+lemma cw_tpair_sn: ∀I,L,V,T. #{L, V} < #{L, ②{I}V.T}.
+#I #L #V #T normalize in ⊢ (? % %); //
+qed.
+
+lemma cw_tpair_dx: ∀I,L,V,T. #{L, T} < #{L, ②{I}V.T}.
+#I #L #V #T normalize in ⊢ (? % %); //
+qed.
+
+lemma cw_tpair_dx_sn: ∀I1,I2,L,V1,V2,T. #{L, V2} < #{L, ②{I1}V1.②{I2}V2.T}.
+#I1 #I2 #L #V1 #V2 #T normalize in ⊢ (? % %); /2 width=1/
+qed.
+
+lemma cw_tpair_dx_sn_shift: ∀a2,I1,I2,L,V1,V2,T.
+ #{L.ⓑ{I2}V2, T} < #{L, ②{I1}V1.ⓑ{a2,I2}V2.T}.
+#a2 #I1 #I2 #L #V1 #V2 #T normalize in ⊢ (? % %); /2 width=1/
+qed.
+