(* 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\80L0,des. â\87©*[Ⓕ, des] L0 ≡ L1 →
- â\88\80T0. â\87§*[des] 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\80L0,des. â¬\87*[Ⓕ, des] L0 ≡ L1 →
+ â\88\80T0. â¬\86*[des] T ≡ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
⦃G, L2, T0⦄ ϵ[RP] 〚A〛.
#RR #RS #RP #H1RP #H2RP #G #L1 #T #A #H elim H -G -L1 -T -A
[ #G #L #k #L0 #des #HL0 #X #H #L2 #HL20