(* Basic_1: was only: nf2_csort_lref *)
lemma cnr_lref_atom (h) (b) (G) (L):
- â\88\80i. â¬\87*[b,ð\9d\90\94â\9d´iâ\9dµ] L â\89\98 â\8b\86 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83#iâ¦\84.
+ â\88\80i. â\87©*[b,ð\9d\90\94â\9d¨iâ\9d©] L â\89\98 â\8b\86 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] #i.
#h #b #G #L #i #Hi #X #H
elim (cpr_inv_lref1_drops … H) -H // * #K #V1 #V2 #HLK
lapply (drops_gen b … HLK) -HLK #HLK
(* Basic_1: was: nf2_lref_abst *)
lemma cnr_lref_abst (h) (G) (L):
- â\88\80K,V,i. â¬\87*[i] L â\89\98 K.â\93\9bV â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83#iâ¦\84.
+ â\88\80K,V,i. â\87©[i] L â\89\98 K.â\93\9bV â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] #i.
#h #G #L #K #V #i #HLK #X #H
elim (cpr_inv_lref1_drops … H) -H // *
#K0 #V1 #V2 #HLK0 #_ #_
qed.
lemma cnr_lref_unit (h) (I) (G) (L):
- â\88\80K,i. â¬\87*[i] L â\89\98 K.â\93¤{I} â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83#iâ¦\84.
+ â\88\80K,i. â\87©[i] L â\89\98 K.â\93¤[I] â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] #i.
#h #I #G #L #K #i #HLK #X #H
elim (cpr_inv_lref1_drops … H) -H // *
#K0 #V1 #V2 #HLK0 #_ #_
(* Basic_1: was: nf2_lift *)
(* Basic_2A1: uses: cnr_lift *)
-lemma cnr_lifts (h) (G): d_liftable1 … (cnr h G).
+lemma cnr_lifts (h) (G): d_liftable1 … (cnr h 0 G).
#h #G #K #T #HT #b #f #L #HLK #U #HTU #U0 #H
elim (cpm_inv_lifts_sn … H … HLK … HTU) -b -L #T0 #HTU0 #HT0
lapply (HT … HT0) -G -K #H destruct /2 width=4 by lifts_mono/
(* Basic_2A1: was: cnr_inv_delta *)
lemma cnr_inv_lref_abbr (h) (G) (L):
- â\88\80K,V,i. â¬\87*[i] L â\89\98 K.â\93\93V â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83#iâ¦\84 → ⊥.
+ â\88\80K,V,i. â\87©[i] L â\89\98 K.â\93\93V â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8d[h,0] #i → ⊥.
#h #G #L #K #V #i #HLK #H
-elim (lifts_total V ð\9d\90\94â\9d´â\86\91iâ\9dµ) #W #HVW
+elim (lifts_total V ð\9d\90\94â\9d¨â\86\91iâ\9d©) #W #HVW
lapply (H W ?) -H [ /3 width=6 by cpm_delta_drops/ ] -HLK #H destruct
elim (lifts_inv_lref2_uni_lt … HVW) -HVW //
qed-.
(* Note: this was missing in Basic_1 *)
(* Basic_2A1: uses: cnr_inv_lift *)
-lemma cnr_inv_lifts (h) (G): d_deliftable1 … (cnr h G).
+lemma cnr_inv_lifts (h) (G): d_deliftable1 … (cnr h 0 G).
#h #G #L #U #HU #b #f #K #HLK #T #HTU #T0 #H
elim (cpm_lifts_sn … H … HLK … HTU) -b -K #U0 #HTU0 #HU0
lapply (HU … HU0) -G -L #H destruct /2 width=4 by lifts_inj/