(* Basic_2A1: uses: snv_lref *)
lemma cnv_lref_drops (h) (a) (G):
- â\88\80I,K,V,i,L. â\9dªG,Kâ\9d« ⊢ V ![h,a] →
- â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9dªG,Lâ\9d« ⊢ #i ![h,a].
+ â\88\80I,K,V,i,L. â\9d¨G,Kâ\9d© ⊢ V ![h,a] →
+ â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9d¨G,Lâ\9d© ⊢ #i ![h,a].
#h #a #G #I #K #V #i elim i -i
[ #L #HV #H
lapply (drops_fwd_isid … H ?) -H // #H destruct
(* Basic_2A1: uses: snv_inv_lref *)
lemma cnv_inv_lref_drops (h) (a) (G):
- â\88\80i,L. â\9dªG,Lâ\9d« ⊢ #i ![h,a] →
- â\88\83â\88\83I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V & â\9dªG,Kâ\9d« ⊢ V ![h,a].
+ â\88\80i,L. â\9d¨G,Lâ\9d© ⊢ #i ![h,a] →
+ â\88\83â\88\83I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V & â\9d¨G,Kâ\9d© ⊢ V ![h,a].
#h #a #G #i elim i -i
[ #L #H
elim (cnv_inv_zero … H) -H #I #K #V #HV #H destruct
qed-.
lemma cnv_inv_lref_pair (h) (a) (G):
- â\88\80i,L. â\9dªG,Lâ\9d« ⊢ #i ![h,a] →
- â\88\80I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9dªG,Kâ\9d« ⊢ V ![h,a].
+ â\88\80i,L. â\9d¨G,Lâ\9d© ⊢ #i ![h,a] →
+ â\88\80I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9d¨G,Kâ\9d© ⊢ V ![h,a].
#h #a #G #i #L #H #I #K #V #HLK
elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #HX
lapply (drops_mono … HLY … HLK) -L #H destruct //
qed-.
lemma cnv_inv_lref_atom (h) (a) (b) (G):
- â\88\80i,L. â\9dªG,Lâ\9d« ⊢ #i ![h,a] → ⇩*[b,𝐔❨i❩] L ≘ ⋆ → ⊥.
+ â\88\80i,L. â\9d¨G,Lâ\9d© ⊢ #i ![h,a] → ⇩*[b,𝐔❨i❩] L ≘ ⋆ → ⊥.
#h #a #b #G #i #L #H #Hi
elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #_
lapply (drops_gen b … HLY) -HLY #HLY
qed-.
lemma cnv_inv_lref_unit (h) (a) (G):
- â\88\80i,L. â\9dªG,Lâ\9d« ⊢ #i ![h,a] →
+ â\88\80i,L. â\9d¨G,Lâ\9d© ⊢ #i ![h,a] →
∀I,K. ⇩[i] L ≘ K.ⓤ[I] → ⊥.
#h #a #G #i #L #H #I #K #HLK
elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #_