lemma cprs_abst: ∀L,V1,V2. L ⊢ V1 ➡* V2 → ∀V,T1,T2. L.ⓛV ⊢ T1 ➡* T2 →
∀a,I. L ⊢ ⓑ{a,I}V1. T1 ➡* ⓑ{a,I}V2. T2.
#L #V1 #V2 #HV12 #V #T1 #T2 #HT12 #a #I @(cprs_ind … HV12) -V2
-[ lapply (cprs_lsubs_trans … HT12 (L.ⓛV1) ?) -HT12 /2 width=2/
+[ lapply (cprs_lsubr_trans … HT12 (L.ⓛV1) ?) -HT12 /2 width=2/
| #V0 #V2 #_ #HV02 #IHV01
@(cprs_trans … IHV01) -V1 /2 width=2/
]
#L #V1 #V2 #W #T1 #T2 #HV12 #HT12 #a @(cprs_ind … HT12) -T2
[ /3 width=1/
| -HV12 #T #T2 #_ #HT2 #IHT1
- lapply (cpr_lsubs_trans … HT2 (L.ⓓV2) ?) -HT2 /2 width=1/ #HT2
+ lapply (cpr_lsubr_trans … HT2 (L.ⓓV2) ?) -HT2 /2 width=1/ #HT2
@(cprs_trans … IHT1) -V1 -W -T1 /3 width=1/
]
qed.