(* Inversion lemmas with sort-irrelevant equivalence for terms **************)
lemma cpm_teqx_inv_lref_sn (h) (n) (G) (L) (i):
- â\88\80X. â\9dªG,Lâ\9d« â\8a¢ #i â\9e¡[h,n] X â\86\92 #i â\89\9b X →
+ â\88\80X. â\9dªG,Lâ\9d« â\8a¢ #i â\9e¡[h,n] X â\86\92 #i â\89\85 X →
∧∧ X = #i & n = 0.
#h #n #G #L #i #X #H1 #H2
-lapply (teqx_inv_lref1 … H2) -H2 #H destruct
+lapply (teqg_inv_lref1 … H2) -H2 #H destruct
elim (cpm_inv_lref1_drops … H1) -H1 // * [| #m ]
#K #V1 #V2 #_ #_ #H -V1
elim (lifts_inv_lref2_uni_lt … H) -H //
qed-.
lemma cpm_teqx_inv_atom_sn (h) (n) (I) (G) (L):
- â\88\80X. â\9dªG,Lâ\9d« â\8a¢ â\93ª[I] â\9e¡[h,n] X â\86\92 â\93ª[I] â\89\9b X →
+ â\88\80X. â\9dªG,Lâ\9d« â\8a¢ â\93ª[I] â\9e¡[h,n] X â\86\92 â\93ª[I] â\89\85 X →
∨∨ ∧∧ X = ⓪[I] & n = 0
| ∃∃s. X = ⋆(⫯[h]s) & I = Sort s & n = 1.
#h #n * #s #G #L #X #H1 #H2