(* Advanced properties ******************************************************)
-lemma cpcs_bind1 (h) (G) (L): â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ⬌*[h] V2 →
- â\88\80I,T1,T2. â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ⬌*[h] T2 →
- â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ⬌*[h] ⓑ[p,I]V2.T2.
+lemma cpcs_bind1 (h) (G) (L): â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬌*[h] V2 →
+ â\88\80I,T1,T2. â\9d¨G,L.â\93\91[I]V1â\9d© ⊢ T1 ⬌*[h] T2 →
+ â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ⬌*[h] ⓑ[p,I]V2.T2.
/3 width=3 by cpcs_trans, cpcs_bind_sn, cpcs_bind_dx/ qed.
-lemma cpcs_bind2 (h) (G) (L): 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 ⬌*[h] T2 →
- â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ⬌*[h] ⓑ[p,I]V2.T2.
+lemma cpcs_bind2 (h) (G) (L): â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬌*[h] V2 →
+ â\88\80I,T1,T2. â\9d¨G,L.â\93\91[I]V2â\9d© ⊢ T1 ⬌*[h] T2 →
+ â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ⬌*[h] ⓑ[p,I]V2.T2.
/3 width=3 by cpcs_trans, cpcs_bind_sn, cpcs_bind_dx/ qed.
(* Advanced properties with r-transition for full local environments ********)
(* Basic_1: was: pc3_wcpr0 *)
-lemma lpr_cpcs_conf (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡[h,0] L2 →
- â\88\80T1,T2. â\9dªG,L1â\9d« â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â\9dªG,L2â\9d« ⊢ T1 ⬌*[h] T2.
+lemma lpr_cpcs_conf (h) (G): â\88\80L1,L2. â\9d¨G,L1â\9d© ⊢ ➡[h,0] L2 →
+ â\88\80T1,T2. â\9d¨G,L1â\9d© â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â\9d¨G,L2â\9d© ⊢ T1 ⬌*[h] T2.
#h #G #L1 #L2 #HL12 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H
/3 width=5 by cpcs_canc_dx, lpr_cprs_conf/
qed-.