(* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
-definition tc_dedropable_sn: predicate (relation3 lenv term term) ≝
- λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≡ K1 →
- ∀K2,T. K1 ⪤**[R, T] K2 → ∀U. ⬆*[f] T ≡ U →
- ∃∃L2. L1 ⪤**[R, U] L2 & ⬇*[b, f] L2 ≡ K2 & L1 ≐[f] L2.
+definition tc_f_dedropable_sn: predicate (relation3 lenv term term) ≝
+ λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 →
+ ∀K2,T. K1 ⪤**[R, T] K2 → ∀U. ⬆*[f] T ≘ U →
+ ∃∃L2. L1 ⪤**[R, U] L2 & ⬇*[b, f] L2 ≘ K2 & L1 ≡[f] L2.
-definition tc_dropable_sn: predicate (relation3 lenv term term) ≝
- λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≡ K1 → 𝐔⦃f⦄ →
- ∀L2,U. L1 ⪤**[R, U] L2 → ∀T. ⬆*[f] T ≡ U →
- ∃∃K2. K1 ⪤**[R, T] K2 & ⬇*[b, f] L2 ≡ K2.
+definition tc_f_dropable_sn: predicate (relation3 lenv term term) ≝
+ λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 → 𝐔⦃f⦄ →
+ ∀L2,U. L1 ⪤**[R, U] L2 → ∀T. ⬆*[f] T ≘ U →
+ ∃∃K2. K1 ⪤**[R, T] K2 & ⬇*[b, f] L2 ≘ K2.
-definition tc_dropable_dx: predicate (relation3 lenv term term) ≝
- λR. ∀L1,L2,U. L1 ⪤**[R, U] L2 →
- ∀b,f,K2. ⬇*[b, f] L2 ≡ K2 → 𝐔⦃f⦄ → ∀T. ⬆*[f] T ≡ U →
- ∃∃K1. ⬇*[b, f] L1 ≡ K1 & K1 ⪤**[R, T] K2.
+definition tc_f_dropable_dx: predicate (relation3 lenv term term) ≝
+ λR. ∀L1,L2,U. L1 ⪤**[R, U] L2 →
+ ∀b,f,K2. ⬇*[b, f] L2 ≘ K2 → 𝐔⦃f⦄ → ∀T. ⬆*[f] T ≘ U →
+ ∃∃K1. ⬇*[b, f] L1 ≘ 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. f_dedropable_sn R → tc_f_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. f_dropable_sn R → tc_f_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. f_dropable_dx R → tc_f_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