(* Properties on relocation *************************************************)
+(* Basic_1: was: subst1_lift_lt *)
lemma cpy_lift_le: ∀G,K,T1,T2,dt,et. ⦃G, K⦄ ⊢ T1 ▶×[dt, et] T2 →
∀L,U1,U2,s,d,e. ⇩[s, d, e] L ≡ K →
⇧[d, e] T1 ≡ U1 → ⇧[d, e] T2 ≡ U2 →
]
qed-.
+(* Basic_1: was: subst1_lift_ge *)
lemma cpy_lift_ge: ∀G,K,T1,T2,dt,et. ⦃G, K⦄ ⊢ T1 ▶×[dt, et] T2 →
∀L,U1,U2,s,d,e. ⇩[s, d, e] L ≡ K →
⇧[d, e] T1 ≡ U1 → ⇧[d, e] T2 ≡ U2 →
(* Inversion lemmas on relocation *******************************************)
+(* Basic_1: was: subst1_gen_lift_lt *)
lemma cpy_inv_lift1_le: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶×[dt, et] U2 →
∀K,s,d,e. ⇩[s, d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 →
dt + et ≤ d →
]
qed-.
+(* Basic_1: was: subst1_gen_lift_ge *)
lemma cpy_inv_lift1_ge: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶×[dt, et] U2 →
∀K,s,d,e. ⇩[s, d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 →
yinj d + e ≤ dt →