some restyling ...

[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 8b33836a250f77f43660632e261970e7b2d8e192..71d38a1ba0fbd4e1652a2c6e73aaa6ef07ec32bd 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
@@ -12,17 +12,17 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/drops_drops.ma".
-include "basic_2/s_computation/fqup_weight.ma".
-include "basic_2/s_computation/fqup_drops.ma".
+include "static_2/relocation/drops_drops.ma".
+include "static_2/s_computation/fqup_weight.ma".
+include "static_2/s_computation/fqup_drops.ma".
 include "basic_2/rt_transition/cpg.ma".
 
-(* COUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
+(* BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *****************)
 
 (* 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
@@ -31,8 +31,8 @@ lemma cpg_delta_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≘ K.ⓓV → ⦃G,
 ]
 qed.
 
-lemma cpg_ell_drops: ∀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
@@ -43,11 +43,11 @@ 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
-                            | ∃∃cV,K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 &
+                            | ∃∃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 &
+                            | ∃∃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/
@@ -61,12 +61,12 @@ 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
-                            | ∃∃cV,i,K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G, K⦄ ⊢ V ⬈[Rt, cV, h] V2 &
+                            | ∃∃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 &
+                            | ∃∃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 *
@@ -115,10 +115,9 @@ 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 +198,10 @@ 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