(* Properties with r-equivalence for terms **********************************)
lemma ntas_zero (h) (a) (G) (L):
- â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 ![h,a] â\86\92 â¦\83G,Lâ¦\84 â\8a¢ T2 ![h,a] â\86\92 â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 :*[h,a,0] T2.
+ â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] â\86\92 â\9dªG,Lâ\9d« â\8a¢ T2 ![h,a] â\86\92 â\9dªG,Lâ\9d« â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 :*[h,a,0] T2.
#h #a #G #L #T1 #T2 #HT1 #HT2 #H
elim (cpcs_inv_cprs … H) -H #T0 #HT10 #HT20
/2 width=3 by ntas_intro/
(* Inversion lemmas with r-equivalence for terms ****************************)
lemma ntas_inv_zero (h) (a) (G) (L):
- â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 :*[h,a,0] T2 →
- â\88§â\88§ â¦\83G,Lâ¦\84 â\8a¢ T1 ![h,a] & â¦\83G,Lâ¦\84 â\8a¢ T2 ![h,a] & â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+ â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 :*[h,a,0] T2 →
+ â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] & â\9dªG,Lâ\9d« â\8a¢ T2 ![h,a] & â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T2.
#h #a #G #L #T1 #T2 * #T0 #HT1 #HT2 #HT20 #HT10
-/3 width=3 by cprs_div, and3_intro/
+/3 width=3 by cprs_div, and3_intro/
qed-.