matita/matita/lib/lambda-delta/reduction/lpr.ma

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  14
  15 include "lambda-delta/reduction/tpr.ma".
  16
  17 (* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
  18
  19 inductive lpr: lenv → lenv → Prop ≝
  20 | lpr_sort: lpr (⋆) (⋆)
  21 | lpr_item: ∀K1,K2,I,V1,V2.
  22             lpr K1 K2 → V1 ⇒ V2 → lpr (K1. 𝕓{I} V1) (K2. 𝕓{I} V2) (*𝕓*)
  23 .
  24
  25 interpretation
  26   "context-free parallel reduction (environment)"
  27   'PRed L1 L2 = (lpr L1 L2).
  28
  29 (* Basic inversion lemmas ***************************************************)
  30
  31 lemma lpr_inv_item1_aux: ∀L1,L2. L1 ⇒ L2 → ∀K1,I,V1. L1 = K1. 𝕓{I} V1 →
  32                          ∃∃K2,V2. K1 ⇒ K2 & V1 ⇒ V2 & L2 = K2. 𝕓{I} V2.
  33 #L1 #L2 * -L1 L2
  34 [ #K1 #I #V1 #H destruct
  35 | #K1 #K2 #I #V1 #V2 #HK12 #HV12 #L #J #W #H destruct - K1 I V1 /2 width=5/
  36 ]
  37 qed.
  38
  39 lemma lpr_inv_item1: ∀K1,I,V1,L2. K1. 𝕓{I} V1 ⇒ L2 →
  40                      ∃∃K2,V2. K1 ⇒ K2 & V1 ⇒ V2 & L2 = K2. 𝕓{I} V2.
  41 /2/ qed.