matita/matita/contribs/lambda-delta/Basic-2/reduction/ltpr_drop.ma

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  14
  15 include "Basic-2/reduction/tpr_lift.ma".
  16 include "Basic-2/reduction/ltpr.ma".
  17
  18 (* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
  19
  20 (* Basic-1: was: wcpr0_drop *)
  21 lemma ltpr_drop_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 -H L1 K1 d e
  24 [ #d #e #X #H >(ltpr_inv_atom1 … H) -H /2/
  25 | #K1 #I #V1 #X #H
  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 -X;
  29   elim (IHLK1 … HL12) -IHLK1 HL12 /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 -X;
  32   elim (tpr_inv_lift … HV12 … HWV1) -HV12 HWV1;
  33   elim (IHLK1 … HL12) -IHLK1 HL12 /3 width=5/
  34 ]
  35 qed.
  36
  37 (* Basic-1: was: wcpr0_drop_back *)
  38 lemma ltpr_drop_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 -H L1 K1 d e
  41 [ #d #e #X #H >(ltpr_inv_atom1 … H) -H /2/
  42 | #K1 #I #V1 #X #H
  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) -IHLK1 HK12 /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 -X;
  48   elim (lift_total W2 d e) #V2 #HWV2
  49   lapply (tpr_lift … HW12 … HWV1 … HWV2) -HW12 HWV1;
  50   elim (IHLK1 … HK12) -IHLK1 HK12 /3 width=5/
  51 ]
  52 qed.