+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "ground_2/lib/star.ma".
-include "basic_2/relocation/seq_seq.ma".
-
-(* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
-
-(* Properties with contextual transitive closure ****************************)
-
-(* Basic_2A1: was: d_liftable_LTC *)
-lemma d2_liftable_sn_CTC: ∀C,S,R. d_liftable2_sn C S R → d_liftable2_sn C S (CTC … R).
-#C #S #R #HR #K #T1 #T2 #H elim H -T2
-[ #T2 #HT12 #b #f #L #HLK #U1 #HTU1
- elim (HR … HT12 … HLK … HTU1) /3 width=3 by inj, ex2_intro/
-| #T #T2 #_ #HT2 #IHT1 #b #f #L #HLK #U1 #HTU1
- elim (IHT1 … HLK … HTU1) -T1 #U #HTU #HU1
- elim (HR … HT2 … HLK … HTU) -HR -K -T /3 width=5 by step, ex2_intro/
-]
-qed-.
-
-(* Basic_2A1: was: d_deliftable_sn_LTC *)
-lemma d2_deliftable_sn_CTC: ∀C,S,R. d_deliftable2_sn C S R → d_deliftable2_sn C S (CTC … R).
-#C #S #R #HR #L #U1 #U2 #H elim H -U2
-[ #U2 #HU12 #b #f #K #HLK #T1 #HTU1
- elim (HR … HU12 … HLK … HTU1) -HR -L -U1 /3 width=3 by inj, ex2_intro/
-| #U #U2 #_ #HU2 #IHU1 #b #f #K #HLK #T1 #HTU1
- elim (IHU1 … HLK … HTU1) -IHU1 -U1 #T #HTU #HT1
- elim (HR … HU2 … HLK … HTU) -HR -L -U /3 width=5 by step, ex2_intro/
-]
-qed-.
-
-lemma co_dropable_sn_CTC: ∀R. co_dropable_sn R → co_dropable_sn (CTC … R).
-#R #HR #b #f #L1 #K1 #HLK1 #Hf #f2 #L2 #H elim H -L2
-[ #L2 #HL12 #f1 #H elim (HR … HLK1 … Hf … HL12 … H) -HR -Hf -f2 -L1
- /3 width=3 by inj, ex2_intro/
-| #L #L2 #_ #HL2 #IH #f1 #H elim (IH … H) -IH
- #K #HK1 #HLK elim (HR … HLK … HL2 … H) -HR -f2 -L
- /3 width=3 by step, ex2_intro/
-]
-qed-.
-
-lemma co_dropable_dx_CTC: ∀R. co_dropable_dx R → co_dropable_dx (CTC … R).
-#R #HR #f2 #L1 #L2 #H elim H -L2
-[ #L2 #HL12 #b #f #K2 #HLK2 #Hf #f1 #Hf2 elim (HR … HL12 … HLK2 … Hf … Hf2) -HR -Hf -f2 -L2
- /3 width=3 by inj, ex2_intro/
-| #L #L2 #_ #HL2 #IHL1 #b #f #K2 #HLK2 #Hf #f1 #Hf2 elim (HR … HL2 … HLK2 … Hf … Hf2) -HR -L2
- #K #HLK #HK2 elim (IHL1 … HLK … Hf … Hf2) -Hf -f2 -L
- /3 width=5 by step, ex2_intro/
-]
-qed-.
-
-lemma co_dedropable_sn_CTC: ∀R. co_dedropable_sn R → co_dedropable_sn (CTC … R).
-#R #HR #b #f #L1 #K1 #HLK1 #f1 #K2 #H elim H -K2
-[ #K2 #HK12 #f2 #Hf elim (HR … HLK1 … HK12 … Hf) -HR -f1 -K1
- /3 width=4 by inj, ex3_intro/
-| #K #K2 #_ #HK2 #IH #f2 #Hf elim (IH … Hf) -IH -K1
- #L #H1L1 #HLK #H2L1 elim (HR … HLK … HK2 … Hf) -HR -f1 -K
- /3 width=6 by seq_trans, step, ex3_intro/
-]
-qed-.