(* Note: this uses length *)
(* Basic_2A1: uses: lsx_lift_le lsx_lift_ge *)
-lemma rsx_lifts (h) (G): d_liftable1_isuni … (λL,T. G ⊢ ⬈*[h,T] 𝐒❪L❫).
+lemma rsx_lifts (h) (G):
+ d_liftable1_isuni … (λL,T. G ⊢ ⬈*𝐒[h,T] L).
#h #G #K #T #H @(rsx_ind … H) -K
#K1 #_ #IH #b #f #L1 #HLK1 #Hf #U #HTU @rsx_intro
#L2 #HL12 #HnL12 elim (lpx_drops_conf … HLK1 … HL12)
(* Inversion lemmas on relocation *******************************************)
(* Basic_2A1: uses: lsx_inv_lift_le lsx_inv_lift_be lsx_inv_lift_ge *)
-lemma rsx_inv_lifts (h) (G): d_deliftable1_isuni … (λL,T. G ⊢ ⬈*[h,T] 𝐒❪L❫).
+lemma rsx_inv_lifts (h) (G):
+ d_deliftable1_isuni … (λL,T. G ⊢ ⬈*𝐒[h,T] L).
#h #G #L #U #H @(rsx_ind … H) -L
#L1 #_ #IH #b #f #K1 #HLK1 #Hf #T #HTU @rsx_intro
#K2 #HK12 #HnK12 elim (drops_lpx_trans … HLK1 … HK12) -HK12
(* Advanced properties ******************************************************)
(* Basic_2A1: uses: lsx_lref_free *)
-lemma rsx_lref_atom_drops (h) (G): ∀L,i. ⇩*[Ⓕ,𝐔❨i❩] L ≘ ⋆ → G ⊢ ⬈*[h,#i] 𝐒❪L❫.
+lemma rsx_lref_atom_drops (h) (G):
+ ∀L,i. ⇩*[Ⓕ,𝐔❨i❩] L ≘ ⋆ → G ⊢ ⬈*𝐒[h,#i] L.
#h #G #L1 #i #HL1
@(rsx_lifts … (#0) … HL1) -HL1 //
qed.
(* Basic_2A1: uses: lsx_lref_skip *)
-lemma rsx_lref_unit_drops (h) (G): ∀I,L,K,i. ⇩[i] L ≘ K.ⓤ[I] → G ⊢ ⬈*[h,#i] 𝐒❪L❫.
+lemma rsx_lref_unit_drops (h) (G):
+ ∀I,L,K,i. ⇩[i] L ≘ K.ⓤ[I] → G ⊢ ⬈*𝐒[h,#i] L.
#h #G #I #L1 #K1 #i #HL1
@(rsx_lifts … (#0) … HL1) -HL1 //
qed.
(* Basic_2A1: uses: lsx_fwd_lref_be *)
lemma rsx_fwd_lref_pair_drops (h) (G):
- ∀L,i. G ⊢ ⬈*[h,#i] 𝐒❪L❫ →
- ∀I,K,V. ⇩[i] L ≘ K.ⓑ[I]V → G ⊢ ⬈*[h,V] 𝐒❪K❫.
+ ∀L,i. G ⊢ ⬈*𝐒[h,#i] L →
+ ∀I,K,V. ⇩[i] L ≘ K.ⓑ[I]V → G ⊢ ⬈*𝐒[h,V] K.
#h #G #L #i #HL #I #K #V #HLK
lapply (rsx_inv_lifts … HL … HLK … (#0) ?) -L
/2 width=2 by rsx_fwd_pair/