]
qed-.
+(* Basic_1: was: thead_x_lift_y_y *)
lemma lift_inv_pair_xy_y: ∀I,T,V,d,e. ⇧[d, e] ②{I} V. T ≡ T → ⊥.
#J #T elim T -T
[ * #i #V #d #e #H
(* Basic forward lemmas *****************************************************)
-lemma tw_lift: ∀d,e,T1,T2. ⇧[d, e] T1 ≡ T2 → #{T1} = #{T2}.
+lemma tw_lift: ∀d,e,T1,T2. ⇧[d, e] T1 ≡ T2 → ♯{T1} = ♯{T2}.
#d #e #T1 #T2 #H elim H -d -e -T1 -T2 normalize //
qed-.