matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lcpcs/lcpcs.etc

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  14
  15 notation "hvbox( L1 ⊢ ⬌* break term 46 L2 )"
  16    non associative with precedence 45
  17    for @{ 'CPConvStar $L1 $L2 }.
  18
  19 include "basic_2/grammar/lenv_px_sn.ma".
  20 include "basic_2/equivalence/cpcs.ma".
  21
  22 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *************)
  23
  24 definition lcpcs: relation lenv ≝ lpx_sn … cpcs.
  25
  26 interpretation "context-sensitive parallel equivalence (local environment)"
  27    'CPConvStar L1 L2 = (lcpcs L1 L2).
  28
  29 (* Basic inversion lemmas ***************************************************)
  30
  31 lemma lcpcs_inv_atom1: ∀L2. ⋆ ⊢ ⬌* L2 → L2 = ⋆.
  32 /2 width=2 by lpx_sn_inv_atom1/ qed-.
  33
  34 lemma lcpcs_inv_pair1: ∀I,K1,V1,L2. K1. ⓑ{I} V1 ⊢ ⬌* L2 →
  35                        ∃∃K2,V2. K1 ⊢ ⬌* K2 & K1 ⊢ V1 ⬌* V2 & L2 = K2. ⓑ{I} V2.
  36 /2 width=1 by lpx_sn_inv_pair1/ qed-.
  37
  38 lemma lcpcs_inv_atom2: ∀L1. L1 ⊢ ⬌* ⋆ → L1 = ⋆.
  39 /2 width=2 by lpx_sn_inv_atom2/ qed-.
  40
  41 lemma lcpcs_inv_pair2: ∀I,L1,K2,V2. L1 ⊢ ⬌* K2. ⓑ{I} V2 →
  42                        ∃∃K1,V1. K1 ⊢ ⬌* K2 & K1 ⊢ V1 ⬌* V2 & L1 = K1. ⓑ{I} V1.
  43 /2 width=1 by lpx_sn_inv_pair2/ qed-.
  44
  45 (* Basic forward lemmas *****************************************************)
  46
  47 lemma lcpcs_fwd_length: ∀L1,L2. L1 ⊢ ⬌* L2 → |L1| = |L2|.
  48 /2 width=2 by lpx_sn_fwd_length/ qed-.