(**************************************************************************)
include "basic_2/reduction/cnx_lift.ma".
-include "basic_2/reduction/fpbc.ma".
include "basic_2/computation/acp.ma".
include "basic_2/computation/csx.ma".
⦃G, L⦄ ⊢ ⬊*[h, g] #i → ⦃G, K⦄ ⊢ ⬊*[h, g] V.
#h #g #I #G #L #K #V #i #HLK #Hi
elim (lift_total V 0 (i+1))
-/4 width=9 by csx_inv_lift, csx_cpx_trans, cpx_delta, ldrop_fwd_ldrop2/
+/4 width=9 by csx_inv_lift, csx_cpx_trans, cpx_delta, ldrop_fwd_drop2/
qed-.
(* Advanced properties ******************************************************)
[ #H destruct elim Hi //
| -Hi * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HV1
lapply (ldrop_mono … HLK0 … HLK) -HLK #H destruct
- /3 width=7 by csx_lift, csx_cpx_trans, ldrop_fwd_ldrop2/
+ /3 width=7 by csx_lift, csx_cpx_trans, ldrop_fwd_drop2/
]
qed.
]
qed-.
-(* Advanced eliminators *****************************************************)
-
-lemma csx_ind_fpbc_fqus: ∀h,g. ∀R:relation3 genv lenv term.
- (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- R G1 L1 T1
- ) →
- ∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → R G2 L2 T2.
-#h #g #R #IH1 #G1 #L1 #T1 #H @(csx_ind … H) -T1
-#T1 @(fqup_wf_ind … G1 L1 T1) -G1 -L1 -T1
-#G1 #L1 #T1 #IH2 #H1 #IH3 #G2 #L2 #T2 #H12 @IH1 -IH1 /2 width=5 by csx_fqus_conf/
-#G #L #T *
-[ #G0 #L0 #T0 #H20 lapply (fqus_strap1_fqu … H12 H20) -G2 -L2 -T2
- #H10 @(IH2 … H10) -IH2 /2 width=5 by csx_fqup_conf/
- #T2 #HT02 #H #G3 #L3 #T3 #HT23 elim (fqup_cpx_trans_neq … H10 … HT02 H) -T0
- /4 width=8 by fqup_fqus_trans, fqup_fqus/
-| #T0 #HT20 #H elim (fqus_cpx_trans_neq … H12 … HT20 H) -T2 /3 width=4 by/
-]
-qed-.
-
-lemma csx_ind_fpbc: ∀h,g. ∀R:relation3 genv lenv term.
- (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- R G1 L1 T1
- ) →
- ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
-/4 width=8 by csx_ind_fpbc_fqus/ qed-.
-
(* Main properties **********************************************************)
theorem csx_acp: ∀h,g. acp (cpx h g) (eq …) (csx h g).