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 a98e061f39d5a61c872c36ca97cf219d573453f3..482a4b12630589d574299b4d83406455da91f572 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".
@@ -21,8 +22,8 @@ include "basic_2/rt_transition/cpg.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma cpg_delta_drops: â\88\80Rt,c,h,G,K,V,V2,i,L,T2. â¬\87*[i] L â\89\98 K.â\93\93V â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[Rt, c, h] V2 →
-                       â¬\86*[â\86\91i] V2 â\89\98 T2 â\86\92  â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88[Rt, c, h] T2.
+lemma cpg_delta_drops: â\88\80Rt,c,h,G,K,V,V2,i,L,T2. â\87©*[i] L â\89\98 K.â\93\93V â\86\92 â¦\83G,Kâ¦\84 â\8a¢ V â¬\88[Rt,c,h] V2 →
+                       â\87§*[â\86\91i] V2 â\89\98 T2 â\86\92  â¦\83G,Lâ¦\84 â\8a¢ #i â¬\88[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
@@ -31,8 +32,8 @@ lemma cpg_delta_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≘ K.ⓓV → ⦃G,
 ]
 qed.
 
-lemma cpg_ell_drops: â\88\80Rt,c,h,G,K,V,V2,i,L,T2. â¬\87*[i] L â\89\98 K.â\93\9bV â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[Rt,c, h] V2 →
-                     â¬\86*[â\86\91i] V2 â\89\98 T2 â\86\92  â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88[Rt, c+ð\9d\9f\98ð\9d\9f\99, h] T2.
+lemma cpg_ell_drops: â\88\80Rt,c,h,G,K,V,V2,i,L,T2. â\87©*[i] L â\89\98 K.â\93\9bV â\86\92 â¦\83G,Kâ¦\84 â\8a¢ V â¬\88[Rt,c,h] V2 →
+                     â\87§*[â\86\91i] V2 â\89\98 T2 â\86\92  â¦\83G,Lâ¦\84 â\8a¢ #i â¬\88[Rt,c+ð\9d\9f\98ð\9d\9f\99,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
@@ -43,12 +44,12 @@ qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpg_inv_lref1_drops: ∀Rt,c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ⬈[Rt,c, h] T2 →
+lemma cpg_inv_lref1_drops: ∀Rt,c,h,G,i,L,T2. ⦃G,L⦄ ⊢ #i ⬈[Rt,c,h] T2 →
                            ∨∨ T2 = #i ∧ c = 𝟘𝟘
-                            | â\88\83â\88\83cV,K,V,V2. â¬\87*[i] L â\89\98 K.â\93\93V & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[Rt, cV, h] V2 &
-                                           â¬\86*[↑i] V2 ≘ T2 & c = cV
-                            | â\88\83â\88\83cV,K,V,V2. â¬\87*[i] L â\89\98 K.â\93\9bV & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[Rt, cV, h] V2 &
-                                           â¬\86*[↑i] V2 ≘ T2 & c = cV + 𝟘𝟙.
+                            | â\88\83â\88\83cV,K,V,V2. â\87©*[i] L â\89\98 K.â\93\93V & â¦\83G,Kâ¦\84 â\8a¢ V â¬\88[Rt,cV,h] V2 &
+                                           â\87§*[↑i] V2 ≘ T2 & c = cV
+                            | â\88\83â\88\83cV,K,V,V2. â\87©*[i] L â\89\98 K.â\93\9bV & â¦\83G,Kâ¦\84 â\8a¢ V â¬\88[Rt,cV,h] V2 &
+                                           â\87§*[↑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/
@@ -61,13 +62,13 @@ lemma cpg_inv_lref1_drops: ∀Rt,c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ⬈[Rt,c, h] T2
 ]
 qed-.
 
-lemma cpg_inv_atom1_drops: ∀Rt,c,h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ⬈[Rt, c, h] T2 →
+lemma cpg_inv_atom1_drops: ∀Rt,c,h,I,G,L,T2. ⦃G,L⦄ ⊢ ⓪{I} ⬈[Rt,c,h] T2 →
                            ∨∨ T2 = ⓪{I} ∧ c = 𝟘𝟘
-                            | ∃∃s. T2 = ⋆(next h s) & I = Sort s & c = 𝟘𝟙
-                            | â\88\83â\88\83cV,i,K,V,V2. â¬\87*[i] L â\89\98 K.â\93\93V & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[Rt, cV, h] V2 &
-                                             â¬\86*[↑i] V2 ≘ T2 & I = LRef i & c = cV
-                            | â\88\83â\88\83cV,i,K,V,V2. â¬\87*[i] L â\89\98 K.â\93\9bV & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[Rt, cV, h] V2 &
-                                             â¬\86*[↑i] V2 ≘ T2 & I = LRef i & c = cV + 𝟘𝟙.
+                            | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s & c = 𝟘𝟙
+                            | â\88\83â\88\83cV,i,K,V,V2. â\87©*[i] L â\89\98 K.â\93\93V & â¦\83G,Kâ¦\84 â\8a¢ V â¬\88[Rt,cV,h] V2 &
+                                             â\87§*[↑i] V2 ≘ T2 & I = LRef i & c = cV
+                            | â\88\83â\88\83cV,i,K,V,V2. â\87©*[i] L â\89\98 K.â\93\9bV & â¦\83G,Kâ¦\84 â\8a¢ V â¬\88[Rt,cV,h] V2 &
+                                             â\87§*[↑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/
@@ -115,10 +116,9 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt →
     elim (IH … HV12 … HLK … HVW1) -HV12 //
     elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
     /3 width=5 by cpg_bind, lifts_bind, ex2_intro/
-  | #cT #T2 #HT12 #HXT2 #H1 #H2 #H3 destruct
-    elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] #U2 #HTU2 #HU12
-    lapply (lifts_trans … HXT2 … HTU2 ??) -T2 [3: |*: // ] #HXU2
-    elim (lifts_split_trans … HXU2 f (𝐔❴↑O❵)) [2: /2 width=1 by after_uni_one_dx/ ]
+  | #cT #T2 #HT21 #HTX2 #H1 #H2 #H3 destruct
+    elim (lifts_trans4_one … HT21 … HTU1) -HTU1 #U2 #HTU2 #HU21
+    elim (IH … HTX2 … HLK … HTU2) [| /3 width=1 by fqup_zeta/ ] -K -V1 -T1 -T2
     /3 width=5 by cpg_zeta, ex2_intro/
   ]
 | * #V1 #T1 #HG #HK #HT #c #X2 #H2 #b #f #L #HLK #X1 #H1 destruct
@@ -199,9 +199,10 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt →
     elim (IH … HW12 … HLK … HVW1) -HW12 //
     elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
     /3 width=5 by cpg_bind, lifts_bind, ex2_intro/
-  | #cU #U2 #HU12 #HXU2 #H1 #H2 #H3 destruct
-    elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] #T2 #HTU2 #HT12
-    elim (lifts_div4_one … HTU2 … HXU2) -U2 /3 width=5 by cpg_zeta, ex2_intro/
+  | #cU #U2 #HU21 #HUX2 #H1 #H2 #H3 destruct
+    elim (lifts_div4_one … HTU1 … HU21) -HTU1 #T2 #HT21 #HTU2
+    elim (IH … HUX2 … HLK … HTU2) [| /3 width=1 by fqup_zeta/ ] -L -W1 -U1 -U2
+    /3 width=5 by cpg_zeta, ex2_intro/
   ]
 | * #W1 #U1 #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct
   elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #HVW1 #HTU1 #H destruct