X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpm_drops.ma;h=38c78dea6644e6979362d7ed92d28b6880125796;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hp=bc9463c958390c5a16ec878d6d4b3f5bf6d30fcf;hpb=647b419e96770d90a82d7a9e5e8843566a9f93ee;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
index bc9463c95..38c78dea6 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
@@ -21,61 +21,62 @@ include "basic_2/rt_transition/cpm.ma".
 
 (* Basic_1: includes: pr0_lift pr2_lift *)
 (* Basic_2A1: includes: cpr_lift *)
-lemma cpm_lifts_sn: ∀n,h,G. d_liftable2_sn … lifts (λL. cpm h G L n).
-#n #h #G #K #T1 #T2 * #c #Hc #HT12 #b #f #L #HLK #U1 #HTU1
+lemma cpm_lifts_sn (h) (n) (G): d_liftable2_sn … lifts (λL. cpm h G L n).
+#h #n #G #K #T1 #T2 * #c #Hc #HT12 #b #f #L #HLK #U1 #HTU1
 elim (cpg_lifts_sn … HT12 … HLK … HTU1) -K -T1
 /3 width=5 by ex2_intro/
 qed-.
 
-lemma cpm_lifts_bi: ∀n,h,G. d_liftable2_bi … lifts (λL. cpm h G L n).
-#n #h #G #K #T1 #T2 * /3 width=11 by cpg_lifts_bi, ex2_intro/
+lemma cpm_lifts_bi (h) (n) (G): d_liftable2_bi … lifts (λL. cpm h G L n).
+#h #n #G #K #T1 #T2 * /3 width=11 by cpg_lifts_bi, ex2_intro/
 qed-.
 
 (* Inversion lemmas with generic slicing for local environments *************)
 
 (* Basic_1: includes: pr0_gen_lift pr2_gen_lift *)
 (* Basic_2A1: includes: cpr_inv_lift1 *)
-lemma cpm_inv_lifts_sn: ∀n,h,G. d_deliftable2_sn … lifts (λL. cpm h G L n).
-#n #h #G #L #U1 #U2 * #c #Hc #HU12 #b #f #K #HLK #T1 #HTU1
+lemma cpm_inv_lifts_sn (h) (n) (G): d_deliftable2_sn … lifts (λL. cpm h G L n).
+#h #n #G #L #U1 #U2 * #c #Hc #HU12 #b #f #K #HLK #T1 #HTU1
 elim (cpg_inv_lifts_sn … HU12 … HLK … HTU1) -L -U1
 /3 width=5 by ex2_intro/
 qed-.
 
-lemma cpm_inv_lifts_bi: ∀n,h,G. d_deliftable2_bi … lifts (λL. cpm h G L n).
-#n #h #G #L #U1 #U2 * /3 width=11 by cpg_inv_lifts_bi, ex2_intro/
+lemma cpm_inv_lifts_bi (h) (n) (G): d_deliftable2_bi … lifts (λL. cpm h G L n).
+#h #n #G #L #U1 #U2 * /3 width=11 by cpg_inv_lifts_bi, ex2_intro/
 qed-.
 
 (* Advanced properties ******************************************************)
 
 (* Basic_1: includes: pr2_delta1 *)
 (* Basic_2A1: includes: cpr_delta *)
-lemma cpm_delta_drops: ∀n,h,G,L,K,V,V2,W2,i.
-                       ⬇*[i] L ≘ K.ⓓV → ⦃G,K⦄ ⊢ V ➡[n,h] V2 →
-                       ⬆*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ➡[n,h] W2.
-#n #h #G #L #K #V #V2 #W2 #i #HLK *
+lemma cpm_delta_drops (h) (n) (G) (L):
+      ∀K,V,V2,W2,i.
+      ⇩[i] L ≘ K.ⓓV → ❪G,K❫ ⊢ V ➡[h,n] V2 →
+      ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ➡[h,n] W2.
+#h #n #G #L #K #V #V2 #W2 #i #HLK *
 /3 width=8 by cpg_delta_drops, ex2_intro/
 qed.
 
-lemma cpm_ell_drops: ∀n,h,G,L,K,V,V2,W2,i.
-                     ⬇*[i] L ≘ K.ⓛV → ⦃G,K⦄ ⊢ V ➡[n,h] V2 →
-                     ⬆*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ➡[↑n,h] W2.
-#n #h #G #L #K #V #V2 #W2 #i #HLK *
+lemma cpm_ell_drops (h) (n) (G) (L):
+      ∀K,V,V2,W2,i.
+      ⇩[i] L ≘ K.ⓛV → ❪G,K❫ ⊢ V ➡[h,n] V2 →
+      ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ➡[h,↑n] W2.
+#h #n #G #L #K #V #V2 #W2 #i #HLK *
 /3 width=8 by cpg_ell_drops, isrt_succ, ex2_intro/
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpm_inv_atom1_drops: ∀n,h,I,G,L,T2. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] T2 →
-                           ∨∨ T2 = ⓪{I} ∧ n = 0
-                            | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s & n = 1
-                            | ∃∃K,V,V2,i. ⬇*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ➡[n,h] V2 &
-                                          ⬆*[↑i] V2 ≘ T2 & I = LRef i
-                            | ∃∃m,K,V,V2,i. ⬇*[i] L ≘ K.ⓛV & ⦃G,K⦄ ⊢ V ➡[m,h] V2 &
-                                            ⬆*[↑i] V2 ≘ T2 & I = LRef i & n = ↑m.
-#n #h #I #G #L #T2 * #c #Hc #H elim (cpg_inv_atom1_drops … H) -H *
+lemma cpm_inv_atom1_drops (h) (n) (G) (L):
+      ∀I,T2. ❪G,L❫ ⊢ ⓪[I] ➡[h,n] T2 →
+      ∨∨ ∧∧ T2 = ⓪[I] & n = 0
+       | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s & n = 1
+       | ∃∃K,V,V2,i. ⇩[i] L ≘ K.ⓓV & ❪G,K❫ ⊢ V ➡[h,n] V2 & ⇧[↑i] V2 ≘ T2 & I = LRef i
+       | ∃∃m,K,V,V2,i. ⇩[i] L ≘ K.ⓛV & ❪G,K❫ ⊢ V ➡[h,m] V2 & ⇧[↑i] V2 ≘ T2 & I = LRef i & n = ↑m.
+#h #n #G #L #I #T2 * #c #Hc #H elim (cpg_inv_atom1_drops … H) -H *
 [ #H1 #H2 destruct lapply (isrt_inv_00 … Hc) -Hc
   /3 width=1 by or4_intro0, conj/
-| #s #H1 #H2 #H3 destruct lapply (isrt_inv_01 … Hc) -Hc
+| #s1 #s2 #H1 #H2 #H3 #H4 destruct lapply (isrt_inv_01 … Hc) -Hc
   /4 width=3 by or4_intro1, ex3_intro, sym_eq/ (**) (* sym_eq *)
 | #cV #i #K #V1 #V2 #HLK #HV12 #HVT2 #H1 #H2 destruct
   /4 width=8 by ex4_4_intro, ex2_intro, or4_intro2/
@@ -85,13 +86,12 @@ lemma cpm_inv_atom1_drops: ∀n,h,I,G,L,T2. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] T2 →
 ]
 qed-.
 
-lemma cpm_inv_lref1_drops: ∀n,h,G,L,T2,i. ⦃G,L⦄ ⊢ #i ➡[n,h] T2 →
-                           ∨∨ T2 = #i ∧ n = 0
-                            | ∃∃K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ➡[n,h] V2 &
-                                        ⬆*[↑i] V2 ≘ T2
-                            | ∃∃m,K,V,V2. ⬇*[i] L ≘ K. ⓛV & ⦃G,K⦄ ⊢ V ➡[m,h] V2 &
-                                          ⬆*[↑i] V2 ≘ T2 & n = ↑m.
-#n #h #G #L #T2 #i * #c #Hc #H elim (cpg_inv_lref1_drops … H) -H *
+lemma cpm_inv_lref1_drops (h) (n) (G) (L):
+      ∀T2,i. ❪G,L❫ ⊢ #i ➡[h,n] T2 →
+      ∨∨ ∧∧ T2 = #i & n = 0
+       | ∃∃K,V,V2. ⇩[i] L ≘ K.ⓓV & ❪G,K❫ ⊢ V ➡[h,n] V2 & ⇧[↑i] V2 ≘ T2
+       | ∃∃m,K,V,V2. ⇩[i] L ≘ K. ⓛV & ❪G,K❫ ⊢ V ➡[h,m] V2 & ⇧[↑i] V2 ≘ T2 & n = ↑m.
+#h #n #G #L #T2 #i * #c #Hc #H elim (cpg_inv_lref1_drops … H) -H *
 [ #H1 #H2 destruct lapply (isrt_inv_00 … Hc) -Hc
   /3 width=1 by or3_intro0, conj/
 | #cV #K #V1 #V2 #HLK #HV12 #HVT2 #H destruct
@@ -104,10 +104,11 @@ qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-fact cpm_fwd_plus_aux (n) (h): ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 →
-                               ∀n1,n2. n1+n2 = n →
-                               ∃∃T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T & ⦃G,L⦄ ⊢ T ➡[n2,h] T2.
-#n #h #G #L #T1 #T2 #H @(cpm_ind … H) -G -L -T1 -T2 -n
+fact cpm_fwd_plus_aux (h) (n) (G) (L):
+     ∀T1,T2. ❪G,L❫ ⊢ T1 ➡[h,n] T2 →
+     ∀n1,n2. n1+n2 = n →
+     ∃∃T. ❪G,L❫ ⊢ T1 ➡[h,n1] T & ❪G,L❫ ⊢ T ➡[h,n2] T2.
+#h #n #G #L #T1 #T2 #H @(cpm_ind … H) -G -L -T1 -T2 -n
 [ #I #G #L #n1 #n2 #H
   elim (plus_inv_O3 … H) -H #H1 #H2 destruct
   /2 width=3 by ex2_intro/
@@ -119,19 +120,19 @@ fact cpm_fwd_plus_aux (n) (h): ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 →
   ]
 | #n #G #K #V1 #V2 #W2 #_ #IH #HVW2 #n1 #n2 #H destruct
   elim IH [|*: // ] -IH #V #HV1 #HV2
-  elim (lifts_total V 𝐔❴↑O❵) #W #HVW
+  elim (lifts_total V 𝐔❨↑O❩) #W #HVW
   /5 width=11 by cpm_lifts_bi, cpm_delta, drops_refl, drops_drop, ex2_intro/
 | #n #G #K #V1 #V2 #W2 #HV12 #IH #HVW2 #x1 #n2 #H
   elim (plus_inv_S3_sn … H) -H *
   [ #H1 #H2 destruct -IH /3 width=3 by cpm_ell, ex2_intro/
   | #n1 #H1 #H2 destruct -HV12
     elim (IH n1) [|*: // ] -IH #V #HV1 #HV2
-    elim (lifts_total V 𝐔❴↑O❵) #W #HVW
+    elim (lifts_total V 𝐔❨↑O❩) #W #HVW
     /5 width=11 by cpm_lifts_bi, cpm_ell, drops_refl, drops_drop, ex2_intro/
   ]
 | #n #I #G #K #T2 #U2 #i #_ #IH #HTU2 #n1 #n2 #H destruct
   elim IH [|*: // ] -IH #T #HT1 #HT2
-  elim (lifts_total T 𝐔❴↑O❵) #U #HTU
+  elim (lifts_total T 𝐔❨↑O❩) #U #HTU
   /5 width=11 by cpm_lifts_bi, cpm_lref, drops_refl, drops_drop, ex2_intro/
 | #n #p #I #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ #IHT #n1 #n2 #H destruct
   elim IHT [|*: // ] -IHT #T #HT1 #HT2
@@ -165,6 +166,7 @@ fact cpm_fwd_plus_aux (n) (h): ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 →
 ]
 qed-.
 
-lemma cpm_fwd_plus (h) (G) (L): ∀n1,n2,T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n1+n2,h] T2 →
-                                ∃∃T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T & ⦃G,L⦄ ⊢ T ➡[n2,h] T2.
+lemma cpm_fwd_plus (h) (G) (L):
+      ∀n1,n2,T1,T2. ❪G,L❫ ⊢ T1 ➡[h,n1+n2] T2 →
+      ∃∃T. ❪G,L❫ ⊢ T1 ➡[h,n1] T & ❪G,L❫ ⊢ T ➡[h,n2] T2.
 /2 width=3 by cpm_fwd_plus_aux/ qed-.