matita/matita/contribs/lambdadelta/basic_2/etc/leq/leq_old.etc

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  14
  15 include "Basic-2/grammar/lenv_length.ma".
  16
  17 (* LOCAL ENVIRONMENT EQUALITY ***********************************************)
  18
  19 interpretation "local environment equality" 'Eq L1 d e L2 = (leq L1 d e L2).
  20
  21 (* Basic properties *********************************************************)
  22
  23 | leq_comp: ∀L1,L2,I1,I2,V1,V2.
  24             leq L1 0 0 L2 → leq (L1. 𝕓{I1} V1) 0 0 (L2. 𝕓{I2} V2)
  25
  26 lemma leq_fwd_length: ∀L1,L2,d,e. L1 [d, e] ≈ L2 → |L1| = |L2|.
  27 #L1 #L2 #d #e #H elim H -H L1 L2 d e; normalize //
  28 qed.
  29
  30 (* Basic inversion lemmas ***************************************************)
  31
  32 lemma leq_inv_sort1_aux: ∀L1,L2,d,e. L1 [d, e] ≈ L2 → L1 = ⋆ → L2 = ⋆.
  33 #L1 #L2 #d #e #H elim H -H L1 L2 d e
  34 [ //
  35 | #L1 #L2 #I1 #I2 #V1 #V2 #_ #_ #H destruct
  36 | #L1 #L2 #I #V #e #_ #_ #H destruct
  37 | #L1 #L2 #I1 #I2 #V1 #V2 #d #e #_ #_ #H destruct
  38 qed.
  39
  40 lemma leq_inv_sort1: ∀L2,d,e. ⋆ [d, e] ≈ L2 → L2 = ⋆.
  41 /2 width=5/ qed.
  42
  43 lemma leq_inv_sort2: ∀L1,d,e. L1 [d, e] ≈ ⋆ → L1 = ⋆.
  44 /3/ qed.