(* Main preservation properties *********************************************)
(* Basic_2A1: uses: snv_preserve *)
(* Main preservation properties *********************************************)
(* Basic_2A1: uses: snv_preserve *)
-lemma cnv_preserve (h) (a): â\88\80G,L,T. â¦\83G,Lâ¦\84 ⊢ T ![h,a] →
+lemma cnv_preserve (h) (a): â\88\80G,L,T. â\9dªG,Lâ\9d« ⊢ T ![h,a] →
(* Advanced preservation properties *****************************************)
lemma cnv_cpms_conf (h) (a) (G) (L):
(* Advanced preservation properties *****************************************)
lemma cnv_cpms_conf (h) (a) (G) (L):
- â\88\80T0. â¦\83G,Lâ¦\84 ⊢ T0 ![h,a] →
- â\88\80n1,T1. â¦\83G,Lâ¦\84 â\8a¢ T0 â\9e¡*[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,Lâ¦\84 ⊢ T0 ➡*[n2,h] T2 →
- â\88\83â\88\83T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n2-n1,h] T & â¦\83G,Lâ¦\84 ⊢ T2 ➡*[n1-n2,h] T.
+ â\88\80T0. â\9dªG,Lâ\9d« ⊢ T0 ![h,a] →
+ â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ T0 â\9e¡*[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T0 ➡*[n2,h] T2 →
+ â\88\83â\88\83T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n2-n1,h] T & â\9dªG,Lâ\9d« ⊢ T2 ➡*[n1-n2,h] T.
- â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ![h,a] →
- â\88\80n,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[n,h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T2 ![h,a].
+ â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ![h,a] →
+ â\88\80n,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[n,h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T2 ![h,a].
/2 width=6 by cnv_cpm_trans_lpr/ qed-.
(* Note: this is the preservation property *)
lemma cnv_cpms_trans (h) (a) (G) (L):
/2 width=6 by cnv_cpm_trans_lpr/ qed-.
(* Note: this is the preservation property *)
lemma cnv_cpms_trans (h) (a) (G) (L):
- â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ![h,a] →
- â\88\80n,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T2 ![h,a].
+ â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ![h,a] →
+ â\88\80n,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T2 ![h,a].
- â\88\80L1,T. â¦\83G,L1â¦\84 â\8a¢ T ![h,a] â\86\92 â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â\9e¡[h] L2 â\86\92 â¦\83G,L2â¦\84 ⊢ T ![h,a].
+ â\88\80L1,T. â\9dªG,L1â\9d« â\8a¢ T ![h,a] â\86\92 â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h] L2 â\86\92 â\9dªG,L2â\9d« ⊢ T ![h,a].
- â\88\80L1,T. â¦\83G,L1â¦\84 â\8a¢ T ![h,a] â\86\92 â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â\9e¡*[h] L2 â\86\92 â¦\83G,L2â¦\84 ⊢ T ![h,a].
+ â\88\80L1,T. â\9dªG,L1â\9d« â\8a¢ T ![h,a] â\86\92 â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡*[h] L2 â\86\92 â\9dªG,L2â\9d« ⊢ T ![h,a].