theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
∀L1,T,A. L1 ⊢ T ⁝ A → ∀L0,des. ⇩*[des] L0 ≡ L1 →
- ∀T0. ⇧*[des] T ≡ T0 → ∀L2. L2 [RP] ⊑ L0 →
- ⦃L2, T0⦄ [RP] ϵ 〚A〛.
+ ∀T0. ⇧*[des] T ≡ T0 → ∀L2. L2 ⊑[RP] L0 →
+ ⦃L2, T0⦄ ϵ[RP] 〚A〛.
#RR #RS #RP #H1RP #H2RP #L1 #T #A #H elim H -L1 -T -A
[ #L #k #L0 #des #HL0 #X #H #L2 #HL20
>(lifts_inv_sort1 … H) -H
(* Basic_1: was: sc3_arity *)
lemma aacr_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
- ∀L,T,A. L ⊢ T ⁝ A → ⦃L, T⦄ [RP] ϵ 〚A〛.
+ ∀L,T,A. L ⊢ T ⁝ A → ⦃L, T⦄ ϵ[RP] 〚A〛.
/2 width=8/ qed.
lemma acp_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →