(* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
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.
+ 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_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.
+ 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_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.
+ 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 *******************)