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

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  14
  15 axiom- lleq_inv_lref_lt_bi: ∀L1,L2,i,d. L1 ⋕[d, #i] L2 → i < d →
  16                            ∀I1,I2,K1,K2,V1,V2. ⇩[0, i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[0, i] L2 ≡ K2.ⓑ{I2}V2 →
  17                            K1 ⋕[d-i-1, V1] K2 ∧ K1 ⋕[d-i-1, V2] K2.
  18
  19 include "Basic-2/grammar/lenv_length.ma".
  20
  21 (* LOCAL ENVIRONMENT EQUALITY ***********************************************)
  22
  23 interpretation "local environment equality" 'Eq L1 d e L2 = (leq L1 d e L2).
  24
  25 (* Basic properties *********************************************************)
  26
  27 | leq_comp: ∀L1,L2,I1,I2,V1,V2.
  28             leq L1 0 0 L2 → leq (L1. 𝕓{I1} V1) 0 0 (L2. 𝕓{I2} V2)
  29
  30 lemma leq_fwd_length: ∀L1,L2,d,e. L1 [d, e] ≈ L2 → |L1| = |L2|.
  31 #L1 #L2 #d #e #H elim H -H L1 L2 d e; normalize //
  32 qed.
  33
  34 (* Basic inversion lemmas ***************************************************)
  35
  36 lemma leq_inv_sort1_aux: ∀L1,L2,d,e. L1 [d, e] ≈ L2 → L1 = ⋆ → L2 = ⋆.
  37 #L1 #L2 #d #e #H elim H -H L1 L2 d e
  38 [ //
  39 | #L1 #L2 #I1 #I2 #V1 #V2 #_ #_ #H destruct
  40 | #L1 #L2 #I #V #e #_ #_ #H destruct
  41 | #L1 #L2 #I1 #I2 #V1 #V2 #d #e #_ #_ #H destruct
  42 qed.
  43
  44 lemma leq_inv_sort1: ∀L2,d,e. ⋆ [d, e] ≈ L2 → L2 = ⋆.
  45 /2 width=5/ qed.
  46
  47 lemma leq_inv_sort2: ∀L1,d,e. L1 [d, e] ≈ ⋆ → L1 = ⋆.
  48 /3/ qed.