first definition of cpm:

[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 c8f0b394fe60de960335be39bbc76192b28d8706..b22fc0938546fb58baf22e32da10e229f9bf71b2 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
@@ -21,8 +21,8 @@ include "basic_2/rt_transition/cpg.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma cpg_delta_drops: â\88\80c,h,G,K,V,V2,i,L,T2. â¬\87*[i] L â\89¡ K.â\93\93V â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[c, h] V2 →
-                       â¬\86*[⫯i] V2 â\89¡ T2 â\86\92  â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡[c, h] T2.
+lemma cpg_delta_drops: â\88\80c,h,G,K,V,V2,i,L,T2. â¬\87*[i] L â\89¡ K.â\93\93V â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[c, h] V2 →
+                       â¬\86*[⫯i] V2 â\89¡ T2 â\86\92  â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88[c, h] T2.
 #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 +31,8 @@ lemma cpg_delta_drops: ∀c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓓV → ⦃G, K
 ]
 qed.
 
-lemma cpg_ell_drops: â\88\80c,h,G,K,V,V2,i,L,T2. â¬\87*[i] L â\89¡ K.â\93\9bV â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[c, h] V2 →
-                     â¬\86*[⫯i] V2 â\89¡ T2 â\86\92  â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡[(â\86\93c)+𝟘𝟙, h] T2.
+lemma cpg_ell_drops: â\88\80c,h,G,K,V,V2,i,L,T2. â¬\87*[i] L â\89¡ K.â\93\9bV â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[c, h] V2 →
+                     â¬\86*[⫯i] V2 â\89¡ T2 â\86\92  â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88[c+𝟘𝟙, h] T2.
 #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 +43,12 @@ qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpg_inv_lref1_drops: â\88\80c,h,G,i,L,T2. â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡[c, h] T2 →
+lemma cpg_inv_lref1_drops: â\88\80c,h,G,i,L,T2. â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88[c, h] T2 →
                            ∨∨ T2 = #i ∧ c = 𝟘𝟘
-                            | â\88\83â\88\83cV,K,V,V2. â¬\87*[i] L â\89¡ K.â\93\93V & â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[cV, h] V2 &
+                            | â\88\83â\88\83cV,K,V,V2. â¬\87*[i] L â\89¡ K.â\93\93V & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[cV, h] V2 &
                                            ⬆*[⫯i] V2 ≡ T2 & c = cV
-                            | â\88\83â\88\83cV,K,V,V2. â¬\87*[i] L â\89¡ K.â\93\9bV & â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[cV, h] V2 &
-                                           ⬆*[⫯i] V2 ≡ T2 & c = (↓cV) + 𝟘𝟙.
+                            | â\88\83â\88\83cV,K,V,V2. â¬\87*[i] L â\89¡ K.â\93\9bV & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[cV, h] V2 &
+                                           ⬆*[⫯i] V2 ≡ T2 & c = cV + 𝟘𝟙.
 #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 +61,13 @@ lemma cpg_inv_lref1_drops: ∀c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ➡[c, h] T2 →
 ]
 qed-.
 
-lemma cpg_inv_atom1_drops: â\88\80c,h,I,G,L,T2. â¦\83G, Lâ¦\84 â\8a¢ â\93ª{I} â\9e¡[c, h] T2 →
+lemma cpg_inv_atom1_drops: â\88\80c,h,I,G,L,T2. â¦\83G, Lâ¦\84 â\8a¢ â\93ª{I} â¬\88[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¡ K.â\93\93V & â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[cV, h] V2 &
+                            | â\88\83â\88\83cV,i,K,V,V2. â¬\87*[i] L â\89¡ K.â\93\93V & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[cV, h] V2 &
                                              ⬆*[⫯i] V2 ≡ T2 & I = LRef i & c = cV
-                            | â\88\83â\88\83cV,i,K,V,V2. â¬\87*[i] L â\89¡ K.â\93\9bV & â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[cV, h] V2 &
-                                             ⬆*[⫯i] V2 ≡ T2 & I = LRef i & c = (↓cV) + 𝟘𝟙.
+                            | â\88\83â\88\83cV,i,K,V,V2. â¬\87*[i] L â\89¡ K.â\93\9bV & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[cV, h] V2 &
+                                             ⬆*[⫯i] V2 ≡ T2 & I = LRef i & c = cV + 𝟘𝟙.
 #c #h * #n #G #L #T2 #H
 [ elim (cpg_inv_sort1 … H) -H *
   /3 width=3 by or4_intro0, or4_intro1, ex3_intro, conj/
@@ -80,6 +80,7 @@ qed-.
 
 (* Properties with generic slicing for local environments *******************)
 
+(* Note: it should use drops_split_trans_pair2 *)
 lemma cpg_lifts: ∀c,h,G. d_liftable2 (cpg h c G).
 #c #h #G #K #T generalize in match c; -c
 @(fqup_wf_ind_eq … G K T) -G -K -T #G0 #K0 #T0 #IH #G #K * *
@@ -94,7 +95,7 @@ lemma cpg_lifts: ∀c,h,G. d_liftable2 (cpg h c G).
   elim (lifts_inv_lref1 … H1) -H1 #i2 #Hf #H destruct
   lapply (drops_trans … HLK … HK0 ??) -HLK [3,6: |*: // ] #H
   elim (drops_split_trans … H) -H [1,6: |*: /2 width=6 by after_uni_dx/ ] #Y #HL0 #HY
-  lapply (drops_inv_tls_at … Hf … HY) -HY #HY
+  lapply (drops_tls_at … Hf … HY) -HY #HY
   elim (drops_inv_skip2 … HY) -HY #L0 #W #HLK0 #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 (𝐔❴⫯i2❵)) #U2 #HWU2
@@ -166,7 +167,7 @@ lemma cpg_inv_lifts1: ∀c,h,G. d_deliftable2_sn (cpg h c G).
   elim (lifts_inv_lref2 … H1) -H1 #i1 #Hf #H destruct
   lapply (drops_split_div … HLK (𝐔❴i1❵) ???) -HLK [4,8: * |*: // ] #Y0 #HK0 #HLY0
   lapply (drops_conf … HL0 … HLY0 ??) -HLY0 [3,6: |*: /2 width=6 by after_uni_dx/ ] #HLY0
-  lapply (drops_inv_tls_at … Hf … HLY0) -HLY0 #HLY0
+  lapply (drops_tls_at … Hf … HLY0) -HLY0 #HLY0
   elim (drops_inv_skip1 … HLY0) -HLY0 #K0 #V #HLK0 #HVW #H destruct
   elim (IH … HW2 … HLK0 … HVW) -IH /2 width=2 by fqup_lref/ -L -L0 -W #V2 #HVW2 #HV2
   lapply (lifts_trans … HVW2 … HWU2 ??) -W2 [3,6: |*: // ] #HVU2