(* Negated inversion lemmas *************************************************)
-lemma tdeq_false_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 → ⊥).
+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/