lemma cpr_subst (h) (G) (L) (U1) (i):
∀K,V. ⇩[i] L ≘ K.ⓓV →
- â\88\83â\88\83U2,T2. â\9dªG,Lâ\9d« ⊢ U1 ➡[h,0] U2 & ⇧[i,1] T2 ≘ U2.
+ â\88\83â\88\83U2,T2. â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,0] U2 & ⇧[i,1] T2 ≘ U2.
#h #G #L #U1 @(fqup_wf_ind_eq (Ⓣ) … G L U1) -G -L -U1
#G0 #L0 #U0 #IH #G #L * *
[ #s #HG #HL #HT #i #K #V #_ destruct -IH
elim (lt_or_eq_or_gt i j) #Hij
[ /3 width=4 by lifts_lref_ge_minus, cpr_refl, ex2_2_intro/
| elim (lifts_total V (𝐔❨↑i❩)) #U2 #HU2
- elim (lifts_split_trans â\80¦ HU2 (ð\9d\90\94â\9d¨iâ\9d©) (ð\9d\90\81❨i,1❩)) [2: @(after_basic_rc i 0) ]
+ elim (lifts_split_trans â\80¦ HU2 (ð\9d\90\94â\9d¨iâ\9d©) (ð\9d\90\9b❨i,1❩)) [2: @(after_basic_rc i 0) ]
/3 width=7 by cpm_delta_drops, ex2_2_intro/
| /3 width=4 by lifts_lref_lt, cpr_refl, ex2_2_intro/
]