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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "Basic_2/reducibility/tpr_lift.ma".
16 include "Basic_2/reducibility/ltpr.ma".
18 (* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
20 (* Basic_1: was: wcpr0_ldrop *)
21 lemma ltpr_ldrop_conf: ∀L1,K1,d,e. ↓[d, e] L1 ≡ K1 → ∀L2. L1 ⇒ L2 →
22 ∃∃K2. ↓[d, e] L2 ≡ K2 & K1 ⇒ K2.
23 #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
24 [ #d #e #X #H >(ltpr_inv_atom1 … H) -H /2 width=3/
26 elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct /3 width=5/
27 | #L1 #K1 #I #V1 #e #_ #IHLK1 #X #H
28 elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
29 elim (IHLK1 … HL12) -L1 /3 width=3/
30 | #L1 #K1 #I #V1 #W1 #d #e #_ #HWV1 #IHLK1 #X #H
31 elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
32 elim (tpr_inv_lift … HV12 … HWV1) -V1
33 elim (IHLK1 … HL12) -L1 /3 width=5/
37 (* Basic_1: was: wcpr0_ldrop_back *)
38 lemma ltpr_ldrop_trans: ∀L1,K1,d,e. ↓[d, e] L1 ≡ K1 → ∀K2. K1 ⇒ K2 →
39 ∃∃L2. ↓[d, e] L2 ≡ K2 & L1 ⇒ L2.
40 #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
41 [ #d #e #X #H >(ltpr_inv_atom1 … H) -H /2 width=3/
43 elim (ltpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct /3 width=5/
44 | #L1 #K1 #I #V1 #e #_ #IHLK1 #K2 #HK12
45 elim (IHLK1 … HK12) -K1 /3 width=5/
46 | #L1 #K1 #I #V1 #W1 #d #e #_ #HWV1 #IHLK1 #X #H
47 elim (ltpr_inv_pair1 … H) -H #K2 #W2 #HK12 #HW12 #H destruct
48 elim (lift_total W2 d e) #V2 #HWV2
49 lapply (tpr_lift … HW12 … HWV1 … HWV2) -W1
50 elim (IHLK1 … HK12) -K1 /3 width=5/