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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 notation "hvbox( L1 ⊢ ⬌* break term 46 L2 )"
16 non associative with precedence 45
17 for @{ 'CPConvStar $L1 $L2 }.
19 include "basic_2/grammar/lenv_px_sn.ma".
20 include "basic_2/equivalence/cpcs.ma".
22 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *************)
24 definition lcpcs: relation lenv ≝ lpx_sn … cpcs.
26 interpretation "context-sensitive parallel equivalence (local environment)"
27 'CPConvStar L1 L2 = (lcpcs L1 L2).
29 (* Basic inversion lemmas ***************************************************)
31 lemma lcpcs_inv_atom1: ∀L2. ⋆ ⊢ ⬌* L2 → L2 = ⋆.
32 /2 width=2 by lpx_sn_inv_atom1/ qed-.
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-.
38 lemma lcpcs_inv_atom2: ∀L1. L1 ⊢ ⬌* ⋆ → L1 = ⋆.
39 /2 width=2 by lpx_sn_inv_atom2/ qed-.
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-.
45 (* Basic forward lemmas *****************************************************)
47 lemma lcpcs_fwd_length: ∀L1,L2. L1 ⊢ ⬌* L2 → |L1| = |L2|.
48 /2 width=2 by lpx_sn_fwd_length/ qed-.