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-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
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-(* v GNU General Public License Version 2 *)
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-
-include "basic_2/reducibility/cpr_lift.ma".
-include "basic_2/reducibility/cpr_ltpss.ma".
-include "basic_2/reducibility/cfpr.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON CLOSURES *************************)
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma cfpr_inv_pair1: ∀I,L,K1,L2,V1,T1,T2. L ⊢ ⦃⋆.ⓑ{I}V1@@K1, T1⦄ ➡ ⦃L2, T2⦄ →
- ∃∃K2,V,V2. V1 ➡ V & L ⊢ V ▶* [0, |L|] V2 &
- L.ⓑ{I}V ⊢ ⦃K1, T1⦄ ➡ ⦃K2, T2⦄ &
- L2 = ⋆.ⓑ{I}V2@@K2.
-* #L #K1 #L2 #V1 #T1 #T2 * >append_length #H
-elim (length_inv_pos_sn_append … H) -H #I2 #K2 #V2 #HK12 #H destruct
->shift_append_assoc >shift_append_assoc normalize in ⊢ (??%%→?); #H
-[ elim (cpr_inv_abbr1 … H) -H *
- [ #V #V0 #T0 #HV1 #HV0 #HT10 #H destruct /3 width=7/
- | #T0 #_ #_ #H destruct
- ]
-| elim (cpr_inv_abst1 … H Abst V2) -H
- #V #T * #V0 #HV10 #HV0 #HT1 #H destruct
- lapply (ltpss_sn_cpr_trans (L.ⓛV0) … 0 (|L|+1) … HT1) -HT1 /2 width=1/ #HT12
- /3 width=7/
-]
-qed-.