H #K #HLK #T #HTU elim(frees_inv_lifts_ex … H … HLK … HTU) -b -L -U
 #f1 #Hf #Hf1 elim (coafter_inv_nxx … Hf) -Hf
 /3 width=5 by frees_eq_repl_back, coafter_isid_inv_sn/
 qed-.
 
-lemma frees_inv_lifts: â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89¡ f2 →
-                       â\88\80f,K. â¬\87*[b, f] L â\89¡ K â\86\92 â\88\80T. â¬\86*[f] T â\89¡ U →
-                       â\88\80f1. f ~â\8a\9a f1 â\89¡ f2 â\86\92 K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ f1.
+lemma frees_inv_lifts: â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85*â¦\83Uâ¦\84 â\89\98 f2 →
+                       â\88\80f,K. â¬\87*[b, f] L â\89\98 K â\86\92 â\88\80T. â¬\86*[f] T â\89\98 U →
+                       â\88\80f1. f ~â\8a\9a f1 â\89\98 f2 â\86\92 K â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 f1.
 #b #f2 #L #U #H #f #K #HLK #T #HTU #f1 #Hf2 elim (frees_inv_lifts_ex … H … HLK … HTU) -b -L -U
 /3 width=7 by frees_eq_repl_back, coafter_inj/
 qed-.
 
-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 →
-                            ∃∃g2. L2 ⊢ 𝐅*⦃V2⦄ ≡ g2 & g2 ⊆ g1.
+(* 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 →
+                            ∃∃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
   lapply (isid_tls n … Hf1) -Hf1 <H1 -f1 #Hf1