(* Basic_1: was: sc3_arity_csubc *)
theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
gcp RR RS RP → gcr RR RS RP RP →
- â\88\80G,L1,T,A. â¦\83G,L1â¦\84 â\8a¢ T â\81\9d A â\86\92 â\88\80b,f,L0. â¬\87*[b,f] L0 ≘ L1 →
- â\88\80T0. â¬\86*[f] T ≘ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
+ â\88\80G,L1,T,A. â¦\83G,L1â¦\84 â\8a¢ T â\81\9d A â\86\92 â\88\80b,f,L0. â\87©*[b,f] L0 ≘ L1 →
+ â\88\80T0. â\87§*[f] T ≘ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
⦃G,L2,T0⦄ ϵ[RP] 〚A〛.
#RR #RS #RP #H1RP #H2RP #G #L1 #T @(fqup_wf_ind_eq (Ⓣ) … G L1 T) -G -L1 -T
#Z #Y #X #IH #G #L1 * [ * | * [ #p ] * ]
lapply (aaa_inv_sort … HA) -HA #H destruct
>(lifts_inv_sort1 … H0) -H0
lapply (acr_gcr … H1RP H2RP (⓪)) #HAtom
- lapply (s4 … HAtom G L2 (Ⓔ)) /2 width=1 by/
+ lapply (s2 … HAtom G L2 (Ⓔ)) /3 width=7 by cp1, simple_atom/
| #i #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
elim (aaa_inv_lref_drops … HA) -HA #I #K1 #V1 #HLK1 #HKV1
elim (lifts_inv_lref1 … H0) -H0 #j #Hf #H destruct