(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
-(* Inversion lemmas with degree-based equivalence for terms *****************)
+(* Inversion lemmas with sort-irrelevant equivalence for terms **************)
-lemma cpm_tdeq_inv_lref_sn (n) (h) (o) (G) (L) (i):
- ∀X. ⦃G,L⦄ ⊢ #i ➡[n,h] X → #i ≛[h,o] X →
+lemma cpm_tdeq_inv_lref_sn (n) (h) (G) (L) (i):
+ ∀X. ⦃G,L⦄ ⊢ #i ➡[n,h] X → #i ≛ X →
∧∧ X = #i & n = 0.
-#n #h #o #G #L #i #X #H1 #H2
+#n #h #G #L #i #X #H1 #H2
lapply (tdeq_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_tdeq_inv_atom_sn (n) (h) (o) (I) (G) (L):
- ∀X. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] X → ⓪{I} ≛[h,o] X →
+lemma cpm_tdeq_inv_atom_sn (n) (h) (I) (G) (L):
+ ∀X. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] X → ⓪{I} ≛ X →
∨∨ ∧∧ X = ⓪{I} & n = 0
- | ∃∃s. X = ⋆(next h s) & I = Sort s & n = 1 & deg h o s 0.
-#n #h #o * #s #G #L #X #H1 #H2
+ | ∃∃s. X = ⋆(⫯[h]s) & I = Sort s & n = 1.
+#n #h * #s #G #L #X #H1 #H2
[ elim (cpm_inv_sort1 … H1) -H1
- cases n -n [| #n ] #H #Hn destruct
+ cases n -n [| #n ] #H #Hn destruct -H2
[ /3 width=1 by or_introl, conj/
- | elim (tdeq_inv_sort1 … H2) -H2 #x #d #Hs
- <(le_n_O_to_eq n) [| /2 width=3 by le_S_S_to_le/ ] -n #Hx #H destruct
- lapply (deg_next … Hs) #H
- lapply (deg_mono … H Hx) -H -Hx #Hd
- lapply (pred_inv_fix_sn … Hd) -Hd #H destruct
- /3 width=4 by refl, ex4_intro, or_intror/
+ | <(le_n_O_to_eq n) [| /2 width=3 by le_S_S_to_le/ ] -n
+ /3 width=3 by ex3_intro, or_intror/
]
| elim (cpm_tdeq_inv_lref_sn … H1 H2) -H1 -H2 /3 width=1 by or_introl, conj/
| elim (cpm_inv_gref1 … H1) -H1 -H2 /3 width=1 by or_introl, conj/