matita/matita/contribs/lambda_delta/Basic_2/reduction/cpr_lift.ma

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  14
  15 include "Basic_2/unfold/tpss_lift.ma".
  16 include "Basic_2/reduction/tpr_lift.ma".
  17 include "Basic_2/reduction/cpr.ma".
  18
  19 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma cpr_delta: ∀L,K,V1,W1,W2,i.
  24                  ↓[0, i] L ≡ K. 𝕓{Abbr} V1 → K ⊢ V1 [0, |L| - i - 1] ≫* W1 →
  25                  ↑[0, i + 1] W1 ≡ W2 → L ⊢ #i ⇒ W2.
  26 #L #K #V1 #W1 #W2 #i #HLK #HVW1 #HW12
  27 @ex2_1_intro [2: // | skip | @tpss_subst /2 width=6/ ] (**) (* /4 width=6/ is too slow *)
  28 qed.
  29
  30 (* Advanced inversion lemmas ************************************************)
  31
  32 (* Basic_1: was: pr2_gen_lref *)
  33 lemma cpr_inv_lref1: ∀L,T2,i. L ⊢ #i ⇒ T2 →
  34                      T2 = #i ∨
  35                      ∃∃K,V1,T1. ↓[0, i] L ≡ K. 𝕓{Abbr} V1 &
  36                                 K ⊢ V1 [0, |L| - i - 1] ≫* T1 &
  37                                 ↑[0, i + 1] T1 ≡ T2 &
  38                                 i < |L|.
  39 #L #T2 #i * #X #H
  40 >(tpr_inv_atom1 … H) -H #H
  41 elim (tpss_inv_lref1 … H) -H /2/
  42 * /3 width=6/
  43 qed.
  44
  45 (* Basic_1: was: pr2_gen_abst *)
  46 lemma cpr_inv_abst1: ∀V1,T1,U2. 𝕔{Abst} V1. T1 ⇒ U2 →
  47                      ∃∃V2,T2. V1 ⇒ V2 & T1 ⇒ T2 & U2 = 𝕔{Abst} V2. T2.
  48 /2/ qed.
  49
  50 (* Relocation properties ****************************************************)
  51
  52 (* Basic_1: was: pr2_lift *)
  53
  54 (* Basic_1: was: pr2_gen_lift *)
  55