λR. ∀K,T. R K T → ∀b,f,L. ⬇*[b, f] L ≡ K →
∀U. ⬆*[f] T ≡ U → R L U.
+definition d_liftable1_isuni: predicate (relation2 lenv term) ≝
+ λR. ∀K,T. R K T → ∀b,f,L. ⬇*[b, f] L ≡ K → 𝐔⦃f⦄ →
+ ∀U. ⬆*[f] T ≡ U → R L U.
+
definition d_deliftable1: predicate (relation2 lenv term) ≝
λR. ∀L,U. R L U → ∀b,f,K. ⬇*[b, f] L ≡ K →
∀T. ⬆*[f] T ≡ U → R K T.
+definition d_deliftable1_isuni: predicate (relation2 lenv term) ≝
+ λR. ∀L,U. R L U → ∀b,f,K. ⬇*[b, f] L ≡ K → 𝐔⦃f⦄ →
+ ∀T. ⬆*[f] T ≡ U → R K T.
+
definition d_liftable2_sn: ∀C:Type[0]. ∀S:rtmap → relation C.
predicate (lenv → relation C) ≝
λC,S,R. ∀K,T1,T2. R K T1 T2 → ∀b,f,L. ⬇*[b, f] L ≡ K →
]
qed-.
-
lemma drops_after_fwd_drop2: ∀b,f2,I,X,K. ⬇*[b, f2] X ≡ K.ⓘ{I} →
∀f1,f. 𝐈⦃f1⦄ → f2 ⊚ ⫯f1 ≡ f → ⬇*[b, f] X ≡ K.
#b #f2 #I #X #K #H #f1 #f #Hf1 #Hf elim (drops_fwd_drop2 … H) -H