(* Properties with parallel rt-transition for full local environments *******)
lemma lpr_cpm_trans (h) (n) (G):
- â\88\80L2,T1,T2. â\9dªG,L2â\9d« ⊢ T1 ➡[h,n] T2 →
- â\88\80L1. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] L2 â\86\92 â\9dªG,L1â\9d« ⊢ T1 ➡*[h,n] T2.
+ â\88\80L2,T1,T2. â\9d¨G,L2â\9d© ⊢ T1 ➡[h,n] T2 →
+ â\88\80L1. â\9d¨G,L1â\9d© â\8a¢ â\9e¡[h,0] L2 â\86\92 â\9d¨G,L1â\9d© ⊢ T1 ➡*[h,n] T2.
#h #n #G #L2 #T1 #T2 #H @(cpm_ind … H) -n -G -L2 -T1 -T2
[ /2 width=3 by/
| /3 width=2 by cpm_cpms/
qed-.
lemma lpr_cpms_trans (h) (n) (G):
- â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡[h,0] L2 →
- â\88\80T1,T2. â\9dªG,L2â\9d« â\8a¢ T1 â\9e¡*[h,n] T2 â\86\92 â\9dªG,L1â\9d« ⊢ T1 ➡*[h,n] T2.
+ â\88\80L1,L2. â\9d¨G,L1â\9d© ⊢ ➡[h,0] L2 →
+ â\88\80T1,T2. â\9d¨G,L2â\9d© â\8a¢ T1 â\9e¡*[h,n] T2 â\86\92 â\9d¨G,L1â\9d© ⊢ T1 ➡*[h,n] T2.
#h #n #G #L1 #L2 #HL12 #T1 #T2 #H @(cpms_ind_sn … H) -n -T1
/3 width=3 by lpr_cpm_trans, cpms_trans/
qed-.
(* Basic_2A1: includes cpr_bind2 *)
lemma cpm_bind2 (h) (n) (G) (L):
- â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h,0] V2 →
- â\88\80I,T1,T2. â\9dªG,L.â\93\91[I]V2â\9d« ⊢ T1 ➡[h,n] T2 →
- â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ➡*[h,n] ⓑ[p,I]V2.T2.
+ â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ➡[h,0] V2 →
+ â\88\80I,T1,T2. â\9d¨G,L.â\93\91[I]V2â\9d© ⊢ T1 ➡[h,n] T2 →
+ â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ➡*[h,n] ⓑ[p,I]V2.T2.
/4 width=5 by lpr_cpm_trans, cpms_bind_dx, lpr_pair/ qed.
(* Basic_2A1: includes cprs_bind2_dx *)
lemma cpms_bind2_dx (h) (n) (G) (L):
- â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h,0] V2 →
- â\88\80I,T1,T2. â\9dªG,L.â\93\91[I]V2â\9d« ⊢ T1 ➡*[h,n] T2 →
- â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ➡*[h,n] ⓑ[p,I]V2.T2.
+ â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ➡[h,0] V2 →
+ â\88\80I,T1,T2. â\9d¨G,L.â\93\91[I]V2â\9d© ⊢ T1 ➡*[h,n] T2 →
+ â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ➡*[h,n] ⓑ[p,I]V2.T2.
/4 width=5 by lpr_cpms_trans, cpms_bind_dx, lpr_pair/ qed.