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14
15 include "basic_2/reducibility/tpr_lift.ma".
16 include "basic_2/computation/tprs.ma".
17
18 (* CONTEXT-FREE PARALLEL COMPUTATION ON TERMS *******************************)
19
20 (* Advanced inversion lemmas ************************************************)
21
22 lemma tprs_inv_abst1: ∀a,V1,T1,U2. ⓛ{a}V1. T1 ➡* U2 →
23                       ∃∃V2,T2. V1 ➡* V2 & T1 ➡* T2 & U2 = ⓛ{a}V2. T2.
24 #a #V1 #T1 #U2 #H @(tprs_ind … H) -U2 /2 width=5/
25 #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
26 elim (tpr_inv_abst1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H destruct /3 width=5/
27 qed-.
28
29 lemma tprs_inv_abst: ∀a,V1,V2,T1,T2. ⓛ{a}V1. T1 ➡* ⓛ{a}V2. T2 →
30                      V1 ➡* V2 ∧ T1 ➡* T2.
31 #a #V1 #V2 #T1 #T2 #H
32 elim (tprs_inv_abst1 … H) -H #V #T #HV1 #HT1 #H destruct /2 width=1/
33 qed-.
34
35 (* Relocation properties ****************************************************)
36
37 (* Note: this was missing in basic_1 *)
38 lemma tprs_lift: t_liftable tprs.
39 /3 width=7/ qed.
40
41 (* Note: this was missing in basic_1 *)
42 lemma tprs_inv_lift1: t_deliftable_sn tprs.
43 /3 width=3 by tpr_inv_lift1, t_deliftable_sn_TC/ qed-.