include "basic_2/rt_transition/cpg_drops.ma".
include "basic_2/rt_transition/cpx.ma".
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS *****************)
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************)
(* Advanced properties ******************************************************)
(* Basic_2A1: was: cpx_delta *)
lemma cpx_delta_drops: ∀h,I,G,L,K,V,V2,W2,i.
- â¬\87*[i] L â\89¡ K.â\93\91{I}V â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[h] V2 →
- â¬\86*[⫯i] V2 â\89¡ W2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡[h] W2.
+ â¬\87*[i] L â\89¡ K.â\93\91{I}V â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[h] V2 →
+ â¬\86*[⫯i] V2 â\89¡ W2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88[h] W2.
#h * #G #L #K #V #V2 #W2 #i #HLK *
/3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
qed.
(* Advanced inversion lemmas ************************************************)
(* Basic_2A1: was: cpx_inv_atom1 *)
-lemma cpx_inv_atom1_drops: â\88\80h,I,G,L,T2. â¦\83G, Lâ¦\84 â\8a¢ â\93ª{I} â\9e¡[h] T2 →
+lemma cpx_inv_atom1_drops: â\88\80h,I,G,L,T2. â¦\83G, Lâ¦\84 â\8a¢ â\93ª{I} â¬\88[h] T2 →
∨∨ T2 = ⓪{I}
| ∃∃s. T2 = ⋆(next h s) & I = Sort s
- | â\88\83â\88\83J,K,V,V2,i. â¬\87*[i] L â\89¡ K.â\93\91{J}V & â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[h] V2 &
+ | â\88\83â\88\83J,K,V,V2,i. â¬\87*[i] L â\89¡ K.â\93\91{J}V & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[h] V2 &
⬆*[⫯i] V2 ≡ T2 & I = LRef i.
#h #I #G #L #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
/4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_intro, ex_intro/
qed-.
(* Basic_2A1: was: cpx_inv_lref1 *)
-lemma cpx_inv_lref1_drops: â\88\80h,G,L,T2,i. â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡[h] T2 →
+lemma cpx_inv_lref1_drops: â\88\80h,G,L,T2,i. â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88[h] T2 →
T2 = #i ∨
- â\88\83â\88\83J,K,V,V2. â¬\87*[i] L â\89¡ K. â\93\91{J}V & â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡[h] V2 &
+ â\88\83â\88\83J,K,V,V2. â¬\87*[i] L â\89¡ K. â\93\91{J}V & â¦\83G, Kâ¦\84 â\8a¢ V â¬\88[h] V2 &
⬆*[⫯i] V2 ≡ T2.
#h #G #L #T1 #i * #c #H elim (cpg_inv_lref1_drops … H) -H *
/4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/
(* Inversion lemmas with generic slicing for local environments *************)
(* Basic_2A1: includes: cpx_inv_lift1 *)
-lemma cpx_inv_lift1: ∀h,G. d_deliftable2_sn (cpx h G).
+lemma cpx_inv_lifts: ∀h,G. d_deliftable2_sn (cpx h G).
#h #G #L #U1 #U2 * #cU #HU12 #b #f #K #HLK #T1 #HTU1
elim (cpg_inv_lifts1 … HU12 … HLK … HTU1) -L -U1
/3 width=4 by ex2_intro, ex_intro/