(* 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\9d©] L â\89\98 â\8b\86 â\86\92 â\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] #i.
+ â\88\80i. â\87©*[b,ð\9d\90\94â\9d¨iâ\9d©] L â\89\98 â\8b\86 â\86\92 â\9d¨G,Lâ\9d© ⊢ ➡𝐍[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\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] #i.
+ â\88\80K,V,i. â\87©[i] L â\89\98 K.â\93\9bV â\86\92 â\9d¨G,Lâ\9d© ⊢ ➡𝐍[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\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] #i.
+ â\88\80K,i. â\87©[i] L â\89\98 K.â\93¤[I] â\86\92 â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] #i.
#h #I #G #L #K #i #HLK #X #H
elim (cpr_inv_lref1_drops … H) -H // *
#K0 #V1 #V2 #HLK0 #_ #_
(* 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\9dªG,Lâ\9d« ⊢ ➡𝐍[h,0] #i → ⊥.
+ â\88\80K,V,i. â\87©[i] L â\89\98 K.â\93\93V â\86\92 â\9d¨G,Lâ\9d© ⊢ ➡𝐍[h,0] #i → ⊥.
#h #G #L #K #V #i #HLK #H
elim (lifts_total V 𝐔❨↑i❩) #W #HVW
lapply (H W ?) -H [ /3 width=6 by cpm_delta_drops/ ] -HLK #H destruct