+
+(* Negated inversion lemmas *************************************************)
+
+lemma tdneq_inv_pair: ∀h,o,I1,I2,V1,V2,T1,T2.
+ (②{I1}V1.T1 ≛[h, o] ②{I2}V2.T2 → ⊥) →
+ ∨∨ I1 = I2 → ⊥
+ | (V1 ≛[h, o] V2 → ⊥)
+ | (T1 ≛[h, o] T2 → ⊥).
+#h #o #I1 #I2 #V1 #V2 #T1 #T2 #H12
+elim (eq_item2_dec I1 I2) /3 width=1 by or3_intro0/ #H destruct
+elim (tdeq_dec h o V1 V2) /3 width=1 by or3_intro1/
+elim (tdeq_dec h o T1 T2) /4 width=1 by tdeq_pair, or3_intro2/
+qed-.