(* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
definition tc_dedropable_sn: predicate (relation3 lenv term term) ≝
- λR. â\88\80b,f,L1,K1. â¬\87*[b, f] L1 â\89¡ K1 →
- â\88\80K2,T. K1 ⪤**[R, T] K2 â\86\92 â\88\80U. â¬\86*[f] T â\89¡ U →
- â\88\83â\88\83L2. L1 ⪤**[R, U] L2 & â¬\87*[b, f] L2 â\89¡ K2 & L1 â\89\90[f] L2.
+ λR. â\88\80b,f,L1,K1. â¬\87*[b, f] L1 â\89\98 K1 →
+ â\88\80K2,T. K1 ⪤**[R, T] K2 â\86\92 â\88\80U. â¬\86*[f] T â\89\98 U →
+ â\88\83â\88\83L2. L1 ⪤**[R, U] L2 & â¬\87*[b, f] L2 â\89\98 K2 & L1 â\89¡[f] L2.
definition tc_dropable_sn: predicate (relation3 lenv term term) ≝
- λR. â\88\80b,f,L1,K1. â¬\87*[b, f] L1 â\89¡ K1 → 𝐔⦃f⦄ →
- â\88\80L2,U. L1 ⪤**[R, U] L2 â\86\92 â\88\80T. â¬\86*[f] T â\89¡ U →
- â\88\83â\88\83K2. K1 ⪤**[R, T] K2 & â¬\87*[b, f] L2 â\89¡ K2.
+ λR. â\88\80b,f,L1,K1. â¬\87*[b, f] L1 â\89\98 K1 → 𝐔⦃f⦄ →
+ â\88\80L2,U. L1 ⪤**[R, U] L2 â\86\92 â\88\80T. â¬\86*[f] T â\89\98 U →
+ â\88\83â\88\83K2. K1 ⪤**[R, T] K2 & â¬\87*[b, f] L2 â\89\98 K2.
definition tc_dropable_dx: predicate (relation3 lenv term term) ≝
λR. ∀L1,L2,U. L1 ⪤**[R, U] L2 →
- â\88\80b,f,K2. â¬\87*[b, f] L2 â\89¡ K2 â\86\92 ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\88\80T. â¬\86*[f] T â\89¡ U →
- â\88\83â\88\83K1. â¬\87*[b, f] L1 â\89¡ K1 & K1 ⪤**[R, T] K2.
+ â\88\80b,f,K2. â¬\87*[b, f] L2 â\89\98 K2 â\86\92 ð\9d\90\94â¦\83fâ¦\84 â\86\92 â\88\80T. â¬\86*[f] T â\89\98 U →
+ â\88\83â\88\83K1. â¬\87*[b, f] L1 â\89\98 K1 & K1 ⪤**[R, T] K2.
(* Properties with generic slicing for local environments *******************)
-lemma dedropable_sn_LTC: ∀R. dedropable_sn R → tc_dedropable_sn R.
+lemma dedropable_sn_CTC: ∀R. dedropable_sn R → tc_dedropable_sn R.
#R #HR #b #f #L1 #K1 #HLK1 #K2 #T #H elim H -K2
[ #K2 #HK12 #U #HTU elim (HR … HLK1 … HK12 … HTU) -K1 -T -HR
/3 width=4 by ex3_intro, inj/
(* Inversion lemmas with generic slicing for local environments *************)
-lemma dropable_sn_LTC: ∀R. dropable_sn R → tc_dropable_sn R.
+lemma dropable_sn_CTC: ∀R. dropable_sn R → tc_dropable_sn R.
#R #HR #b #f #L1 #K1 #HLK1 #Hf #L2 #U #H elim H -L2
[ #L2 #HL12 #T #HTU elim (HR … HLK1 … HL12 … HTU) -L1 -U -HR
/3 width=3 by inj, ex2_intro/
]
qed-.
-lemma dropable_dx_LTC: ∀R. dropable_dx R → tc_dropable_dx R.
+lemma dropable_dx_CTC: ∀R. dropable_dx R → tc_dropable_dx R.
#R #HR #L1 #L2 #U #H elim H -L2
[ #L2 #HL12 #b #f #K2 #HLK2 #Hf #T #HTU
elim (HR … HL12 … HLK2 … HTU) -L2 -U -HR