- advances towards strong normalization

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / drops_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
index 06a2eb84e10399a76eb88695661943561215bba6..7fae70bdae0a4d2f860913f0b3a013586ef3d634 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
@@ -17,6 +17,20 @@ include "basic_2/relocation/drops_weight.ma".
 
 (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
 
+(* Main properties on generic relocation ************************************)
+
+lemma d_liftable2_sn_bi: ∀R. d_liftable2_sn R → d_liftable2_bi R.
+#R #HR #K #T1 #T2 #HT12 #b #f #L #HLK #U1 #HTU1 #U2 #HTU2
+elim (HR … HT12 … HLK … HTU1) -HR -K -T1 #X #HTX #HUX
+<(lifts_mono … HTX … HTU2) -T2 -U2 -b -f //
+qed-.
+
+lemma d_deliftable2_sn_bi: ∀R. d_deliftable2_sn R → d_deliftable2_bi R.
+#R #HR #L #U1 #U2 #HU12 #b #f #K #HLK #T1 #HTU1 #T2 #HTU2
+elim (HR … HU12 … HLK … HTU1) -HR -L -U1 #X #HUX #HTX
+<(lifts_inj … HUX … HTU2) -U2 -T2 -b -f //
+qed-.
+
 (* Main properties **********************************************************)
 
 (* Basic_2A1: includes: drop_conf_ge drop_conf_be drop_conf_le *)
@@ -31,7 +45,7 @@ theorem drops_conf: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≡ L →
   #g #Hg #H destruct /3 width=3 by drops_inv_drop1/
 | #f1 #I #K1 #K #V1 #V #_ #HV1 #IH #b2 #f #L2 #HL2 #f2 #Hf elim (after_inv_pxx … Hf) -Hf [1,3: * |*:// ]
   #g2 #g #Hf #H1 #H2 destruct
-  [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, lifts_div/
+  [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, lifts_div3/
   | /4 width=3 by drops_inv_drop1, drops_drop/
   ]
 ]
@@ -87,7 +101,7 @@ qed-.
 (* Basic_2A1: includes: drop_mono *)
 lemma drops_mono: ∀b1,f,L,L1. ⬇*[b1, f] L ≡ L1 →
                   ∀b2,L2. ⬇*[b2, f] L ≡ L2 → L1 = L2.
-#b1 #f #L #L1 lapply (isid_after_dx 𝐈𝐝 … f)
+#b1 #f #L #L1 lapply (after_isid_dx 𝐈𝐝 … f)
 /3 width=8 by drops_conf, drops_fwd_isid/
 qed-.
 
@@ -125,3 +139,9 @@ lapply (drops_eq_repl_back … Hf1 … H12) -Hf1 #H0
 lapply (drops_mono … H0 … Hf2) -L #H
 destruct /2 width=1 by and3_intro/
 qed-.
+
+lemma drops_inv_uni: ∀L,i. ⬇*[Ⓕ, 𝐔❴i❵] L ≡ ⋆ → ∀I,K,V. ⬇*[i] L ≡ K.ⓑ{I}V → ⊥.
+#L #i #H1 #I #K #V #H2
+lapply (drops_F … H2) -H2 #H2
+lapply (drops_mono … H2 … H1) -L -i #H destruct
+qed-.