(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
-definition IH_cnv_cpm_tdeq_cpm_trans (a) (h): relation3 genv lenv term ≝
- λG,L,T1. ⦃G, L⦄ ⊢ T1 ![a,h] →
- ∀n1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → T1 ≛ T →
+definition IH_cnv_cpm_tdeq_cpm_trans (h) (a): relation3 genv lenv term ≝
+ λG,L,T1. ⦃G,L⦄ ⊢ T1 ![h,a] →
+ ∀n1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → T1 ≛ T →
∀n2,T2. ⦃G,L⦄ ⊢ T ➡[n2,h] T2 →
∃∃T0. ⦃G,L⦄ ⊢ T1 ➡[n2,h] T0 & ⦃G,L⦄ ⊢ T0 ➡[n1,h] T2 & T0 ≛ T2.
(* Transitive properties restricted rt-transition for terms *****************)
-fact cnv_cpm_tdeq_cpm_trans_sub (a) (h) (G0) (L0) (T0):
- (∀G,L,T. ⦃G0, L0, T0⦄ >[h] ⦃G, L, T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
- (â\88\80G,L,T. â¦\83G0,L0,T0â¦\84 â\8a\90+ â¦\83G,L,Tâ¦\84 â\86\92 IH_cnv_cpm_tdeq_cpm_trans a h G L T) →
- ∀G,L,T1. G0 = G → L0 = L → T0 = T1 → IH_cnv_cpm_tdeq_cpm_trans a h G L T1.
-#a #h #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
+fact cnv_cpm_tdeq_cpm_trans_sub (h) (a) (G0) (L0) (T0):
+ (∀G,L,T. ⦃G0,L0,T0⦄ >[h] ⦃G,L,T⦄ → IH_cnv_cpm_trans_lpr h a G L T) →
+ (â\88\80G,L,T. â¦\83G0,L0,T0â¦\84 â¬\82+ â¦\83G,L,Tâ¦\84 â\86\92 IH_cnv_cpm_tdeq_cpm_trans h a G L T) →
+ ∀G,L,T1. G0 = G → L0 = L → T0 = T1 → IH_cnv_cpm_tdeq_cpm_trans h a G L T1.
+#h #a #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
[ #I #_ #_ #_ #_ #n1 #X1 #H1X #H2X #n2 #X2 #HX2 destruct -G0 -L0 -T0
elim (cpm_tdeq_inv_atom_sn … H1X H2X) -H1X -H2X *
[ #H1 #H2 destruct /2 width=4 by ex3_intro/
]
qed-.
-fact cnv_cpm_tdeq_cpm_trans_aux (a) (h) (G0) (L0) (T0):
- (∀G,L,T. ⦃G0, L0, T0⦄ >[h] ⦃G, L, T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
- IH_cnv_cpm_tdeq_cpm_trans a h G0 L0 T0.
-#a #h #G0 #L0 #T0
+fact cnv_cpm_tdeq_cpm_trans_aux (h) (a) (G0) (L0) (T0):
+ (∀G,L,T. ⦃G0,L0,T0⦄ >[h] ⦃G,L,T⦄ → IH_cnv_cpm_trans_lpr h a G L T) →
+ IH_cnv_cpm_tdeq_cpm_trans h a G0 L0 T0.
+#h #a #G0 #L0 #T0
@(fqup_wf_ind (Ⓣ) … G0 L0 T0) -G0 -L0 -T0 #G0 #L0 #T0 #IH #IH0
/5 width=10 by cnv_cpm_tdeq_cpm_trans_sub, fqup_fpbg_trans/
qed-.