X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Fdrops_length.ma;h=7543a555908d738cef29fc8917f313c131c60fc8;hp=a5974d9c44a774ab01ad6d9aa8f3169671b7bbce;hb=222044da28742b24584549ba86b1805a87def070;hpb=d3636c8688ec08cc39eb7ce6c1918b25bbccc349

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_length.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_length.ma
index a5974d9c4..7543a5559 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_length.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_length.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/grammar/lenv_length.ma".
+include "basic_2/syntax/lenv_length.ma".
 include "basic_2/relocation/drops.ma".
 
 (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
@@ -20,105 +20,105 @@ include "basic_2/relocation/drops.ma".
 (* Forward lemmas with length for local environments ************************)
 
 (* Basic_2A1: includes: drop_fwd_length_le4 *)
-lemma drops_fwd_length_le4: ∀L1,L2,c,f. ⬇*[c, f] L1 ≡ L2 → |L2| ≤ |L1|.
-#L1 #L2 #c #f #H elim H -L1 -L2 -f /2 width=1 by le_S, le_S_S/
+lemma drops_fwd_length_le4: ∀b,f,L1,L2. ⬇*[b, f] L1 ≘ L2 → |L2| ≤ |L1|.
+#b #f #L1 #L2 #H elim H -f -L1 -L2 /2 width=1 by le_S, le_S_S/
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_eq1 *)
-theorem drops_fwd_length_eq1: ∀L1,K1,c1,c2,f. ⬇*[c1, f] L1 ≡ K1 →
-                              ∀L2,K2. ⬇*[c2, f] L2 ≡ K2 →
+theorem drops_fwd_length_eq1: ∀b1,b2,f,L1,K1. ⬇*[b1, f] L1 ≘ K1 →
+                              ∀L2,K2. ⬇*[b2, f] L2 ≘ K2 →
                               |L1| = |L2| → |K1| = |K2|.
-#L1 #K1 #c1 #c2 #f #HLK1 elim HLK1 -L1 -K1 -f
+#b1 #b2 #f #L1 #K1 #HLK1 elim HLK1 -f -L1 -K1
 [ #f #_ #L2 #K2 #HLK2 #H lapply (length_inv_zero_sn … H) -H
   #H destruct elim (drops_inv_atom1 … HLK2) -HLK2 //
-| #I1 #L1 #K1 #V1 #f #_ #IH #X2 #K2 #HX #H elim (length_inv_succ_sn … H) -H
-  #I2 #L2 #V2 #H12 #H destruct lapply (drops_inv_drop1 … HX) -HX
+| #f #I1 #L1 #K1 #_ #IH #X2 #K2 #HX #H elim (length_inv_succ_sn … H) -H
+  #I2 #L2 #H12 #H destruct lapply (drops_inv_drop1 … HX) -HX
   #HLK2 @(IH … HLK2 H12) (**) (* auto fails *)
-| #I1 #L1 #K1 #V1 #V2 #f #_ #_ #IH #X2 #Y2 #HX #H elim (length_inv_succ_sn … H) -H
-  #I2 #L2 #V2 #H12 #H destruct elim (drops_inv_skip1 … HX) -HX
-  #K2 #W2 #HLK2 #_ #H destruct
-  lapply (IH … HLK2 H12) -f /2 width=1 by/ (**) (* full auto fails *)
+| #f #I1 #I2 #L1 #K1 #_ #_ #IH #X2 #Y2 #HX #H elim (length_inv_succ_sn … H) -H
+  #I2 #L2 #H12 #H destruct elim (drops_inv_skip1 … HX) -HX
+  #I2 #K2 #HLK2 #_ #H destruct
+  lapply (IH … HLK2 H12) -f >length_bind >length_bind /2 width=1 by/ (**) (* full auto fails *)
 ]
 qed-.  
 
 (* forward lemmas with finite colength assignment ***************************)
 
-lemma drops_fwd_fcla: ∀L1,L2,f. ⬇*[Ⓣ, f] L1 ≡ L2 →
-                      ∃∃n. 𝐂⦃f⦄ ≡ n & |L1| = |L2| + n.
-#L1 #L2 #f #H elim H -L1 -L2 -f
+lemma drops_fwd_fcla: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≘ L2 →
+                      ∃∃n. 𝐂⦃f⦄ ≘ n & |L1| = |L2| + n.
+#f #L1 #L2 #H elim H -f -L1 -L2
 [ /4 width=3 by fcla_isid, ex2_intro/
-| #I #L1 #L2 #V #f #_ * /3 width=3 by fcla_next, ex2_intro, eq_f/
-| #I #L1 #L2 #V1 #V2 #f #_ #_ * /3 width=3 by fcla_push, ex2_intro/
+| #f #I #L1 #L2 #_ * >length_bind /3 width=3 by fcla_next, ex2_intro, eq_f/
+| #f #I1 #I2 #L1 #L2 #_ #_ * >length_bind >length_bind /3 width=3 by fcla_push, ex2_intro/
 ]
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length *)
-lemma drops_fcla_fwd: ∀L1,L2,f,n. ⬇*[Ⓣ, f] L1 ≡ L2 → 𝐂⦃f⦄ ≡ n →
+lemma drops_fcla_fwd: ∀f,L1,L2,n. ⬇*[Ⓣ, f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n →
                       |L1| = |L2| + n.
-#l1 #l2 #f #n #Hf #Hn elim (drops_fwd_fcla … Hf) -Hf
-#m #Hm #H <(fcla_mono … Hm … Hn) -f //
+#f #l1 #l2 #n #Hf #Hn elim (drops_fwd_fcla … Hf) -Hf
+#k #Hm #H <(fcla_mono … Hm … Hn) -f //
 qed-.
 
-lemma drops_fwd_fcla_le2: ∀L1,L2,f. ⬇*[Ⓣ, f] L1 ≡ L2 →
-                          ∃∃n. 𝐂⦃f⦄ ≡ n & n ≤ |L1|.
-#L1 #L2 #f #H elim (drops_fwd_fcla … H) -H /2 width=3 by ex2_intro/
+lemma drops_fwd_fcla_le2: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≘ L2 →
+                          ∃∃n. 𝐂⦃f⦄ ≘ n & n ≤ |L1|.
+#f #L1 #L2 #H elim (drops_fwd_fcla … H) -H /2 width=3 by ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_le2 *)
-lemma drops_fcla_fwd_le2: ∀L1,L2,f,n. ⬇*[Ⓣ, f] L1 ≡ L2 → 𝐂⦃f⦄ ≡ n →
+lemma drops_fcla_fwd_le2: ∀f,L1,L2,n. ⬇*[Ⓣ, f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n →
                           n ≤ |L1|.
-#L1 #L2 #f #n #H #Hn elim (drops_fwd_fcla_le2 … H) -H
-#m #Hm #H <(fcla_mono … Hm … Hn) -f //
+#f #L1 #L2 #n #H #Hn elim (drops_fwd_fcla_le2 … H) -H
+#k #Hm #H <(fcla_mono … Hm … Hn) -f //
 qed-.
 
-lemma drops_fwd_fcla_lt2: ∀L1,I2,K2,V2,f. ⬇*[Ⓣ, f] L1 ≡ K2.ⓑ{I2}V2 →
-                          ∃∃n. 𝐂⦃f⦄ ≡ n & n < |L1|.
-#L1 #I2 #K2 #V2 #f #H elim (drops_fwd_fcla … H) -H
+lemma drops_fwd_fcla_lt2: ∀f,L1,I2,K2. ⬇*[Ⓣ, f] L1 ≘ K2.ⓘ{I2} →
+                          ∃∃n. 𝐂⦃f⦄ ≘ n & n < |L1|.
+#f #L1 #I2 #K2 #H elim (drops_fwd_fcla … H) -H
 #n #Hf #H >H -L1 /3 width=3 by le_S_S, ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_lt2 *)
-lemma drops_fcla_fwd_lt2: ∀L1,I2,K2,V2,f,n.
-                          ⬇*[Ⓣ, f] L1 ≡ K2.ⓑ{I2}V2 → 𝐂⦃f⦄ ≡ n →
+lemma drops_fcla_fwd_lt2: ∀f,L1,I2,K2,n.
+                          ⬇*[Ⓣ, f] L1 ≘ K2.ⓘ{I2} → 𝐂⦃f⦄ ≘ n →
                           n < |L1|.
-#L1 #I2 #K2 #V2 #f #n #H #Hn elim (drops_fwd_fcla_lt2 … H) -H
-#m #Hm #H <(fcla_mono … Hm … Hn) -f //
+#f #L1 #I2 #K2 #n #H #Hn elim (drops_fwd_fcla_lt2 … H) -H
+#k #Hm #H <(fcla_mono … Hm … Hn) -f //
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_lt4 *)
-lemma drops_fcla_fwd_lt4: ∀L1,L2,f,n. ⬇*[Ⓣ, f] L1 ≡ L2 → 𝐂⦃f⦄ ≡ n → 0 < n →
+lemma drops_fcla_fwd_lt4: ∀f,L1,L2,n. ⬇*[Ⓣ, f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n → 0 < n →
                           |L2| < |L1|.
-#L1 #L2 #f #n #H #Hf #Hn lapply (drops_fcla_fwd … H Hf) -f
+#f #L1 #L2 #n #H #Hf #Hn lapply (drops_fcla_fwd … H Hf) -f
 /2 width=1 by lt_minus_to_plus_r/ qed-.
 
 (* Basic_2A1: includes: drop_inv_length_eq *)
-lemma drops_inv_length_eq: ∀L1,L2,f. ⬇*[Ⓣ, f] L1 ≡ L2 → |L1| = |L2| → 𝐈⦃f⦄.
-#L1 #L2 #f #H #HL12 elim (drops_fwd_fcla … H) -H
+lemma drops_inv_length_eq: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≘ L2 → |L1| = |L2| → 𝐈⦃f⦄.
+#f #L1 #L2 #H #HL12 elim (drops_fwd_fcla … H) -H
 #n #Hn <HL12 -L2 #H lapply (discr_plus_x_xy … H) -H
 /2 width=3 by fcla_inv_xp/
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_eq2 *)
-theorem drops_fwd_length_eq2: ∀L1,L2,K1,K2,f. ⬇*[Ⓣ, f] L1 ≡ K1 → ⬇*[Ⓣ, f] L2 ≡ K2 →
+theorem drops_fwd_length_eq2: ∀f,L1,L2,K1,K2. ⬇*[Ⓣ, f] L1 ≘ K1 → ⬇*[Ⓣ, f] L2 ≘ K2 →
                               |K1| = |K2| → |L1| = |L2|.
-#L1 #L2 #K1 #K2 #f #HLK1 #HLK2 #HL12
+#f #L1 #L2 #K1 #K2 #HLK1 #HLK2 #HL12
 elim (drops_fwd_fcla … HLK1) -HLK1 #n1 #Hn1 #H1 >H1 -L1
 elim (drops_fwd_fcla … HLK2) -HLK2 #n2 #Hn2 #H2 >H2 -L2
 <(fcla_mono … Hn2 … Hn1) -f //
 qed-.
 
-theorem drops_conf_div: ∀L1,L2,f1,f2. ⬇*[Ⓣ, f1] L1 ≡ L2 → ⬇*[Ⓣ, f2] L1 ≡ L2 →
-                        ∃∃n. 𝐂⦃f1⦄ ≡ n & 𝐂⦃f2⦄ ≡ n.
-#L1 #L2 #f1 #f2 #H1 #H2
+theorem drops_conf_div: ∀f1,f2,L1,L2. ⬇*[Ⓣ, f1] L1 ≘ L2 → ⬇*[Ⓣ, f2] L1 ≘ L2 →
+                        ∃∃n. 𝐂⦃f1⦄ ≘ n & 𝐂⦃f2⦄ ≘ n.
+#f1 #f2 #L1 #L2 #H1 #H2
 elim (drops_fwd_fcla … H1) -H1 #n1 #Hf1 #H1
 elim (drops_fwd_fcla … H2) -H2 #n2 #Hf2 >H1 -L1 #H
 lapply (injective_plus_r … H) -L2 #H destruct /2 width=3 by ex2_intro/
 qed-.
 
-theorem drops_conf_div_fcla: ∀L1,L2,f1,f2,n1,n2.
-                             ⬇*[Ⓣ, f1] L1 ≡ L2 → ⬇*[Ⓣ, f2] L1 ≡ L2 → 𝐂⦃f1⦄ ≡ n1 → 𝐂⦃f2⦄ ≡ n2 →
+theorem drops_conf_div_fcla: ∀f1,f2,L1,L2,n1,n2.
+                             ⬇*[Ⓣ, f1] L1 ≘ L2 → ⬇*[Ⓣ, f2] L1 ≘ L2 → 𝐂⦃f1⦄ ≘ n1 → 𝐂⦃f2⦄ ≘ n2 →
                              n1 = n2.
-#L1 #L2 #f1 #f2 #n1 #n2 #Hf1 #Hf2 #Hn1 #Hn2
+#f1 #f2 #L1 #L2 #n1 #n2 #Hf1 #Hf2 #Hn1 #Hn2
 lapply (drops_fcla_fwd … Hf1 Hn1) -f1 #H1
 lapply (drops_fcla_fwd … Hf2 Hn2) -f2 >H1 -L1
 /2 width=1 by injective_plus_r/