(* Properties on relocation *************************************************)
-lemma crx_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ 𝐑[h, g]⦃T⦄ → ∀L,s,d,e. ⇩[s, d, e] L ≡ K →
- ∀U. ⇧[d, e] T ≡ U → ⦃G, L⦄ ⊢ 𝐑[h, g]⦃U⦄.
+lemma crx_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ ➡[h, g] 𝐑⦃T⦄ → ∀L,s,d,e. ⇩[s, d, e] L ≡ K →
+ ∀U. ⇧[d, e] T ≡ U → ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃U⦄.
#h #g #G #K #T #H elim H -K -T
[ #K #k #l #Hkl #L #s #d #e #_ #X #H
>(lift_inv_sort1 … H) -X /2 width=2 by crx_sort/
]
qed.
-lemma crx_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ 𝐑[h, g]⦃U⦄ → ∀K,s,d,e. ⇩[s, d, e] L ≡ K →
- ∀T. ⇧[d, e] T ≡ U → ⦃G, K⦄ ⊢ 𝐑[h, g]⦃T⦄.
+lemma crx_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃U⦄ → ∀K,s,d,e. ⇩[s, d, e] L ≡ K →
+ ∀T. ⇧[d, e] T ≡ U → ⦃G, K⦄ ⊢ ➡[h, g] 𝐑⦃T⦄.
#h #g #G #L #U #H elim H -L -U
[ #L #k #l #Hkl #K #s #d #e #_ #X #H
>(lift_inv_sort2 … H) -X /2 width=2 by crx_sort/