(* Advanced properties ******************************************************)
(* Note: apparently this was missing in basic_1 *)
-lemma cprs_delta: ∀L,K,V,V2,i.
- ⇩[0, i] L ≡ K. ⓓV → K ⊢ V ➡* V2 →
- ∀W2. ⇧[0, i + 1] V2 ≡ W2 → L ⊢ #i ➡* W2.
-#L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=6/ ]
+lemma cprs_delta: ∀G,L,K,V,V2,i.
+ ⇩[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡* V2 →
+ ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡* W2.
+#G #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=6 by cpr_cprs, cpr_delta/ ]
#V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
-lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
-elim (lift_total V1 0 (i+1)) /4 width=11 by cpr_lift, cprs_strap1/
+lapply (ldrop_fwd_drop2 … HLK) -HLK #HLK
+elim (lift_total V1 0 (i+1)) /4 width=12 by cpr_lift, cprs_strap1/
qed.
(* Advanced inversion lemmas ************************************************)
(* Basic_1: was: pr3_gen_lref *)
-lemma cprs_inv_lref1: ∀L,T2,i. L ⊢ #i ➡* T2 →
+lemma cprs_inv_lref1: ∀G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡* T2 →
T2 = #i ∨
- ∃∃K,V1,T1. ⇩[0, i] L ≡ K. ⓓV1 &
- K ⊢ V1 ➡* T1 &
+ ∃∃K,V1,T1. ⇩[i] L ≡ K.ⓓV1 & ⦃G, K⦄ ⊢ V1 ➡* T1 &
⇧[0, i + 1] T1 ≡ T2.
-#L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1/
+#G #L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1 by or_introl/
#T #T2 #_ #HT2 *
[ #H destruct
- elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1/
- * /4 width=6/
+ elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
+ * /4 width=6 by cpr_cprs, ex3_3_intro, or_intror/
| * #K #V1 #T1 #HLK #HVT1 #HT1
- lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
- elim (cpr_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T /4 width=6/
+ lapply (ldrop_fwd_drop2 … HLK) #H0LK
+ elim (cpr_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T
+ /4 width=6 by cprs_strap1, ex3_3_intro, or_intror/
]
qed-.
(* Relocation properties ****************************************************)
(* Basic_1: was: pr3_lift *)
-lemma cprs_lift: l_liftable cprs.
-/3 width=9/ qed.
+lemma cprs_lift: ∀G. l_liftable (cprs G).
+/3 width=10 by l_liftable_LTC, cpr_lift/ qed.
(* Basic_1: was: pr3_gen_lift *)
-lemma cprs_inv_lift1: l_deliftable_sn cprs.
-/3 width=5 by l_deliftable_sn_LTC, cpr_inv_lift1/
+lemma cprs_inv_lift1: ∀G. l_deliftable_sn (cprs G).
+/3 width=6 by l_deliftable_sn_LTC, cpr_inv_lift1/
qed-.