(* Properties concerning partial unfold on local environments ***************)
-lemma ltpss_cpr_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
- ∀T1,T2. L1 ⊢ T1 ➡ T2 → L2 ⊢ T1 ⬌* T2.
+lemma ltpss_dx_cpr_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
+ ∀T1,T2. L1 ⊢ T1 ➡ T2 → L2 ⊢ T1 ⬌* T2.
#L1 #L2 #d #e #HL12 #T1 #T2 *
-lapply (ltpss_weak_all … HL12)
->(ltpss_fwd_length … HL12) -HL12 #HL12 #T #HT1 #HT2
-elim (ltpss_tpss_conf … HT2 … HL12) -L1 #T0 #HT0 #HT20
+lapply (ltpss_dx_weak_all … HL12)
+>(ltpss_dx_fwd_length … HL12) -HL12 #HL12 #T #HT1 #HT2
+elim (ltpss_dx_tpss_conf … HT2 … HL12) -L1 #T0 #HT0 #HT20
@(cprs_div … T0) /3 width=3/ (**) (* /4/ is too slow *)
qed.
-lemma ltpss_cprs_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
- ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2.
+lemma ltpss_dx_cprs_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
+ ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2.
#L1 #L2 #d #e #HL12 #T1 #T2 #H @(cprs_ind … H) -T2 //
#T #T2 #_ #HT2 #IHT1
@(cpcs_trans … IHT1) -T1 /2 width=5/
qed.
-lemma ltpss_cpcs_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
- ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
+lemma ltpss_dx_cpcs_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
+ ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
#L1 #L2 #d #e #HL12 #T1 #T2 #H
elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
@(cpcs_canc_dx … T) /2 width=5/