(* Basic_2A1: uses: snv_lref *)
lemma cnv_lref_drops (h) (a) (G):
∀I,K,V,i,L. ⦃G,K⦄ ⊢ V ![h,a] →
- â¬\87*[i] L ≘ K.ⓑ{I}V → ⦃G,L⦄ ⊢ #i ![h,a].
+ â\87©*[i] L ≘ K.ⓑ{I}V → ⦃G,L⦄ ⊢ #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):
∀i,L. ⦃G,L⦄ ⊢ #i ![h,a] →
- â\88\83â\88\83I,K,V. â¬\87*[i] L ≘ K.ⓑ{I}V & ⦃G,K⦄ ⊢ V ![h,a].
+ â\88\83â\88\83I,K,V. â\87©*[i] L ≘ K.ⓑ{I}V & ⦃G,K⦄ ⊢ V ![h,a].
#h #a #G #i elim i -i
[ #L #H
elim (cnv_inv_zero … H) -H #I #K #V #HV #H destruct
lemma cnv_inv_lref_pair (h) (a) (G):
∀i,L. ⦃G,L⦄ ⊢ #i ![h,a] →
- â\88\80I,K,V. â¬\87*[i] L ≘ K.ⓑ{I}V → ⦃G,K⦄ ⊢ V ![h,a].
+ â\88\80I,K,V. â\87©*[i] L ≘ K.ⓑ{I}V → ⦃G,K⦄ ⊢ 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¦\83G,Lâ¦\84 â\8a¢ #i ![h,a] â\86\92 â¬\87*[b,𝐔❴i❵] L ≘ ⋆ → ⊥.
+ â\88\80i,L. â¦\83G,Lâ¦\84 â\8a¢ #i ![h,a] â\86\92 â\87©*[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
lemma cnv_inv_lref_unit (h) (a) (G):
∀i,L. ⦃G,L⦄ ⊢ #i ![h,a] →
- â\88\80I,K. â¬\87*[i] L ≘ K.ⓤ{I} → ⊥.
+ â\88\80I,K. â\87©*[i] L ≘ K.ⓤ{I} → ⊥.
#h #a #G #i #L #H #I #K #HLK
elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #_
lapply (drops_mono … HLY … HLK) -L #H destruct