matita/matita/contribs/lambda_delta/Basic_2/static/lsuba.ma

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  14
  15 include "Basic_2/static/aaa.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
  18
  19 inductive lsuba: relation lenv ≝
  20 | lsuba_atom: lsuba (⋆) (⋆)
  21 | lsuba_pair: ∀I,L1,L2,V. lsuba L1 L2 → lsuba (L1. ⓑ{I} V) (L2. ⓑ{I} V)
  22 | lsuba_abbr: ∀L1,L2,V,W,A. L1 ⊢ V ÷ A → L2 ⊢ W ÷ A →
  23               lsuba L1 L2 → lsuba (L1. ⓓV) (L2. ⓛW)
  24 .
  25
  26 interpretation
  27   "local environment refinement (atomic arity assigment)"
  28   'CrSubEqA L1 L2 = (lsuba L1 L2).
  29
  30 (* Basic inversion lemmas ***************************************************)
  31
  32 fact lsuba_inv_pair2_aux: ∀L1,L2. L1 ÷⊑ L2 → ∀I,K2,W. L2 = K2. ⓑ{I} W →
  33                           (∃∃K1. K1 ÷⊑ K2 & L1 = K1. ⓑ{I} W) ∨
  34                           ∃∃K1,V,A. K1 ⊢ V ÷ A & K2 ⊢ W ÷ A & K1 ÷⊑ K2 &
  35                                     L1 = K1. ⓓV & I = Abst.
  36 #L1 #L2 * -L1 -L2
  37 [ #I #K2 #W #H destruct
  38 | #J #L1 #L2 #V #HL12 #I #K2 #W #H destruct /3 width=3/
  39 | #L1 #L2 #V1 #W2 #A #HV1 #HW2 #HL12 #I #K2 #W #H destruct /3 width=7/
  40 ]
  41 qed.
  42
  43 lemma lsuba_inv_pair2: ∀I,L1,K2,W. L1 ÷⊑ K2. ⓑ{I} W →
  44                        (∃∃K1. K1 ÷⊑ K2 & L1 = K1. ⓑ{I} W) ∨
  45                        ∃∃K1,V,A. K1 ⊢ V ÷ A & K2 ⊢ W ÷ A & K1 ÷⊑ K2 &
  46                                  L1 = K1. ⓓV & I = Abst.
  47 /2 width=3/ qed-.
  48
  49 (* Basic properties *********************************************************)
  50
  51 lemma lsuba_refl: ∀L. L ÷⊑ L.
  52 #L elim L -L // /2 width=1/
  53 qed.