(* Inversion lemmas with sort-irrelevant equivalence for terms **************)
lemma cpm_teqx_inv_lref_sn (n) (h) (G) (L) (i):
- â\88\80X. â¦\83G,Lâ¦\84 ⊢ #i ➡[n,h] X → #i ≛ X →
+ â\88\80X. â\9dªG,Lâ\9d« ⊢ #i ➡[n,h] X → #i ≛ X →
∧∧ X = #i & n = 0.
#n #h #G #L #i #X #H1 #H2
lapply (teqx_inv_lref1 … H2) -H2 #H destruct
qed-.
lemma cpm_teqx_inv_atom_sn (n) (h) (I) (G) (L):
- â\88\80X. â¦\83G,Lâ¦\84 â\8a¢ â\93ª{I} â\9e¡[n,h] X â\86\92 â\93ª{I} ≛ X →
- ∨∨ ∧∧ X = ⓪{I} & n = 0
+ â\88\80X. â\9dªG,Lâ\9d« â\8a¢ â\93ª[I] â\9e¡[n,h] X â\86\92 â\93ª[I] ≛ X →
+ ∨∨ ∧∧ X = ⓪[I] & n = 0
| ∃∃s. X = ⋆(⫯[h]s) & I = Sort s & n = 1.
#n #h * #s #G #L #X #H1 #H2
[ elim (cpm_inv_sort1 … H1) -H1