(* Advanced dproperties *****************************************************)
(* Basic_2A1: uses: snv_lref *)
-lemma cnv_lref_drops (a) (h) (G): ∀I,K,V,i,L. ⦃G, K⦄ ⊢ V ![a, h] →
- ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, L⦄ ⊢ #i ![a, h].
+lemma cnv_lref_drops (a) (h) (G): ∀I,K,V,i,L. ⦃G,K⦄ ⊢ V ![a,h] →
+ ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G,L⦄ ⊢ #i ![a,h].
#a #h #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 (a) (h) (G):
- ∀i,L. ⦃G, L⦄ ⊢ #i ![a, h] →
- ∃∃I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ![a, h].
+ ∀i,L. ⦃G,L⦄ ⊢ #i ![a,h] →
+ ∃∃I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V & ⦃G,K⦄ ⊢ V ![a,h].
#a #h #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 (a) (h) (G):
- ∀i,L. ⦃G, L⦄ ⊢ #i ![a, h] →
- ∀I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ![a, h].
+ ∀i,L. ⦃G,L⦄ ⊢ #i ![a,h] →
+ ∀I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G,K⦄ ⊢ V ![a,h].
#a #h #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 (a) (h) (b) (G):
- ∀i,L. ⦃G, L⦄ ⊢ #i ![a, h] →
+ ∀i,L. ⦃G,L⦄ ⊢ #i ![a,h] →
⬇*[b,𝐔❴i❵] L ≘ ⋆ → ⊥.
#a #h #b #G #i #L #H #Hi
elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #_
qed-.
lemma cnv_inv_lref_unit (a) (h) (G):
- ∀i,L. ⦃G, L⦄ ⊢ #i ![a, h] →
+ ∀i,L. ⦃G,L⦄ ⊢ #i ![a,h] →
∀I,K. ⬇*[i] L ≘ K.ⓤ{I} → ⊥.
#a #h #G #i #L #H #I #K #HLK
elim (cnv_inv_lref_drops … H) -H #Z #Y #X #HLY #_