+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/reducibility/tpr.ma".
-
-(* CONTEXT-FREE NORMAL TERMS ************************************************)
-
-definition tnf: predicate term โ NF โฆ tpr (eq โฆ).
-
-interpretation
- "context-free normality (term)"
- 'Normal T = (tnf T).
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma tnf_inv_abst: โa,V,T. ๐โฆโ{a}V.Tโฆ โ ๐โฆVโฆ โง ๐โฆTโฆ.
-#a #V1 #T1 #HVT1 @conj
-[ #V2 #HV2 lapply (HVT1 (โ{a}V2.T1) ?) -HVT1 /2 width=1/ -HV2 #H destruct //
-| #T2 #HT2 lapply (HVT1 (โ{a}V1.T2) ?) -HVT1 /2 width=1/ -HT2 #H destruct //
-]
-qed-.
-
-lemma tnf_inv_appl: โV,T. ๐โฆโV.Tโฆ โ โงโง ๐โฆVโฆ & ๐โฆTโฆ & ๐โฆTโฆ.
-#V1 #T1 #HVT1 @and3_intro
-[ #V2 #HV2 lapply (HVT1 (โV2.T1) ?) -HVT1 /2 width=1/ -HV2 #H destruct //
-| #T2 #HT2 lapply (HVT1 (โV1.T2) ?) -HVT1 /2 width=1/ -HT2 #H destruct //
-| generalize in match HVT1; -HVT1 elim T1 -T1 * // #a * #W1 #U1 #_ #_ #H
- [ elim (lift_total V1 0 1) #V2 #HV12
- lapply (H (โ{a}W1.โV2.U1) ?) -H /2 width=3/ -HV12 #H destruct
- | lapply (H (โ{a}V1.U1) ?) -H /2 width=1/ #H destruct
-]
-qed-.
-
-lemma tnf_inv_abbr: โV,T. ๐โฆ+โV.Tโฆ โ โฅ.
-#V #T #H elim (is_lift_dec T 0 1)
-[ * #U #HTU
- lapply (H U ?) -H /2 width=3/ #H destruct
- elim (lift_inv_pair_xy_y โฆ HTU)
-| #HT
- elim (tps_full (โ) V T (โ. โV) 0 ?) // #T2 #T1 #HT2 #HT12
- lapply (H (+โV.T2) ?) -H /2 width=3/ -HT2 #H destruct /3 width=2/
-]
-qed.
-
-lemma tnf_inv_cast: โV,T. ๐โฆโV.Tโฆ โ โฅ.
-#V #T #H lapply (H T ?) -H /2 width=1/ #H
-@discr_tpair_xy_y //
-qed-.