(* Main inversion lemmas ****************************************************)
theorem lveq_inv_bind: ∀K1,K2. K1 ≋ⓧ*[0,0] K2 →
- ∀I1,I2,m1,m2. K1.ⓘ{I1} ≋ⓧ*[m1,m2] K2.ⓘ{I2} →
+ ∀I1,I2,m1,m2. K1.ⓘ[I1] ≋ⓧ*[m1,m2] K2.ⓘ[I2] →
∧∧ 0 = m1 & 0 = m2.
#K1 #K2 #HK #I1 #I2 #m1 #m2 #H
lapply (lveq_fwd_length_eq … HK) -HK #HK
#L1 #L2 #HL #n1 #n2 #Hn #m1 #m2 #Hm
elim (lveq_fwd_length … Hn) -Hn #H1 #H2 destruct
elim (lveq_fwd_length … Hm) -Hm #H1 #H2 destruct
->length_bind >eq_minus_S_pred >(eq_minus_O … HL)
-/3 width=4 by plus_minus, and3_intro/
+>length_bind >nminus_succ_dx >(nle_inv_eq_zero_minus … HL)
+/3 width=4 by nminus_plus_comm_23, and3_intro/
qed-.
theorem lveq_inj_void_dx_le: ∀K1,K2. |K1| ≤ |K2| →