update in ground_2, static_2, basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpg_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma
index 3a079605548c2641e51709370e89bebf189b285c..9ea5a2521c53fd943bcf3936f257e0bdb2e19c47 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/xoa/ex_5_5.ma".
 include "static_2/relocation/drops_drops.ma".
 include "static_2/s_computation/fqup_weight.ma".
 include "static_2/s_computation/fqup_drops.ma".
@@ -21,53 +22,57 @@ include "basic_2/rt_transition/cpg.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma cpg_delta_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⇩*[i] L ≘ K.ⓓV → ⦃G,K⦄ ⊢ V ⬈[Rt,c,h] V2 →
-                       ⇧*[↑i] V2 ≘ T2 →  ⦃G,L⦄ ⊢ #i ⬈[Rt,c,h] T2.
+lemma cpg_delta_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⇩[i] L ≘ K.ⓓV → ❪G,K❫ ⊢ V ⬈[Rt,c,h] V2 →
+                       ⇧[↑i] V2 ≘ T2 →  ❪G,L❫ ⊢ #i ⬈[Rt,c,h] T2.
 #Rt #c #h #G #K #V #V2 #i elim i -i
 [ #L #T2 #HLK lapply (drops_fwd_isid … HLK ?) // #H destruct /3 width=3 by cpg_delta/
 | #i #IH #L0 #T0 #H0 #HV2 #HVT2
   elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct
-  elim (lifts_split_trans â\80¦ HVT2 (ð\9d\90\94â\9d´â\86\91iâ\9dµ) (ð\9d\90\94â\9d´1â\9dµ) ?) -HVT2 /3 width=3 by cpg_lref/
+  elim (lifts_split_trans â\80¦ HVT2 (ð\9d\90\94â\9d¨â\86\91iâ\9d©) (ð\9d\90\94â\9d¨1â\9d©) ?) -HVT2 /3 width=3 by cpg_lref/
 ]
 qed.
 
-lemma cpg_ell_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⇩*[i] L ≘ K.ⓛV → ⦃G,K⦄ ⊢ V ⬈[Rt,c,h] V2 →
-                     ⇧*[↑i] V2 ≘ T2 →  ⦃G,L⦄ ⊢ #i ⬈[Rt,c+𝟘𝟙,h] T2.
+lemma cpg_ell_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⇩[i] L ≘ K.ⓛV → ❪G,K❫ ⊢ V ⬈[Rt,c,h] V2 →
+                     ⇧[↑i] V2 ≘ T2 →  ❪G,L❫ ⊢ #i ⬈[Rt,c+𝟘𝟙,h] T2.
 #Rt #c #h #G #K #V #V2 #i elim i -i
 [ #L #T2 #HLK lapply (drops_fwd_isid … HLK ?) // #H destruct /3 width=3 by cpg_ell/
 | #i #IH #L0 #T0 #H0 #HV2 #HVT2
   elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct
-  elim (lifts_split_trans â\80¦ HVT2 (ð\9d\90\94â\9d´â\86\91iâ\9dµ) (ð\9d\90\94â\9d´1â\9dµ) ?) -HVT2 /3 width=3 by cpg_lref/
+  elim (lifts_split_trans â\80¦ HVT2 (ð\9d\90\94â\9d¨â\86\91iâ\9d©) (ð\9d\90\94â\9d¨1â\9d©) ?) -HVT2 /3 width=3 by cpg_lref/
 ]
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpg_inv_lref1_drops: â\88\80Rt,c,h,G,i,L,T2. â¦\83G,Lâ¦\84 ⊢ #i ⬈[Rt,c,h] T2 →
+lemma cpg_inv_lref1_drops: â\88\80Rt,c,h,G,i,L,T2. â\9dªG,Lâ\9d« ⊢ #i ⬈[Rt,c,h] T2 →
                            ∨∨ T2 = #i ∧ c = 𝟘𝟘
-                            | ∃∃cV,K,V,V2. ⇩*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ⬈[Rt,cV,h] V2 &
-                                           ⇧*[↑i] V2 ≘ T2 & c = cV
-                            | ∃∃cV,K,V,V2. ⇩*[i] L ≘ K.ⓛV & ⦃G,K⦄ ⊢ V ⬈[Rt,cV,h] V2 &
-                                           ⇧*[↑i] V2 ≘ T2 & c = cV + 𝟘𝟙.
+                            | ∃∃cV,K,V,V2. ⇩[i] L ≘ K.ⓓV & ❪G,K❫ ⊢ V ⬈[Rt,cV,h] V2 &
+                                           ⇧[↑i] V2 ≘ T2 & c = cV
+                            | ∃∃cV,K,V,V2. ⇩[i] L ≘ K.ⓛV & ❪G,K❫ ⊢ V ⬈[Rt,cV,h] V2 &
+                                           ⇧[↑i] V2 ≘ T2 & c = cV + 𝟘𝟙.
 #Rt #c #h #G #i elim i -i
 [ #L #T2 #H elim (cpg_inv_zero1 … H) -H * /3 width=1 by or3_intro0, conj/
   /4 width=8 by drops_refl, ex4_4_intro, or3_intro2, or3_intro1/
 | #i #IH #L #T2 #H elim (cpg_inv_lref1 … H) -H * /3 width=1 by or3_intro0, conj/
   #I #K #V2 #H #HVT2 #H0 destruct elim (IH … H) -IH -H
-  [ * #H1 #H2 destruct lapply (lifts_inv_lref1_uni … HVT2) -HVT2 #H destruct /3 width=1 by or3_intro0, conj/ ] *
+  [ * #H1 #H2 destruct
+    lapply (lifts_inv_lref1_uni … HVT2) -HVT2 #H destruct
+    /3 width=1 by or3_intro0, conj/
+  ] *
   #cV #L #W #W2 #HKL #HW2 #HWV2 #H destruct
-  lapply (lifts_trans … HWV2 … HVT2 ??) -V2
+  lapply (lifts_trans … HWV2 … HVT2 ??) -V2 [3,6: |*: // ] #H
+  lapply (lifts_uni … H) -H #H
   /4 width=8 by drops_drop, ex4_4_intro, or3_intro2, or3_intro1/
 ]
 qed-.
 
-lemma cpg_inv_atom1_drops: â\88\80Rt,c,h,I,G,L,T2. â¦\83G,Lâ¦\84 â\8a¢ â\93ª{I} ⬈[Rt,c,h] T2 →
-                           ∨∨ T2 = ⓪{I} ∧ c = 𝟘𝟘
+lemma cpg_inv_atom1_drops: â\88\80Rt,c,h,I,G,L,T2. â\9dªG,Lâ\9d« â\8a¢ â\93ª[I] ⬈[Rt,c,h] T2 →
+                           ∨∨ T2 = ⓪[I] ∧ c = 𝟘𝟘
                             | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s & c = 𝟘𝟙
-                            | ∃∃cV,i,K,V,V2. ⇩*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ⬈[Rt,cV,h] V2 &
-                                             ⇧*[↑i] V2 ≘ T2 & I = LRef i & c = cV
-                            | ∃∃cV,i,K,V,V2. ⇩*[i] L ≘ K.ⓛV & ⦃G,K⦄ ⊢ V ⬈[Rt,cV,h] V2 &
-                                             ⇧*[↑i] V2 ≘ T2 & I = LRef i & c = cV + 𝟘𝟙.
+                            | ∃∃cV,i,K,V,V2. ⇩[i] L ≘ K.ⓓV & ❪G,K❫ ⊢ V ⬈[Rt,cV,h] V2 &
+                                             ⇧[↑i] V2 ≘ T2 & I = LRef i & c = cV
+                            | ∃∃cV,i,K,V,V2. ⇩[i] L ≘ K.ⓛV & ❪G,K❫ ⊢ V ⬈[Rt,cV,h] V2 &
+                                             ⇧[↑i] V2 ≘ T2 & I = LRef i & c = cV + 𝟘𝟙.
 #Rt #c #h * #n #G #L #T2 #H
 [ elim (cpg_inv_sort1 … H) -H *
   /3 width=3 by or4_intro0, or4_intro1, ex3_intro, conj/
@@ -100,7 +105,7 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt →
   elim (drops_inv_skip2 … HY) -HY #Z #L0 #HLK0 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #W #HVW #H destruct
   elim (IH … HV2 … HLK0 … HVW) -IH /2 width=2 by fqup_lref/ -K -K0 -V #W2 #HVW2 #HW2
-  elim (lifts_total W2 (ð\9d\90\94â\9d´â\86\91i2â\9dµ)) #U2 #HWU2
+  elim (lifts_total W2 (ð\9d\90\94â\9d¨â\86\91i2â\9d©)) #U2 #HWU2
   lapply (lifts_trans … HVW2 … HWU2 ??) -HVW2 [3,6: |*: // ] #HVU2
   lapply (lifts_conf … HVT2 … HVU2 f ?) -V2 [1,3: /2 width=3 by after_uni_succ_sn/ ]
   /4 width=8 by cpg_ell_drops, cpg_delta_drops, drops_inv_gen, ex2_intro/
@@ -138,7 +143,7 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt →
       elim (IH … HV12 … HLK … HVW1) -HV12 -HVW1 // #W2 #HVW2 #HW12
       elim (IH … HY12 … HLK … HYZ1) -HY12 //
       elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
-      elim (lifts_total W2 (ð\9d\90\94â\9d´1â\9dµ)) #W20 #HW20
+      elim (lifts_total W2 (ð\9d\90\94â\9d¨1â\9d©)) #W20 #HW20
       lapply (lifts_trans … HVW2 … HW20 ??) -HVW2 [3: |*: // ] #H
       lapply (lifts_conf … HV20 … H (⫯f) ?) -V2 /2 width=3 by after_uni_one_sn/
       /4 width=9 by cpg_theta, lifts_bind, lifts_flat, ex2_intro/
@@ -178,7 +183,7 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt →
   [ #H1 #H2 destruct /3 width=3 by cpg_refl, ex2_intro/ ]
   #cW #L0 #W #W2 #HL0 #HW2 #HWU2 #H destruct
   elim (lifts_inv_lref2 … H1) -H1 #i1 #Hf #H destruct
-  lapply (drops_split_div â\80¦ HLK (ð\9d\90\94â\9d´i1â\9dµ) ???) -HLK [4,8: * |*: // ] #Y0 #HK0 #HLY0
+  lapply (drops_split_div â\80¦ HLK (ð\9d\90\94â\9d¨i1â\9d©) ???) -HLK [4,8: * |*: // ] #Y0 #HK0 #HLY0
   lapply (drops_conf … HL0 … HLY0 ??) -HLY0 [3,6: |*: /2 width=6 by after_uni_dx/ ] #HLY0
   lapply (drops_tls_at … Hf … HLY0) -HLY0 #HLY0
   elim (drops_inv_skip1 … HLY0) -HLY0 #Z #K0 #HLK0 #HZ #H destruct