(* Basic_1: was: csubc_drop1_conf_rev *)
lemma ldrops_lsubc_trans: ∀RR,RS,RP.
acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
- ∀G,L1,K1,des. ⇩*[des] L1 ≡ K1 → ∀K2. G ⊢ K1 ⊑[RP] K2 →
- ∃∃L2. G ⊢ L1 ⊑[RP] L2 & ⇩*[des] L2 ≡ K2.
+ ∀G,L1,K1,des. ⇩*[Ⓕ, des] L1 ≡ K1 → ∀K2. G ⊢ K1 ⊑[RP] K2 →
+ ∃∃L2. G ⊢ L1 ⊑[RP] L2 & ⇩*[Ⓕ, des] L2 ≡ K2.
#RR #RS #RP #Hacp #Hacr #G #L1 #K1 #des #H elim H -L1 -K1 -des
-[ /2 width=3/
+[ /2 width=3 by ldrops_nil, ex2_intro/
| #L1 #L #K1 #des #d #e #_ #HLK1 #IHL #K2 #HK12
elim (ldrop_lsubc_trans … Hacp Hacr … HLK1 … HK12) -Hacp -Hacr -K1 #K #HLK #HK2
- elim (IHL … HLK) -IHL -HLK /3 width=5/
+ elim (IHL … HLK) -IHL -HLK /3 width=5 by ldrops_cons, ex2_intro/
]
qed-.