(* Properties with parallel rt-transition for full local environments *******)
lemma lpr_cpm_trans (n) (h) (G):
- â\88\80L2,T1,T2. â¦\83G,L2â¦\84 ⊢ T1 ➡[n,h] T2 →
- â\88\80L1. â¦\83G,L1â¦\84 â\8a¢ â\9e¡[h] L2 â\86\92 â¦\83G,L1â¦\84 ⊢ T1 ➡*[n,h] T2.
+ â\88\80L2,T1,T2. â\9dªG,L2â\9d« ⊢ T1 ➡[n,h] T2 →
+ â\88\80L1. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h] L2 â\86\92 â\9dªG,L1â\9d« ⊢ T1 ➡*[n,h] T2.
#n #h #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 (n) (h) (G):
- â\88\80L1,L2. â¦\83G,L1â¦\84 ⊢ ➡[h] L2 →
- â\88\80T1,T2. â¦\83G,L2â¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â¦\83G,L1â¦\84 ⊢ T1 ➡*[n,h] T2.
+ â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡[h] L2 →
+ â\88\80T1,T2. â\9dªG,L2â\9d« â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â\9dªG,L1â\9d« ⊢ T1 ➡*[n,h] T2.
#n #h #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 (n) (h) (G) (L):
- â\88\80V1,V2. â¦\83G,Lâ¦\84 ⊢ V1 ➡[h] V2 →
- â\88\80I,T1,T2. â¦\83G,L.â\93\91{I}V2â¦\84 ⊢ T1 ➡[n,h] T2 →
- â\88\80p. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V1.T1 â\9e¡*[n,h] â\93\91{p,I}V2.T2.
+ â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h] V2 →
+ â\88\80I,T1,T2. â\9dªG,L.â\93\91[I]V2â\9d« ⊢ T1 ➡[n,h] T2 →
+ â\88\80p. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V1.T1 â\9e¡*[n,h] â\93\91[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 (n) (h) (G) (L):
- â\88\80V1,V2. â¦\83G,Lâ¦\84 ⊢ V1 ➡[h] V2 →
- â\88\80I,T1,T2. â¦\83G,L.â\93\91{I}V2â¦\84 ⊢ T1 ➡*[n,h] T2 →
- â\88\80p. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V1.T1 â\9e¡*[n,h] â\93\91{p,I}V2.T2.
+ â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h] V2 →
+ â\88\80I,T1,T2. â\9dªG,L.â\93\91[I]V2â\9d« ⊢ T1 ➡*[n,h] T2 →
+ â\88\80p. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V1.T1 â\9e¡*[n,h] â\93\91[p,I]V2.T2.
/4 width=5 by lpr_cpms_trans, cpms_bind_dx, lpr_pair/ qed.