-(* Basic_1: was: term_dec *)
-axiom term_eq_dec: ∀T1,T2:term. Decidable (T1 = T2).
+lemma eq_false_inv_tpair_dx: ∀I,V1,T1,V2,T2.
+ (②{I} V1. T1 = ②{I} V2. T2 → False) →
+ (T1 = T2 → False) ∨ (T1 = T2 ∧ (V1 = V2 → False)).
+#I #V1 #T1 #V2 #T2 #H
+elim (term_eq_dec T1 T2) /3 width=1/ #HT12 destruct
+@or_intror @conj // #HT12 destruct /2 width=1/
+qed-.
+
+lemma eq_false_inv_beta: ∀V1,V2,W1,W2,T1,T2.
+ (ⓐV1. ⓛW1. T1 = ⓐV2. ⓛW2 .T2 →False) →
+ (W1 = W2 → False) ∨
+ (W1 = W2 ∧ (ⓓV1. T1 = ⓓV2. T2 → False)).
+#V1 #V2 #W1 #W2 #T1 #T2 #H
+elim (eq_false_inv_tpair_sn … H) -H
+[ #HV12 elim (term_eq_dec W1 W2) /3 width=1/
+ #H destruct @or_intror @conj // #H destruct /2 width=1/
+| * #H1 #H2 destruct
+ elim (eq_false_inv_tpair_sn … H2) -H2 /3 width=1/
+ * #H #HT12 destruct
+ @or_intror @conj // #H destruct /2 width=1/
+]
+qed.