(* EXAMPLES *****************************************************************)
-(* Extended validy (basic_2B) vs. restricted validity (basic_1A) ************)
+(* Extended validy (λδ-2A) vs. restricted validity (λδ-1B) ******************)
(* Note: extended validity of a closure, height of cnv_appl > 1 *)
-lemma cnv_extended (h) (p): ∀G,L,s. ⦃G, L.ⓛ⋆s.ⓛⓛ{p}⋆s.⋆s.ⓛ#0⦄ ⊢ ⓐ#2.#0 !*[h].
+lemma cnv_extended (h) (p) (G) (L):
+ ∀s. ❪G,L.ⓛ⋆s.ⓛⓛ[p]⋆s.⋆s.ⓛ#0❫ ⊢ ⓐ#2.#0 ![h,𝛚].
#h #p #G #L #s
@(cnv_appl … 2 p … (⋆s) … (⋆s))
[ //
qed.
(* Note: restricted validity of the η-expanded closure, height of cnv_appl = 1 **)
-lemma vnv_restricted (h) (p): ∀G,L,s. ⦃G, L.ⓛ⋆s.ⓛⓛ{p}⋆s.⋆s.ⓛⓛ{p}⋆s.ⓐ#0.#1⦄ ⊢ ⓐ#2.#0 ![h].
+lemma cnv_restricted (h) (p) (G) (L):
+ ∀s. ❪G,L.ⓛ⋆s.ⓛⓛ[p]⋆s.⋆s.ⓛⓛ[p]⋆s.ⓐ#0.#1❫ ⊢ ⓐ#2.#0 ![h,𝟐].
#h #p #G #L #s
@(cnv_appl … 1 p … (⋆s) … (ⓐ#0.#2))
-[ /2 width=1 by ylt_inj/
+[ //
| /4 width=1 by cnv_sort, cnv_zero, cnv_lref/
| @cnv_zero
@cnv_bind //
@(cnv_appl … 1 p … (⋆s) … (⋆s))
- [ /2 width=1 by ylt_inj/
+ [ //
| /2 width=1 by cnv_sort, cnv_zero/
| /4 width=1 by cnv_sort, cnv_zero, cnv_lref, cnv_bind/
| /2 width=3 by cpms_ell, lifts_sort/